JP2004239323A - Dynamic vibration absorber - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a dynamic vibration absorber with relatively simple setting of parameters, and in which a large vibration restricting effect to a subject structure. <P>SOLUTION: The subject structure (of a mass M) is supported through a spring (of a spring constant K) and a damper (of a damping coefficient C) to the ground vibratablein a vertical direction (with a displacement x). A first additive mass body (of a mass m1) is supported through a spring (of a spring constant k1) and a damper (of a damping coefficient c1) to the subject structure in a vibratable state ain a vertical direction (with a displacement y1). A second additive mass body (of a mass m2) is supported through a spring (of a spring constant k2) and a damper (of a damping coefficient c2) to the first additive mass body in a vibratable state in a vertical direction (with a displacement y2). Where natural frequencies of the subject structure, the first additive mass body, and the second additive mass, in the vertical direction, as sole systems, are respectively referred to as f<SB>M</SB>, f<SB>m1</SB>, f<SB>m2</SB>, then they are set to satisfy f<SB>m1</SB>>f<SB>M</SB>and f<SB>m2</SB><f<SB>M</SB>. <P>COPYRIGHT: (C)2004,JPO&NCIPI

Description

【００２６】
図１に示した制振対象構造物、第１及び第２の付加質量体の運動方程式は、主系に働く外力をｆ（＝Ｆ_０ｓｉｎωｔ）として、それぞれ次の式（４）〜（６）のように表される。
【００２７】
【数２】

【００２８】
ところで、動吸振器の設計とは、動吸振器の質量、ばね定数及び減衰係数を決めることである。通常の付加系を１つだけ有する動吸振器の場合、動吸振器の質量（主系に対する質量比）が決まると、ばね定数及び減衰係数の２つのパラメータを決めればよい。直列二重動吸振器では、上述した総質量比を決定した後、第一動吸振器と第二動吸振器との内部質量比（ｕ１／ｕ）、各動吸振器のばね定数及び減衰係数という５つのパラメータを求めなければならない。
【００２９】
これらパラメータを最適に決定する一つの手法として、主系である制振対象構造物のコンプライアンスの最大値を最小にするパラメータを求めるという手法が用いられる。しかしながら、そのような最適化されたパラメータを式（４）〜（６）の解析的な解として求めることができないので、総質量比が０．０２から０．２の範囲（単に実用的な範囲として例示する範囲に過ぎない）で数値計算解として求めた結果を表１に示す。求めるべきパラメータとは、総質量比が決められたときのｍ１＋ｍ２に対するｍ１の質量比（質量比比率）ｕ１／ｕ、各動吸振器のばね定数及び減衰係数である。
【００３０】
なお、表１においては、各付加質量体のばね定数及び減衰係数の代わりに、第１及び第２の付加質量体の単独系としての鉛直方向の固有振動数ｆ_ｍ１、ｆ_ｍ２と制振対象構造物の単独系としての鉛直方向の固有振動数ｆ_Ｍとの比ｐｉ（ｐ１、ｐ２：それぞれ式（７）で表される）と、第１及び第２の付加質量体の単独系としての減衰比ζｉ（ζ１、ζ２：それぞれ式（８）で表される）とが示されている。
【００３１】
【表１】

【００３２】
【数３】

【００３３】
表１から分かるように、総質量比が０．０２から０．２の範囲において、最適な固有振動数の比ｐ１は１より若干大きく（ｐ１＞１）、最適な固有振動数の比ｐ２は１より若干小さく（ｐ２＜１）、最適な減衰比ζ１は実質的にゼロである。また、最適な質量比ｕ１／ｕは総質量比が大きくなるに連れて小さくなる。図２は表１に示された特性を説明するためのグラフであって、図２（ａ）は総質量比が大きくなるに連れて最適な質量比ｕ１／ｕが小さくなる様子を示している。図２（ｂ）は、総質量比が大きくなるに連れて最適な質量比ｕ１、ｕ２が大きくなる様子を示している。図２（ｃ）は、総質量比が大きくなるに連れて最適な比ｐ１が増加し比ｐ２が減少すると共に最適な減衰比ζ２が増加する様子を示している。
【００３４】
なお、アクセレランスおよびモビリティの最大値を最小にするという条件で最適パラメータを決定した場合にもパラメータの特性として同様の結果が得られる。
【００３５】
＜制振性能＞
通常の付加系を１つだけもつ動吸振器（単一動吸振器）、付加系を２つ持つ並列動吸振器（並列二重動吸振器）、付加系を４つ持つ並列動吸振器（並列四重動吸振器）、付加系を６つ持つ並列動吸振器（並列六重動吸振器）、図１に示した直列二重動吸振器のそれぞれについて、制振対象構造物の減衰がゼロという条件でコンプライアンスの最大値が最小となるようにパラメータが最適化された場合における制振対象構造物のコンプライアンスの最大値を総質量比が０．０２から０．２の範囲において数値計算で求めたものが表２である。表２から分かるように、図１に示した直列二重動吸振器によると、並列六重動吸振器と同程度又はこれ以上にコンプライアンスを小さな値に抑制することができる。また、総質量比５％での直列二重動吸振器の制振効果は質量比８．２５％での単一動吸振器の制振効果に相当し、総質量比１０％での直列二重動吸振器の制振効果は質量比１６．５％での単一動吸振器の制振効果に相当する。このように、本発明の直列動吸振器は、優れた制振効果を奏する。
【００３６】
【表２】

【００３７】
＜比較例１＞
図３は、コンプライアンスの最大値を最小にするという上述した最適化条件で決定されたパラメータが採用されたときにおける主系のコンプライアンス曲線の一例（総質量比５％）である。このとき、図３に示すように、コンプライアンス曲線は主系及び２つの付加系の３つの自由度に対応した３つの極大値を有しており、これら極大値は等しい値になっている。なお、図３においてＦｒｅｑｕｅｎｃｙ Ｒａｔｉｏ（振動数比）１は主系の固有振動数に対応している。
【００３８】
次に、固有振動数の比ｐ１、ｐ２だけが最適状態から変動した場合（すなわち、最適状態がある原因でｐ１＜１且つｐ２＞１、ｐ１＜１且つｐ２＝１、ｐ１＝１且つｐ２＝１、又は、ｐ１＝１且つｐ２＞１となり他のパラメータが変化しない場合）にコンプライアンス曲線がどのように変化するかについて説明する。表３に、このときの各パラメータを示す。
【００３９】
【表３】

【００４０】
数値計算の結果、表３に示す各場合について、コンプライアンス曲線は、図４（ａ）〜（ｄ）のようになった。図４（ａ）はｐ１＜１且つｐ２＞１、図４（ｂ）はｐ１＜１且つｐ２＝１、図４（ｃ）はｐ１＝１且つｐ２＝１、そして、図４（ｄ）はｐ１＝１且つｐ２＞１の場合のコンプライアンス曲線をそれぞれ描いたものである。この結果から分かるように、ｐ１＞１且つｐ２＜１を満たさない場合には、コンプライアンスの最大値を十分に小さくすることができず、直列二重動吸振器の制振効果が小さくなってしまう。
【００４１】
＜比較例２＞
次に、比ｐ１、ｐ２が最適状態から変動し他のパラメータをそれに合わせて再最適化することができる場合（すなわち、最適状態がある原因でｐ１＜１（ｐ１＝０．９７５）且つｐ２＞１（ｐ２＝１．０２５）、ｐ１＜１（ｐ１＝０．９７５）且つｐ２＝１、ｐ１＝１且つｐ２＝１、ｐ１＝１且つｐ２＞１（ｐ２＝１．０２５）となり他のパラメータが再最適化される場合）にコンプライアンス曲線がどのように変化するかについて説明する。
【００４２】
数値計算の結果、他のパラメータは表４に示すように再最適化される。なお、ｐ１＜１（ｐ１＝０．９７５）且つｐ２＞１（ｐ２＝１．０２５）の場合には再最適化を行うことができないので、ｐ１＝０．９９５、ｐ２＝１．００５としてその他のパラメータの再最適化を行った。そして、これら各場合について、コンプライアンス曲線は、図５（ａ）〜（ｄ）のようになった。図５（ａ）はｐ１＜１且つｐ２＞１、図５（ｂ）はｐ１＜１且つｐ２＝１、図５（ｃ）はｐ１＝１且つｐ２＝１、そして、図５（ｄ）はｐ１＝１且つｐ２＞１の場合のコンプライアンス曲線をそれぞれ描いたものである。
【００４３】
この結果から分かるように、ｐ１＞１且つｐ２＜１を満たさない場合には、たとえその他のパラメータを再最適化できるとしても、図４のときよりも改善されるもののコンプライアンスの最大値を十分に小さくすることができず、直列二重動吸振器の制振効果が小さくなってしまう。
【００４４】
【表４】

【００４５】
＜アクセレランス＞
単一動吸振器、並列二重動吸振器、並列四重動吸振器、図１に示した直列二重動吸振器のそれぞれについて、制振対象構造物の減衰がゼロという条件でアクセレランスの最大値が最小となるようにパラメータが最適化された場合における制振対象構造物のアクセレランスの最大値を総質量比が０．０２から０．２の範囲において数値計算で求めたものが表５である。
【００４６】
表５から分かるように、図１に示した直列二重動吸振器によると、並列四重動吸振器と同程度又はこれ以上にアクセレランスを小さな値に抑制することができる。また、総質量比５％での直列二重動吸振器の制振効果と単一動吸振器の制振効果とを比較すると、共振ピーク値が２０．３２％減少する。
【００４７】
【表５】

【００４８】
＜インパルス応答＞
総質量比が５％の場合について、単一動吸振器、並列二重動吸振器、図１に示した直列二重動吸振器を用いたときのそれぞれのインパルス応答を図６に示す。図６（ａ）は主系、図６（ｂ）は第一動吸振器、図６（ｃ）は第二動吸振器に対応している。図６（ａ）を参照すると、主系のインパルス応答において、直列二重動吸振器による１周期めの振動波形には制振効果がほとんど見られないが、直列二重動吸振器による２周期め以降の振動波形には並列二重動吸振器よりも顕著な制振効果が見られる。
【００４９】
図６（ｂ）を参照すると、直列二重動吸振器の第一動吸振器のインパルス応答はその他の動吸振器と大差がなく、図６（ｃ）を参照すると、直列二重動吸振器の第二動吸振器のインパルス応答は並列二重動吸振器よりも却って大きいことが分かる。このように、付加系の運動が大きくなることが本発明による直列二重動吸振器の効果を示しているといえる。
【００５０】
＜動吸振器の調整＞
一般的に、主系の固有振動数が変化する場合、動吸振器の最適効果を維持するためには動吸振器のばね係数及び減衰係数を調整しなければならない。前述したように本発明による直列二重動吸振器の場合、第一動吸振器の減衰比が極めて小さくなるように設定されるので特段の減衰性能が必要ないため、調整に必要なパラメータは三つしかなく、並列二重動吸振器、並列四重動吸振器よりも調整は易しいものとなる。また、本発明による直列二重動吸振器においては、主系の固有振動数が変化する場合、第二動吸振器を調整するだけで最適状態の復元が可能という特徴も有するのである。最適状態では、第二動吸振器の質量が第一動吸振器の質量よりかなり小さいので、第二動吸振器のパラメータのみを調整すればよいことは実際の作業負担を大きく軽減する。
【００５１】
第二動吸振器を調整するだけで最適状態の復元が可能という点について、以下データを挙げて説明する。表６に、主系の固有振動数が０．９０から１．０２まで変化したときに第一動吸振器に関するパラメータを変えずに第二動吸振器に関するパラメータのみを調整したときの結果を示す。図７に調整前後の主系のコンプライアンス曲線を比較して示す。
【００５２】
【表６】

【００５３】
表６と図７から、主系の固有振動数が元の振動数より小さくなるほど、第二動吸振器の質量を大きくすることによって、制振効果の殆ど変わらない良好な結果が得られることが分かる。ただし、主系の固有振動数が元の振動数より大きくなると、第二動吸振器の質量比を小さくしなければならず、このときの制振効果はもとのものより若干劣化する。なお、主系の固有振動数が第一動吸振器の振動数より大きくなると、第二動吸振器に関するパラメータの調整だけでは十分な制振効果が得られなくなる可能性もある。
【００５４】
＜制振対象構造物の減衰がゼロの場合と減衰が存在する場合との比較＞
上述の直列二重動吸振器では、制振対象構造物の減衰がゼロという条件でパラメータが最適化された場合における制振対象構造物のコンプライアンス及びアクセレランスなどについて説明したが、例えば、制振対象構造物に減衰が存在している場合では、図３のようにコンプライアンス曲線における３つの極値はほぼ等しい値とならない。つまり、制振対象構造物の減衰がゼロという条件で最適化されたパラメータを、例えば減衰が５％存在する制振対象構造物に採用すると、図８に示すようなコンプライアンス曲線が得られ、コンプライアンス曲線における３つの極値は等しくならず、最適化されたパラメータは減衰が存在する制振対象構造物に対して最適にならない。
【００５５】
＜コンプライアンス最適化＞
次いで、制振対象構造物に減衰が存在する場合でのコンプライアンス最適化について説明する。なお、直列二重動吸振器を設置しようとする一般的な制振対象構造物の減衰は小さく、また減衰を付加して効果が高いのは制振対象構造物の減衰が約６％以下の領域と考えられる。したがって、制振対象構造物に存在する減衰を０〜６％まで変化する場合のコンプライアンス最適化について、直列二重動吸振器のパラメータの変化範囲を計算する。
【００５６】
図９は、制振対象構造物の減衰が０〜６％まで変化する場合のコンプライアンス最適化において、各質量体のパラメータの特性を示しており、（ａ）は、第１の付加質量体と第２の付加質量体の各質量比の変化曲線の一例であり、（ｂ）は、第１の付加質量体と第２の付加質量体の各固有振動数の比の変化曲線の一例であり、（ｃ）は、第２の付加質量体の減衰比の変化曲線の一例である。なお、図９における変化曲線の変化範囲は総質量比で０．００５〜０．２の範囲で示している。
【００５７】
図９（ａ）に示すようにそれぞれの変化曲線において、制振対象構造物の減衰が増加すると、第１の付加質量体の質量比ｕ１は小さくなる傾向を示し、第２の付加質量体の質量比ｕ２は大きくなる傾向を示す。第２の付加質量体の質量比ｕ２の変化曲線の式（９）は図９（ａ）から近似式として得られ、式（９）から第２の付加質量体の質量比ｕ２のパラメータを求め、第１の付加質量体の質量比ｕ１は、ｕ１＝ｕ−ｕ２から求めることができる。ここで、ζは制振対象構造物の減衰比である。
【００５８】
【数４】

【００５９】
図９（ｂ）に示すようにそれぞれの変化曲線において、制振対象構造物の減衰が増加すると、第１の付加質量体の固有振動数の比ｐ１は小さくなる傾向を示し、第２の付加質量体の固有振動数の比ｐ２も小さくなる傾向を示す。第１及び第２の付加質量体の変化曲線の式（１０）、式（１１）も同様に図９（ｂ）から近似式として得られ、式（１０）、（１１）から第１及び第２の付加質量体の固有振動数の比ｐ１、ｐ２のパラメータが求められる。
【００６０】
【数５】

【００６１】
図９（ｃ）に示すようにそれぞれの変化曲線において、制振対象構造物の減衰が増加すると、第２の付加質量体の減衰比ζ２は大きくなる。なお、第１の付加質量体の減衰比ζ１は前述と同様に実質的にゼロである。第２の付加質量体の減衰比ζ２の変化曲線の式（１２）も同様に図９（ｃ）から近似式として得られ、式（１２）から第２の付加質量体の減衰比ζ２が求められる。
【００６２】
【数６】

【００６３】
このように制振対象構造物の減衰が０〜６％まで変化する場合における直列二重動吸振器のパラメータの変化範囲を図９に示し近似式を得ることで、制振対象構造物の減衰に応じた直列二重動吸振器のパラメータの最適値を算出して選ぶことが可能となる。例えば、制振対象構造物の減衰比ζが５％で、直列二重動吸振器の総質量比ｕが５％である場合のコンプライアンスの最大値を最小にするという最適化条件で決定されたパラメータを表７に示し、そのパラメータが採用されたときにおける主系のコンプライアンス曲線を図１０に示す。図１０に示すコンプライアンス曲線における３つの極値はほぼ等しくなり、図８と比べて直列二重動吸振器のパラメータは最適値といえる。
【００６４】
【表７】

【００６５】
＜アクセレランスの最適化＞
続いて、制振対象構造物に存在する減衰を０〜６％まで変化する場合のアクセレランス最適化について、直列二重動吸振器のパラメータの変化範囲を計算する。
【００６６】
図１１は、制振対象構造物の減衰が０〜６％まで変化する場合のアクセレランス最適化において、各質量体のパラメータの特性を示しており、（ａ）は、第１の付加質量体と第２の付加質量体の各質量比の変化曲線の一例であり、（ｂ）は、第１の付加質量体と第２の付加質量体の各固有振動数の比の変化曲線の一例であり、（ｃ）は、第２の付加質量体の減衰比の変化曲線の一例である。なお、図１１における変化曲線の変化範囲は総質量比で０．００５〜０．２の範囲で示している。
【００６７】
図１１（ａ）に示すようにそれぞれの変化曲線において、制振対象構造物の減衰が増加すると、第１の付加質量体の質量比ｕ１は小さくなる傾向を示し、第２の付加質量体の質量比ｕ２は大きくなる傾向を示す。第２の付加質量体の質量比ｕ２の変化曲線の式（１３）は図１１（ａ）から近似式として得られ、式（１３）から第２の付加質量体の質量比ｕ２のパラメータを求め、第１の付加質量体の質量比ｕ１は、ｕ１＝ｕ−ｕ２から求めることができる。
【００６８】
【数７】

【００６９】
図１１（ｂ）に示すようにそれぞれの変化曲線において、制振対象構造物の減衰が増加すると、第１の付加質量体の固有振動数の比ｐ１は大きくなる傾向を示し、第２の付加質量体の固有振動数の比ｐ２も大きくなる傾向を示す。第１及び第２の付加質量体の変化曲線の式（１４）、式（１５）も同様に図１１（ｂ）から近似式として得られ、式（１４）、（１５）から第１及び第２の付加質量体の固有振動数の比ｐ１、ｐ２のパラメータが求められる。
【００７０】
【数８】

【００７１】
図１１（ｃ）に示すようにそれぞれの変化曲線において、制振対象構造物の減衰が増加すると、第２の付加質量体の減衰比ζ２は大きくなる。なお、第１の付加質量体の減衰比ζ１は前述と同様に実質的にゼロである。第２の付加質量体の減衰比ζ２の変化曲線の式（１６）も同様に図１１（ｃ）から近似式として得られ、式（１６）から第２の付加質量体の減衰比ζ２が求められる。
【００７２】
【数９】

【００７３】
このように制振対象構造物の減衰が０〜６％まで変化する場合における直列二重動吸振器のパラメータの変化範囲を図１１に示し近似式を得ることで、制振対象構造物の減衰に応じた直列二重動吸振器のパラメータの最適値を算出して選ぶことが可能となる。例えば、制振対象構造物の減衰比ζが５％で、直列二重動吸振器の総質量比ｕが５％である場合のアクセレランスの最大値を最小にするという最適化条件で決定されたパラメータを表８に示し、そのパラメータが採用されたときにおける主系のアクセレランス曲線を図１２に示す。図１２に示すアクセレランス曲線における３つの極値はほぼ等しくなり、直列二重動吸振器のパラメータは最適値といえる。
【００７４】
【表８】

【００７５】
＜モビリティ最適化＞
続いて、制振対象構造物に存在する減衰を０〜６％まで変化する場合のモビリティ最適化について、直列二重動吸振器のパラメータの変化範囲を計算する。
【００７６】
図１３は、制振対象構造物の減衰が０〜６％まで変化する場合のモビリティ最適化において、各質量体のパラメータの特性を示しており、（ａ）は、第１の付加質量体と第２の付加質量体の各質量比の変化曲線の一例であり、（ｂ）は、第１の付加質量体と第２の付加質量体の各固有振動数の比の変化曲線の一例であり、（ｃ）は、第２の付加質量体の減衰比の変化曲線の一例である。なお、図１３における変化曲線の変化範囲を総質量比で０．００５〜０．２の範囲で示している。
【００７７】
図１３（ａ）に示すようにそれぞれの変化曲線において、制振対象構造物の減衰が増加すると、第１の付加質量体の質量比ｕ１は小さくなる傾向を示し、第２の付加質量体の質量比ｕ２は大きくなる傾向を示す。第２の付加質量体の質量比ｕ２の変化曲線の式（１７）は図１３（ａ）から近似式として得られ、式（１７）から第２の付加質量体の質量比ｕ２のパラメータを求め、第１の付加質量体の質量比ｕ１は、ｕ１＝ｕ−ｕ２から求めることができる。
【００７８】
【数１０】

【００７９】
図１３（ｂ）に示すようにそれぞれの変化曲線において、制振対象構造物の減衰が増加すると、第１の付加質量体の固有振動数の比ｐ１は大きくなる傾向を示し、第２の付加質量体の固有振動数の比ｐ２は小さくなる傾向を示す。第１及び第２の付加質量体の変化曲線の式（１８）、式（１９）も同様に図１３（ｂ）から近似式として得られ、式（１８）、（１９）から第１及び第２の付加質量体の固有振動数の比ｐ１、ｐ２のパラメータが求められる。
【００８０】
【数１１】

【００８１】
図１３（ｃ）に示すようにそれぞれの変化曲線において、制振対象構造物の減衰が増加すると、第２の付加質量体の減衰比ζ２は大きくなる。なお、第１の付加質量体の減衰比ζ１は前述と同様に実質的にゼロである。第２の付加質量体の減衰比ζ２の変化曲線の式（２０）も同様に図１３（ｃ）から近似式として得られ、式（２０）から第２の付加質量体の減衰比ζ２が求められる。
【００８２】
【数１２】

【００８３】
このように制振対象構造物の減衰が０〜６％まで変化する場合における直列二重動吸振器のパラメータの変化範囲を図１３に示し近似式を得ることで、制振対象構造物の減衰に応じた直列二重動吸振器のパラメータの最適値を算出して選ぶことが可能となる。例えば、制振対象構造物の減衰比ζが５％で、二重動吸振器の総質量比ｕが５％である場合のモビリティの最大値を最小にするという最適化条件で決定されたパラメータを表９に示し、そのパラメータが採用されたときにおける主系のモビリティ曲線を図１４に示す。図１４に示すモビリティ曲線における３つの極値はほぼ等しくなり、直列二重動吸振器のパラメータは最適値といえる。
【００８４】
【表９】

【００８５】
以上のように、制振対象構造物の減衰が０〜６％まで変化する場合の３つの最適化（コンプライアンス最適化、アクセレランス最適化及びモビリティ最適化）での第１の付加質量体と第２の付加質量体の各質量比ｕ１、ｕ２及び第２の付加質量体の減衰比ζ２の変化傾向は同様になり、変化幅（コンプライアンス最適化、アクセレランス最適化及びモビリティ最適化におけるそれぞれの変化曲線のズレによる幅）についても大きな違いがない。一方、第１の付加質量体と第２の付加質量体の各固有振動数の比の変化傾向は違うが、第１の付加質量体の固有振動数の比は常に１より大きく、第２の付加質量体の固有振動数の比は常に１より小さいものとなる。
【００８６】
また、制振対象構造物の減衰が０〜６％まで変化する場合での３つの最適化における第２の付加質量体の減衰比ζ２の変化曲線の一例を図１５に示しており、それぞれの変化曲線で囲まれる範囲内に３つの最適化による第２の付加質量体の減衰比ζ２が存在する。図１５から制振対象構造物の減衰が０％時の第２の付加質量体の減衰比ζ２ｍｉｎを求める近似式（２１）が得られ、制振対象構造物の減衰が６％時の第２の付加質量体の減衰比ζ２ｍａｘを求める近似式（２２）が得られる。そのため、制振対象構造物の減衰が０〜６％まで変化する場合における第２の付加質量体の減衰比ζ２を求めることが可能となる。なお、本発明において、主系のコンプライアンス、アクセレランス、モビリティの少なくともいずれか１つを十分に低下させることができる減衰比ζ２は、上述した式（２１）、（２２）に表されたものに限定されない。例えば、第２の付加質量体の減衰比がζ２＝ａ×ｕ^ｂ−ｃによって示されるとき、ａを０．８０より大きく（ａ＞０．８０）、ｂを０．３２より大きく（ｂ＞０．３２）、且つ、ｃを０．０８より小さく（ｃ＜０．０８）すれば、主系のコンプライアンス、アクセレランス、モビリティの少なくともいずれか１つを十分に低下させることができる減衰比ζ２を得ることができる。
【００８７】
【数１３】

【００８８】
＜最適設計：直列三重動吸振器＞
続いて図１６に、本発明による付加質量体が３個の場合の動吸振器の模式図を示す。図１６において、第３の付加質量体（質量ｍ３）が鉛直方向（変位ｙ３）に振動可能な状態でバネ（ばね定数ｋ３）及びダンパ（減衰係数ｃ３）を介して前述した直列二重動吸振器の第２の付加質量体に支持されており、制振対象構造物に対して直列３段に接続された構成になっている。つまり、この直列三重動吸振器は、前述した直列二重動吸振器の第二動吸振器に動吸振器（第三動吸振器）１個が接続されたものである。なお、前述した直列二重動吸振器と同様なものについては、同記号で示し説明を省略する。
【００８９】
なお、以下の説明において、式（２３）、（２４）に示すように、総質量比（質量Ｍに対する質量（ｍ１＋ｍ２＋ｍ３）の比率）をｕ、質量Ｍに対する質量ｍ１、ｍ２、ｍ３の質量比をそれぞれｕ１、ｕ２、ｕ３（ｕ＝ｕ１＋ｕ２＋ｕ３）とする。
【００９０】
【数１４】

【００９１】
図１６に示した制振対象構造物、第１、第２および第３の付加質量体の運動方程式は、主系に働く外力をｆ（＝Ｆ_０ｓｉｎωｔ）として、それぞれ上述した式（４）及び式（５）、次の式（２５）及び式（２６）のように表される。
【００９２】
【数１５】

【００９３】
直列三重動吸振器の設計では、上述したように総質量比ｕを決定した後、第一動吸振器と第二動吸振器と第三動吸振器の内部質量比（ｕ１／ｕ、ｕ２／ｕ）、各動吸振器のばね定数及び減衰係数という８つのパラメータを求めなければならない。
【００９４】
前述したように、主系である制振対象構造物のコンプライアンスの最大値を最小にするパラメータは解析的な解として求めることができないので、総質量比が０．０２から０．２の範囲で数値計算解として求めた結果を表１０に示す。求めるべきパラメータとは、総質量比が決められたときのｍ１＋ｍ２＋ｍ３に対するｍ１の質量比（質量比比率）ｕ１／ｕ、ｍ１＋ｍ２＋ｍ３に対するｍ２の質量比（質量比比率）ｕ２／ｕ、各動吸振器のばね定数及び減衰係数である。
【００９５】
なお、表１０においては、各付加質量体のばね定数及び減衰係数の代わりに、第１、第２及び第３の付加質量体の単独系としての鉛直方向の固有振動数ｆ_ｍ１、ｆ_ｍ２、ｆ_ｍ３と制振対象構造物の単独系としての鉛直方向の固有振動数ｆ_Ｍとの比ｐｉ（ｐ１、ｐ２、ｐ３：それぞれ式（７）で表される）と、第１、第２及び第３の付加質量体の単独系としての減衰比ζｉ（ζ１、ζ２、ζ３：それぞれ式（８）で表される）とが示されている。また、質量比（質量比比率）ｕ１／ｕ、ｕ２／ｕは表１０中に示していない。
【００９６】
【表１０】

【００９７】
表１０から分かるように、総質量比が０．０２から０．２の範囲において、最適な固有振動数の比ｐ１は１より若干大きく（ｐ１＞１）、最適な固有振動数の比ｐ２は固有振動数の比ｐ１より若干大きく（ｐ１＜ｐ２）、最適な固有振動数の比ｐ３は１より若干小さく（ｐ３＜１）、最適な減衰比ζ１、ζ２は実質的にゼロである。図１７は表１０に示された特性を説明するためのグラフであって、図１７（ａ）は総質量比が大きくなるに連れて最適な質量比ｕ１、ｕ２、ｕ３が大きくなる様子を示している。図１７（ｂ）は、総質量比が大きくなるに連れて最適な比ｐ１、ｐ２が増加し比ｐ３が減少すると共に最適な減衰比ζ３が増加する様子を示している。
【００９８】
なお、アクセレランスの最大値を最小にするという条件で最適パラメータを決定した場合にもパラメータの特性として後述するように同様の結果が得られる。
【００９９】
＜制振性能＞
通常の付加系を１つだけもつ動吸振器（単一動吸振器）、付加系を２つ持つ並列動吸振器（並列二重動吸振器）、付加系を４つ持つ並列動吸振器（並列四重動吸振器）、付加系を６つ持つ並列動吸振器（並列六重動吸振器）、図１に示した直列二重動吸振器、図１６に示した直列三重動吸振器のそれぞれについて、減衰がゼロという条件でコンプライアンスの最大値が最小となるようにパラメータが最適化された場合における制振対象構造物のコンプライアンスの最大値を総質量比が０．０２から０．２の範囲において数値計算で求めたものが表１１である。表１１から分かるように、図１６に示した直列三重動吸振器によると、直列二重動吸振器以上に最大コンプライアンスを小さな値に抑制することができる。このように、本発明の直列三重動吸振器は、より優れた制振効果を奏する。
【０１００】
【表１１】

【０１０１】
＜比較例＞
図１８は、コンプライアンスの最大値を最小にするという上述した最適化条件で決定されたパラメータが採用されたときにおける主系のコンプライアンス曲線の一例（総質量比５％）である。このとき、図１８に示すように、コンプライアンス曲線は主系及び３つの付加系の３つの自由度に対応した４つの極大値を有しており、これら極大値は等しい値になっている。また、図１８より直列三重動吸振器は、単一動吸振器、並列二重動吸振器及び直列二重動吸振器と比較して最大コンプライアンスをより小さな値に抑制していることがわかる。なお、図１８においてＦｒｅｑｕｅｎｃｙ Ｒａｔｉｏ（振動数比）１は主系の固有振動数に対応している。
【０１０２】
＜アクセレランス＞
次いで、主系である制振対象構造物のアクセレランスの最大値を最小にするパラメータも上述と同様に式（４）、（５）、（２５）、（２６）の解析的な解として求めることができないので、総質量比が０．０２から０．２の範囲で数値計算解として求めた結果を表１２に示す。求めるべきパラメータとは、総質量比が決められたときのｍ１＋ｍ２＋ｍ３に対するｍ１の質量比（質量比比率）ｕ１／ｕ、ｍ１＋ｍ２＋ｍ３に対するｍ２の質量比（質量比比率）ｕ２／ｕ、各動吸振器のばね定数及び減衰係数である。
【０１０３】
なお、表１２においては、各付加質量体のばね定数及び減衰係数の代わりに、第１、第２及び第３の付加質量体の単独系としての鉛直方向の固有振動数ｆ_ｍ１、ｆ_ｍ２、ｆ_ｍ３と制振対象構造物の単独系としての鉛直方向の固有振動数ｆ_Ｍとの比ｐ１〜ｐ３と、第１、第２及び第３の付加質量体の単独系としての減衰比ζ１〜ζ３とが示されている。また、質量比（質量比比率）ｕ１／ｕ、ｕ２／ｕは表１２中に示していない。
【０１０４】
【表１２】

【０１０５】
図１９は、表１２に示された特性を説明するためのグラフであって、図１９（ａ）は総質量比が大きくなるにつれて最適な質量比ｕ１、ｕ２、ｕ３が大きくなる様子を示している。図１９（ｂ）は総質量比が大きくなるにつれて最適な比ｐ１、ｐ２が増加し比ｐ３が減少すると共に最適な減衰比ζ３が増加する様子を示している。
【０１０６】
＜制振性能＞
通常の付加系を１つだけもつ動吸振器（単一動吸振器）、付加系を２つ持つ並列動吸振器（並列二重動吸振器）、付加系を４つ持つ並列動吸振器（並列四重動吸振器）、図１に示した直列二重動吸振器、図１６に示した直列三重動吸振器のそれぞれについて、制振対象構造物の減衰がゼロという条件でアクセレランスの最大値が最小となるようにパラメータが最適化された場合における制振対象構造物のアクセレランスの最大値を総質量比が０．０２から０．２の範囲において数値計算で求めたものが表１３である。表１３から分かるように、図１６に示した直列三重動吸振器によると、直列二重動吸振器以上に最大アクセレランスを小さな値に抑制することができる。このように、本発明の直列三重動吸振器は、より優れた制振効果を奏する。
【０１０７】
【表１３】

【０１０８】
＜比較例＞
図２０は、アクセレランスの最大値を最小にするという上述した最適化条件で決定されたパラメータが採用されたときにおける主系のコンプライアンス曲線の一例（総質量比５％）である。このとき、図２０に示すように、アクセレランス曲線は主系及び３つの付加系の３つの自由度に対応した４つの極大値を有しており、これら極大値は等しい値になっている。また、図２０より直列三重動吸振器は、単一動吸振器、並列二重動吸振器及び直列二重動吸振器と比較して最大アクセレランスをより小さな値に抑制していることがわかる。なお、図２０においてＦｒｅｑｕｅｎｃｙ Ｒａｔｉｏ（振動数比）１は主系の固有振動数に対応している。
【０１０９】
＜複合式動吸振器の構成＞
続いて図２１に、上述した直列二重動吸振器が並列に配置された場合の並列動吸振器の模式図を示す。図２１において、制振対象構造物（質量Ｍ）は、鉛直方向（変位ｘ）に振動可能な状態でバネ（ばね定数Ｋ）及びダンパ（減衰係数Ｃ）を介して地面に支持されている。また、図２１中左方側の第１の付加質量体（質量ｍ１１）は、鉛直方向（変位ｙ１１）に振動可能な状態でバネ（ばね定数ｋ１１）を介して制振対象構造物に支持されており、第２の付加質量体（質量ｍ１２）は、鉛直方向（変位ｙ１２）に振動可能な状態でバネ（ばね定数ｋ１２）及びダンパ（減衰係数係数ｃ１２）を介して第１の付加質量体に支持されている。また、図２１中右方側の第１の付加質量体（質量ｍ２１）は、鉛直方向（変位ｙ２１）に振動可能な状態でバネ（ばね定数ｋ２１）を介して制振対象構造物に支持されており、第２の付加質量体（質量ｍ２２）は、鉛直方向（変位ｙ２２）に振動可能な状態でバネ（ばね定数ｋ２２）及びダンパ（減衰係数ｃ２２）を介して第１の付加質量体に支持されている。つまり、２つの直列二重動吸振器（第１の直列二重動吸振器１００、第２の直列二重動吸振器２００）が制振対象構造物の上面で並列に接続された構成になっている。なお、上述した直列二重動吸振器の第一動吸振器には、制振対象構造物に接続するダンパが設けられているが、減衰は実質的にゼロとなるために並列動吸振器（複合式動吸振器）のそれぞれの第一動吸振器には、制振対象構造物と接続するダンパが設けられていない。
【０１１０】
＜コンプライアンス＞
このような複合式動吸振器において、主系である制振対象構造物のコンプライアンスの最大値を最小にするパラメータも解析的な解として求めることができないので、総質量比が０．０２から０．２の範囲で数値計算解として求めた結果を表１４に示す。
【０１１１】
なお、表１４においては、各付加質量体のばね定数及び減衰係数の代わりに、各直列二重動吸振器の第１及び第２の付加質量体の単独系としての鉛直方向の固有振動数ｆ_ｍ１１、ｆ_ｍ１２、ｆ_ｍ２１、ｆ_ｍ２２と制振対象構造物の単独系としての鉛直方向の固有振動数ｆ_Ｍとの比ｐ１１、ｐ１２、ｐ２１、ｐ２２と、第１及び第２の直列動吸振器のそれぞれの第２の付加質量体の単独系としての減衰比ζ１２、ζ２２とが示されている。
【０１１２】
【表１４】

【０１１３】
表１４から分かるように、総質量比が０．０２から０．２の範囲において、最適な固有振動数の比ｐ１１は１より若干大きく（ｐ１１＞１）、最適な固有振動数の比ｐ１２は１より若干小さく（ｐ１２＜１）、最適な固有振動数の比ｐ２１は１より若干小さく（ｐ２１＜１）、最適な固有振動数の比ｐ２２は１より若干小さい（ｐ２２＜１）。
【０１１４】
図２２は表１４に示された特性を説明するためのグラフであって、図２２（ａ）、（ｂ）は総質量比が大きくなるに連れて第１及び第２の直列二重動吸振器の最適な質量比ｕ１１、ｕ１２、ｕ２１、ｕ２２が大きくなる様子を示している。図２２（ｃ）は、総質量比が大きくなるに連れて第１の直列二重動吸振器の最適な比ｐ１１が増加し比ｐ１２が減少すると共に最適な減衰比ζ１２が増加する様子を示している。図２２（ｄ）は、総質量比が大きくなるに連れて第２の直列二重動吸振器の最適な比ｐ２１、ｐ２２が減少すると共に最適な減衰比ζ２２が増加する様子を示している。
【０１１５】
なお、アクセレランスの最大値を最小にするという条件で最適パラメータを決定した場合にもパラメータの特性として同様の結果が得られる。
【０１１６】
＜制振性能＞
通常の付加系を１つだけもつ動吸振器（単一動吸振器）、付加系を２つ持つ並列動吸振器（並列二重動吸振器）、付加系を４つ持つ並列動吸振器（並列四重動吸振器）、付加系を６つ持つ並列動吸振器（並列六重動吸振器）、図１に示した直列二重動吸振器、図２１に示した複合式動吸振器のそれぞれについて、制振対象構造物の減衰がゼロという条件でコンプライアンスの最大値が最小となるようにパラメータが最適化された場合における制振対象構造物のコンプライアンスの最大値を総質量比が０．０２から０．２の範囲において数値計算で求めたものが表１５である。表１５から分かるように、図２１に示した複合式動吸振器によると、直列二重動吸振器以上に最大コンプライアンスを小さな値に抑制することができる。このように、本発明の複合式動吸振器は、より優れた制振効果を奏する。
【０１１７】
【表１５】

【０１１８】
＜比較例＞
図２３は、コンプライアンスの最大値を最小にするという上述した最適化条件で決定されたパラメータが採用されたときにおける主系のコンプライアンス曲線の一例（総質量比５％）である。このとき、図２３に示すように、コンプライアンス曲線は主系及び４つの付加系の５つの自由度に対応した５つの極大値を有しており、これら極大値は等しい値になっている。また、図２３より複合式動吸振器は、単一動吸振器、並列二重動吸振器及び直列二重動吸振器と比較して最大コンプライアンスをより小さな値に抑制していることがわかる。なお、図２３においてＦｒｅｑｕｅｎｃｙ Ｒａｔｉｏ（振動数比）１は主系の固有振動数に対応している。
【０１１９】
【発明の実施の形態】
以下、本発明の好適な実施の形態について、図面を参照しつつ説明する。
【０１２０】
＜第１の実施の形態＞
図２４は、本発明の第１の実施の形態による直列二重動吸振器が設置された住宅の模式図である。図２５は、図２４の拡大図であって直列二重動吸振器を描いた模式図である。図２４に示すように、主系である住宅４０の屋根裏付近には、本実施の形態による直列二重動吸振器１が設置されている。直列二重動吸振器１は、屋根裏の設置面４０ａ上に設置された第一動吸振器２と、その上に載置された第二動吸振器３とから構成されている。
【０１２１】
図２５に示すように、第一動吸振器２は、付加質量体２１と、設置面４０ａと付加質量体２１との間に配置されて付加質量体２１を鉛直方向に振動可能に支持する複数のバネ要素（弾性体）２２とを含んでいる。バネ要素２２としては、例えばコイルバネが用いられる。
【０１２２】
第二動吸振器３は、付加質量体２１の上方に配置された付加質量体３１と、付加質量体２１と付加質量体３１との間に配置されて付加質量体３１を鉛直方向に振動可能に支持する複数のバネ要素（弾性体）３２及び減衰要素３３とを含んでいる。バネ要素３２としては、例えばコイルバネが用いられる。減衰要素３３はダンパとして適切な減衰係数を有するものが用いられる。
【０１２３】
本実施の形態において、付加質量体２１、３１の質量、バネ要素２２、３２のばね定数、減衰要素３３の減衰係数は、住宅のコンプライアンス又はアクセレランスの最大値を最小にするように最適化された値（つまり、付加質量体２１の単独系としての鉛直方向の固有振動数が住宅４０の鉛直方向の固有振動数よりも高く、付加質量体３１の単独系としての鉛直方向の固有振動数が住宅４０の鉛直方向の固有振動数よりも低くなるような値）となっている。また、バネ要素２２として減衰係数ができるだけ小さくゼロに近いものを用いることが好ましい。また、付加質量体２１の質量を付加質量体３１よりも大きくし両者の質量比は総質量比に応じて変化させることが好ましい。このようにすることで、住宅４０の鉛直方向の振動が十分に抑制される。
【０１２４】
＜第２の実施の形態＞
図２６は、本発明の第２の実施の形態による直列二重動吸振器の模式図である。図２６に描いた動吸振器６１は、制振対象構造物の設置面９０ａ上に設置された第一動吸振器７０と、その上に載置された第二動吸振器８０とから構成されている。
【０１２５】
図２６に示すように、第一動吸振器７０は、付加質量体７１と、設置面９０ａと付加質量体７１との間に配置されて付加質量体７１を水平方向に振動可能に支持する複数のバネ要素（弾性体）７２とを含んでいる。バネ要素７２としては、例えば合成ゴムと薄金属層とが積層された積層ゴムなどが用いられる。
【０１２６】
第二動吸振器８０は、付加質量体７１の上方に配置された付加質量体８１と、付加質量体７１の上面から上方に向けて突出した２本の支柱８４と、付加質量体８１と支柱８４との間にそれぞれ配置されて付加質量体８１を水平方向に振動可能に支持する複数のバネ要素（弾性体）８２及び減衰要素８３とを含んでいる。バネ要素８２としては、例えばコイルバネが用いられる。減衰要素８３はダンパとして適切な減衰係数を有するものが用いられる。また、付加質量体８１の下面には付加質量体８１の水平方向への振動が妨げられることがないように車輪８１ａが取り付けられている。
【０１２７】
本実施の形態において、付加質量体７１、８１の質量、バネ要素７２、８２のばね定数、減衰要素８３の減衰係数は、制振対象構造物のコンプライアンス又はアクセレランスの最大値を最小にするように最適化された値（つまり、付加質量体７１の単独系としての水平方向の固有振動数が制振対象構造物の水平方向の固有振動数よりも高く、付加質量体８１の水平方向の単独系としての固有振動数が制振対象構造物の水平方向の固有振動数よりも低くなるような値）となっている。また、バネ要素７２として減衰係数ができるだけ小さくゼロに近いものを用いることが好ましい。また、付加質量体７１の質量を付加質量体８１よりも大きくし両者の質量比は総質量比に応じて変化させることが好ましい。このようにすることで、制振対象構造物の水平方向の振動が十分に抑制される。
【０１２８】
＜第３の実施の形態＞
図２７は、本発明の第３の実施の形態による直列二重動吸振器の模式的な斜視図である。図２７に描いた動吸振器１０１は、制振対象構造物の設置面１９０ａ上に設置された第一動吸振器１２０と、その上に載置された４つの第二動吸振器１３０とから構成されている。
【０１２９】
図２７に示すように、第一動吸振器１２０は、付加質量体１２１と、設置面１９０ａと付加質量体１２１との間に配置されて付加質量体１２１を水平２方向（ｘ方向、ｙ方向）に振動可能に支持する４つのバネ要素（弾性体）１２２と、ｘ方向のばね定数調整用のバネ要素１２３と、ｙ方向のばね定数調整用のバネ要素１２４とを含んでいる。バネ要素１２２としては、例えば合成ゴムと薄金属層とが積層された積層ゴムなどが用いられる。また、バネ要素１２３、１２４としては、例えば板ばねが用いられる。
【０１３０】
４つの第二動吸振器１３０のうちの２つはｘ方向に振動可能となっており、残りの２つはｙ方向に振動可能となっている。各第二動吸振器１３０は、付加質量体１２１の上方に配置された付加質量体１３１と、付加質量体１２１の上面から各付加質量体１３１の両横においてそれぞれ上方に向けて突出した２本の支柱１３４と、付加質量体１３１と支柱１３４との間にそれぞれ配置されて付加質量体１３１をｘ方向又はｙ方向に振動可能に支持する複数のバネ要素（弾性体）１３２及び減衰要素１３３とを含んでいる。バネ要素１３２としては、例えばコイルバネが用いられる。減衰要素１３３はダンパとして適切な減衰係数を有するものが用いられる。また、付加質量体１３１の下面には付加質量体１３１の水平方向への振動が妨げられることがないように車輪１３１ａが取り付けられている。
【０１３１】
本実施の形態において、付加質量体１２１、１３１の質量、バネ要素１２２、１３２のばね定数、減衰要素１３３の減衰係数は、制振対象構造物のコンプライアンス又はアクセレランスの最大値を最小にするように最適化された値（つまり、付加質量体１２１の単独系としてのｘ方向及びｙ方向の固有振動数が制振対象構造物のｘ方向及びｙ方向の固有振動数よりも高く、付加質量体１３１のｘ方向及びｙ方向の単独系としての固有振動数が制振対象構造物のｘ方向及びｙ方向の固有振動数よりも低くなるような値）となっている。また、バネ要素１２２として減衰係数ができるだけ小さくゼロに近いものを用いることが好ましい。また、付加質量体１２１の質量を４つの付加質量体１３１の合計よりも大きくし両者の質量比は総質量比に応じて変化させることが好ましい。このようにすることで、制振対象構造物の水平２方向の振動が十分に抑制される。
【０１３２】
＜第４の実施の形態＞
図２８は、本発明の第４の実施の形態による直列二重動吸振器の模式図である。図２８に描いた動吸振器２０１は、制振対象構造物の設置面２４０ａ上に設置された第一動吸振器２１０と、その上に載置された第二動吸振器２２０とから構成されている。
【０１３３】
図２８に示すように、第一動吸振器２１０は、付加質量体２１１と、設置面２４０ａと付加質量体２１１との間に配置されて付加質量体２１１を鉛直方向に振動可能に支持するバネ要素２１２とを含んでいる。バネ要素２１２としては、例えばコイルバネが用いられる。
【０１３４】
第二動吸振器２２０は、付加質量体２１１の上方に配置された付加質量体２２１と、付加質量体２１１と付加質量体２２１との間に配置されて付加質量体を鉛直方向に振動可能に支持するバネ要素（弾性体）２２２及び減衰要素２２３と、付加質量体２２１の両横から水平にそれぞれ延出した支柱２２４と設置面２４０ａとの間に配置されて付加質量体２２１を鉛直方向に振動可能に支持する複数のバネ要素２２５とを含んでなる。バネ要素２２２、２２５としては、例えばコイルバネが用いられる。減衰要素２２３はダンパとして適切な減衰係数を有するものが用いられる。
【０１３５】
本実施の形態において、付加質量体２１１、２２１の質量、バネ要素２１２、２２２、２２５のばね定数、減衰要素２２３の減衰係数は、制振対象構造物のコンプライアンス又はアクセレランスの最大値を最小にするように最適化された値（つまり、付加質量体２１１の単独系としての鉛直方向の固有振動数が制振対象構造物の鉛直方向の固有振動数よりも高く、付加質量体２２１の単独系としての鉛直方向の固有振動数が制振対象構造物の鉛直方向の固有振動数よりも低くなるような値）となっている。また、バネ要素２１２として減衰係数ができるだけ小さくゼロに近いものを用いることが好ましい。また、付加質量体２１１の質量を付加質量体２２１よりも大きくし両者の質量比は総質量比に応じて変化させることが好ましい。このようにすることで、制振対象構造物の鉛直方向の振動が十分に抑制される。
【０１３６】
＜第５の実施の形態＞
図２９は、本発明の第５の実施の形態による直列二重動吸振器の模式図である。図２９に描いた動吸振器２５０は、制振対象構造物の設置面２９０ａ上に設置された第一動吸振器２６０と、その上に載置された第二動吸振器２７０とから構成されている。
【０１３７】
図２９に示すように、第一動吸振器２６０は、付加質量体２６１と、設置面２９０ａと付加質量体２６１との間に配置されて付加質量体２６１を鉛直方向に振動可能に支持するバネ要素２６２とを含んでいる。バネ要素２６２としては、例えばコイルバネが用いられる。
【０１３８】
第二動吸振器２７０は、付加質量体２６１の上方に配置された付加質量体２７１と、付加質量体２６１と付加質量体２７１との間に配置されて付加質量体２７１を鉛直方向に振動可能に支持するバネ要素（弾性体）２７２と、付加質量体２７１の両横から水平にそれぞれ延出した支柱２７５と設置面２９０ａとの間に配置されて付加質量体２７１を鉛直方向に振動可能に支持するバネ要素２７３及び減衰要素２７４とを含んでなる。バネ要素２７２、２７３としては、例えばコイルバネが用いられる。減衰要素２７４はダンパとして適切な減衰係数を有するものが用いられる。
【０１３９】
本実施の形態において、付加質量体２６１、２７１の質量、バネ要素２６２、２７２、２７３のばね定数、減衰要素２７４の減衰係数は、制振対象構造物のコンプライアンス又はアクセレランスの最大値を最小にするように最適化された値（つまり、付加質量体２６１の単独系としての鉛直方向の固有振動数が制振対象構造物の鉛直方向の固有振動数よりも高く、付加質量体２７１の単独系としての鉛直方向の固有振動数が制振対象構造物の鉛直方向の固有振動数よりも低くなるような値）となっている。また、バネ要素２６２として減衰係数ができるだけ小さくゼロに近いものを用いることが好ましい。また、付加質量体２６１の質量を付加質量体２７１よりも大きくし両者の質量比は総質量比に応じて変化させることが好ましい。このようにすることで、制振対象構造物の鉛直方向の振動が十分に抑制される。
【０１４０】
＜第６の実施の形態＞
図３０は、本発明の第６の実施の形態による直列二重動吸振器の模式図である。図３０に描いた動吸振器３０１は、制振対象構造物の設置面３４０ａ上に設置された第一動吸振器３１０と、その上に載置された第二動吸振器３２０とから構成されている。
【０１４１】
図３０に示すように、第一動吸振器３１０は、付加質量体３１１と、設置面３４０ａと付加質量体３１１との間に配置されて付加質量体３１１を鉛直方向に振動可能に支持するバネ要素３１２とを含んでいる。バネ要素３１２としては、例えばコイルバネが用いられる。
【０１４２】
第二動吸振器３２０は、付加質量体３１１の上方に配置された付加質量体３２１と、付加質量体３１１と付加質量体３２１との間に配置されて付加質量体３２１を鉛直方向に振動可能に支持するバネ要素（弾性体）３２２及び減衰要素３２３と、付加質量体３２１の両横から水平にそれぞれ延出した支柱３２４と設置面３４０ａとの間に配置されて付加質量体３２１を鉛直方向に振動可能に支持するバネ要素３２５及び減衰要素３２６とを含んでなる。バネ要素３２２、３２５としては、例えばコイルバネが用いられる。減衰要素３２３、３２６はダンパとして適切な減衰係数を有するものが用いられる。
【０１４３】
本実施の形態において、付加質量体３１１、３２１の質量、バネ要素３１２、３２２、３２５のばね定数、減衰要素３２３、３２６の減衰係数は、制振対象構造物のコンプライアンス又はアクセレランスの最大値を最小にするように最適化された値（つまり、付加質量体３１１の単独系としての鉛直方向の固有振動数が制振対象構造物の鉛直方向の固有振動数よりも高く、付加質量体３２１の単独系としての鉛直方向の固有振動数が制振対象構造物の鉛直方向の固有振動数よりも低くなるような値）となっている。また、バネ要素３１２として減衰係数ができるだけ小さくゼロに近いものを用いることが好ましい。また、付加質量体３１１の質量を付加質量体３２１よりも大きくし両者の質量比は総質量比に応じて変化させることが好ましい。このようにすることで、制振対象構造物の鉛直方向の振動が十分に抑制される。
【０１４４】
＜第７の実施の形態＞
図３１は、本発明の第７の実施の形態による直列三重動吸振器の模式図である。図３１に描いた動吸振器３５１は、制振対象構造物の設置面３９０ａ上に設置された第一動吸振器３６０と、その第一動吸振器３６０の上に載置された第二動吸振器３７０と、さらに第二動吸振器３７０の上に載置された第三動吸振器から構成されている。
【０１４５】
図３１に示すように、第一動吸振器３６０は、付加質量体３６１と、設置面３９０ａと付加質量体３６１との間に配置されて付加質量体３６１を鉛直方向に振動可能に支持するバネ要素３６２とを含んでいる。バネ要素３６２としては、例えばコイルバネが用いられる。
【０１４６】
第二動吸振器３７０は、付加質量体３６１の上方に配置された付加質量体３７１と、付加質量体３６１と付加質量体３７１との間に配置されて付加質量体３７１を鉛直方向に振動可能に支持するバネ要素（弾性体）３７２とを含んでなる。バネ要素３７２としては、例えばコイルバネが用いられる。
【０１４７】
第三動吸振器３８０は、付加質量体３７１の上方に配置された付加質量体３８１と、付加質量体３７１と付加質量体３８１との間に配置されて付加質量体３８１を鉛直方向に振動可能に支持するバネ要素（弾性体）３８２及び減衰要素３８３とを含んでなる。バネ要素３８２としては、例えばコイルバネが用いられる。減衰要素３８３はダンパとして適切な減衰係数を有するものが用いられる。
【０１４８】
本実施の形態において、付加質量体３６１、３７１、３８１の質量、バネ要素３６２、３７２、３８２のばね定数、減衰要素３８３の減衰係数は、制振対象構造物のコンプライアンス又はアクセレランスの最大値を最小にするように最適化された値（つまり、付加質量体３６１の単独系としての鉛直方向の固有振動数が制振対象構造物の鉛直方向の固有振動数よりも高く、付加質量体３７１の単独系としての鉛直方向の固有振動数が付加質量体３６１の鉛直方向の固有振動数よりも高く、付加質量体３８１の単独系としての鉛直方向の固有振動数が制振対象構造物の鉛直方向の固有振動数よりも低くなるような値）となっている。また、バネ要素３６２、３７２として減衰係数ができるだけ小さくゼロに近いものを用いることが好ましい。また、付加質量体３６１の質量を付加質量体３７１、３８１よりも大きくし、三者の質量比は総質量比に応じて変化させることが好ましい。このようにすることで、制振対象構造物の鉛直方向の振動が十分に抑制される。
【０１４９】
＜第８の実施の形態＞
図３２は、本発明の第８の実施の形態による複合式動吸振器が設置された住宅の模式図である。図３３は、図３２の拡大図であって、（ａ）は複合式動吸振器の正面図であり、（ｂ）は複合式動吸振器の側面図である。図３２に示すように住宅４００には、各階に天井３９９と床３９８とが設けられている。天井３９９と床３９８との間には鉛直方向の梁３９７が配置され、それらを連結している。この梁３９７には、本実施の形態による複合式動吸振器４０１が設置されている。複合式動吸振器４０１は、図３３（ａ）、（ｂ）に示すように梁３９７の中央位置に設けられた固定部３９６に固定された２組の第一動吸振器４１０、４２０と、その上に載置された４つの第二動吸振器４３０とから構成されている。
【０１５０】
図３３（ａ）に示すように、２組の第一動吸振器４１０、４２０は、固定部３９６の両端面３９６ａで固定されて互いに対称となるように配置されている２つのバネ要素（弾性体）４１２、４２２と、それらバネ要素４１２、４２２の両端部にそれぞれ設けられた４つの付加質量体４１１、４２１とを含んでいる。つまり、図３３（ｂ）に示すように一方のバネ要素４２２の両端部には、２つの付加質量体４２１がそれぞれ配置されており、１組の第一動吸振器４２０を構成している。また、他方のバネ要素４１２の両端部にも、２つの付加質量体４１１がそれぞれ配置されており、１組の第一動吸振器４１０を構成している。そして、２つのバネ要素４１２、４２２が固定部３９６で並列に固定されることで、これら第一動吸振器４１０、４２０が並列に配置されることになる。また、４つの付加質量体４１１、４２１は、それぞれに対応した位置のバネ要素４１２、４２２の端部を挟むようにして固定されている。また、２つのバネ要素４１２、４２２は、それぞれの付加質量体４１１、４２１を鉛直方向に振動可能に支持している。バネ要素４１２、４２２としては、例えば板ばねが用いられる。
【０１５１】
４つの第二動吸振器４３０は、それぞれの付加質量体４１１、４２１の上方に配置された付加質量体４３１と、それぞれの付加質量体４１１、４２１と付加質量体４３１との間に配置されてそれぞれの付加質量体４３１を鉛直方向に振動可能に支持する複数のバネ要素（弾性体）４３２及び減衰要素４３３とを含んでいる。複数のバネ要素４３２としては、例えばコイルバネが用いられる。また、複数の減衰要素４３３はダンパとして適切な減衰係数を有するものが用いられる。
【０１５２】
本実施の形態において、付加質量体４１１、４２１、４３１の質量、バネ要素４１２、４２２、４３２のばね定数、減衰要素４３３の減衰係数は、住宅４００のコンプライアンスまたはアクセレランスの最大値を最小にするように最適化された値（つまり、付加質量体４１１の単独系としての鉛直方向の固有振動数が住宅４００の鉛直方向の固有振動数よりも高く、付加質量体４２１の単独系としての鉛直方向の固有振動数が住宅４００の鉛直方向の固有振動数よりも低く、付加質量体４３１の単独系としての鉛直方向の固有振動数が住宅４００の鉛直方向の固有振動数よりも低くなるような値）となっている。また、バネ要素４１２、４２２として減衰係数ができるだけ小さくゼロに近いものを用いることが好ましい。また、４つの付加質量体４１１、４２１のそれぞれの質量を４つの付加質量体４３１のそれぞれの質量より大きくし、両者の質量比は総質量比に応じて変化させることが好ましい。このようにすることで、住宅４００の鉛直方向の振動が十分に抑制される。
【０１５３】
＜第９の実施の形態＞
図３４は、本発明の第９の実施の形態による複合式動吸振器の模式図であり、（ａ）は正面図であり、（ｂ）は側面図である。図３４（ａ）に描いた複合式動吸振器４５１は、上述と同様に制振対象構造物の天井４４９と床４４８との間に配置され、それらと連結する梁４４７の中央部に設置されている。複合式動吸振器４５１は、図３４（ａ）、（ｂ）に示すように梁４４７の中央位置に設けられた固定部４４６に固定された２組の第一動吸振器４６０、４７０と、その上に載置された４つの第二動吸振器４８０とから構成されている。
【０１５４】
図３４（ａ）に示すように、２組の第一動吸振器４６０、４７０は、固定部４４６の両端面４４６ａで固定されて互いに対称となるように配置されている２つのバネ要素（弾性体）４６２、４７２と、それらバネ要素４６２、４７２の両端部にそれぞれ設けられた４つの付加質量体４６１、４７１とを含んでいる。つまり、図３４（ｂ）に示すように一方のバネ要素４７２の両端部には、２つの付加質量体４７１がそれぞれ配置されており、１組の第一動吸振器４７０を構成している。また、他方のバネ要素４６２の両端部にも、２つの付加質量体４６１がそれぞれ配置されており、１組の第一動吸振器４６０を構成している。そして、２つのバネ要素４６２、４７２が固定部４４６で並列に固定されることで、これら第一動吸振器４６０、４７０が並列に配置されることになる。また、４つの付加質量体４６１、４７１は、それぞれに対応した位置のバネ要素４６２、４７２の端部を挟むようにして固定されている。また、２つのバネ要素４６２、４７２は、それぞれの付加質量体４６１、４７１を鉛直方向に振動可能に支持している。バネ要素４６２、４７２としては、例えば板ばねが用いられる。
【０１５５】
４つの第二動吸振器４８０は、それぞれの付加質量体４６１、４７１の上方に配置された付加質量体４８１と、それぞれの付加質量体４６１、４７１の上面から上方に向けて突出した１本の支柱４８４と、その支柱４８４の中央部から付加質量体４８１の下面と接続されるように配置されて付加質量体４８１を鉛直方向に振動可能に支持する複数のバネ要素（弾性体）４８２及び付加質量体４８１の下面に接続された部分のバネ要素４８２と付加質量体４６１、４７１との間に配置された減衰要素４８３とを含んでいる。バネ要素４８２としては、例えば板ばねが用いられる。減衰要素４８３はダンパとして適切な減衰係数を有するエラストマー（粘弾性体）が用いられる。
【０１５６】
本実施の形態において、付加質量体４６１、４７１、４８１の質量、バネ要素４６２、４７２、４８２のばね定数、減衰要素４８３の減衰係数は、制振対象構造物のコンプライアンスまたはアクセレランスの最大値を最小にするように最適化された値（つまり、付加質量体４６１の単独系としての鉛直方向の固有振動数が制振対象構造物の鉛直方向の固有振動数よりも高く、付加質量体４７１の単独系としての鉛直方向の固有振動数が制振対象構造物の鉛直方向の固有振動数よりも低く、付加質量体４８１の単独系としての鉛直方向の固有振動数が制振対象構造物の鉛直方向の固有振動数よりも低くなるような値）となっている。また、バネ要素４６２、４７２として減衰係数ができるだけ小さくゼロに近いものを用いることが好ましい。また、４つの付加質量体４６１、４７１のそれぞれの質量を４つの付加質量体４８１のそれぞれの質量より大きくし、両者の質量比は総質量比に応じて変化させることが好ましい。このようにすることで、制振対象構造物の鉛直方向の振動が十分に抑制される。
【０１５７】
＜その他の実施の形態＞
以上、本発明の好適な実施の形態について説明したが、本発明の適用範囲は広く様々な実施の形態を想定することができる。したがって、本発明は上述の実施の形態に限られるものではなく、特許請求の範囲に記載した限りにおいて様々な設計変更が可能である。基本的には、上述の第１又は第２の実施の形態のように、第一動吸振器の上に１つの第二動吸振器を載置したものが原型であるが、第３の実施の形態のように第二動吸振器が複数台に分割設置されていてもよい。もちろん、第４〜６の実施の形態のように第二動吸振器に接続されているバネ要素及び減衰要素が制振対象構造物に接続されていても良い。また、第３の実施の形態の第一動吸振器と第二動吸振器との間に、その第一動吸振器と同様な動吸振器を配置して直列三重動吸振器としも実施可能である。
【０１５８】
また、第７の実施の形態の第三動吸振器の上にさらに第四動吸振器を載置されているような構成でも実施可能である。また、第８又は第９の実施の形態のように、直列二重動吸振器を一つの制振対象構造物に並列に配置する構成だけでなく、直列三重動吸振器を一つの制振対象構造物に並列に配置する構成でも実施可能である。また、総質量比の範囲は０．０２から０．２の範囲に限られず、この範囲外においても本発明を適用することは可能である。
【０１５９】
【発明の効果】
以上説明したように、本発明によると、パラメータ設定が比較的簡易であると共に制振対象構造物の振動抑制効果が大きい直列及び並列動吸振器が得られる。
【図面の簡単な説明】
【図１】付加質量体が２個の場合の本発明による動吸振器の模式図である。
【図２】本発明の動吸振器に係るパラメータの特性を説明するためのグラフである。
【図３】本発明の動吸振器における主系のコンプライアンス曲線の一例を描いたグラフである。
【図４】本発明の比較例の動吸振器における主系のコンプライアンス曲線の一例を描いたグラフである。
【図５】本発明の別の比較例の動吸振器における主系のコンプライアンス曲線の一例を描いたグラフである。
【図６】本発明及び従来技術の動吸振器におけるインパルス応答特性を描いたグラフである。
【図７】主系の固有振動数が変化したときに第一動吸振器に関するパラメータを変えずに第二動吸振器に関するパラメータのみを調整したときにおいて、調整前後の主系のコンプライアンス曲線を描いたグラフである。
【図８】減衰が存在する主系に対して、主系の減衰をゼロという条件で最適化された本発明の動吸振器を用いた場合のコンプライアンス曲線の一例を描いたグラフである。
【図９】主系に減衰が存在する条件でコンプライアンス最適化された場合の本発明の動吸振器に係るパラメータの特性を説明するためのグラフであり、（ａ）は第１の付加質量体と第２の付加質量体の各質量比の変化曲線の一例であり、（ｂ）は第１の付加質量体と第２の付加質量体の各固有振動数の比の変化曲線の一例であり、（ｃ）は第２の付加質量体の減衰比の変化曲線の一例である。
【図１０】本発明の動吸振器における主系のコンプライアンス曲線の一例を描いたグラフである。
【図１１】主系に減衰が存在する条件でアクセレランス最適化された場合の本発明の動吸振器に係るパラメータの特性を説明するためのグラフであり、（ａ）は第１の付加質量体と第２の付加質量体の各質量比の変化曲線の一例であり、（ｂ）は第１の付加質量体と第２の付加質量体の各固有振動数の比の変化曲線の一例であり、（ｃ）は第２の付加質量体の減衰比の変化曲線の一例である。
【図１２】本発明の動吸振器における主系のアクセレランス曲線の一例を描いたグラフである。
【図１３】主系に減衰が存在する条件でモビリティ最適化された場合の本発明の動吸振器に係るパラメータの特性を説明するためのグラフであり、（ａ）は第１の付加質量体と第２の付加質量体の各質量比の変化曲線の一例であり、（ｂ）は第１の付加質量体と第２の付加質量体の各固有振動数の比の変化曲線の一例であり、（ｃ）は第２の付加質量体の減衰比の変化曲線の一例である。
【図１４】本発明の動吸振器における主系のモビリティ曲線の一例を描いたグラフである。
【図１５】主系のコンプライアンス最適化、アクセレランス最適化、モビリティ最適化においての本発明の動吸振器における第２の付加質量体の減衰比の変化範囲を示すグラフである。
【図１６】付加質量体が３個の場合の本発明による動吸振器の模式図である。
【図１７】主系のコンプライアンス最適化においての本発明の動吸振器に係るパラメータの特性を説明するためのグラフである。
【図１８】単一動吸振器、並列二重動吸振器及び本発明の直列二重動吸振器及び直列三重動吸振器における主系のコンプライアンス曲線の一例を描いたグラフである。
【図１９】主系のアクセレランス最適化においての本発明の動吸振器に係るパラメータの特性を説明するためのグラフである。
【図２０】単一動吸振器、並列二重動吸振器及び本発明の直列二重動吸振器及び直列三重動吸振器における主系のアクセレランス曲線の一例を描いたグラフである。
【図２１】２個の付加質量体が直列に配置された動吸振器を２つ並列に配置された本発明による並列動吸振器の模式図である。
【図２２】本発明の並列動吸振器に係るパラメータの特性を説明するためのグラフである。
【図２３】単一動吸振器、並列二重動吸振器及び本発明の直列二重動吸振器及び並列動吸振器における主系のコンプライアンス曲線を描いたグラフである。
【図２４】本発明の第１の実施の形態による直列二重動吸振器が設置された住宅の模式図である。
【図２５】図２４の拡大図であって、本発明の第１の実施の形態による直列二重動吸振器を描いた模式図である。
【図２６】本発明の第２の実施の形態による直列二重動吸振器の模式図である。
【図２７】本発明の第３の実施の形態による直列二重動吸振器の模式的な斜視図である。
【図２８】本発明の第４の実施の形態による直列二重動吸振器の模式的な図である。
【図２９】本発明の第５の実施の形態による直列二重動吸振器の模式的な図である。
【図３０】本発明の第６の実施の形態による直列二重動吸振器の模式的な図である。
【図３１】本発明の第７の実施の形態による直列三重動吸振器の模式的な図である。
【図３２】本発明の第８の実施の形態による複合式動吸振器が設置された住宅の模式図である。
【図３３】図３２の拡大図であって、（ａ）は複合式動吸振器の正面図であり、（ｂ）は複合式動吸振器の側面図である。
【図３４】本発明の第９の実施の形態による複合式動吸振器の模式図であり、（ａ）は正面図であり、（ｂ）は側面図である。
【符号の説明】
１ 直列二重動吸振器
２ 第一動吸振器
３ 第二動吸振器
２１ 付加質量体（第１の付加質量体）
２２ バネ要素
３１ 付加質量体（第２の付加質量体）
３２ バネ要素
３３ 減衰要素[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a dynamic vibration absorber used for suppressing vibration of a structure to be damped.
[0002]
[Prior art]
The dynamic vibration absorber has an additional mass added to the structure to be damped as the main system, and is used to suppress the vibration of many structures such as buildings, bridges, machines, vehicles, and ships. Used. A commonly used dynamic vibration absorber is a structure in which an additional mass body, a spring, and a damper are added as an additional system to a structure to be damped as a main system.
[0003]
As such a dynamic vibration absorber, a parallel multiple dynamic vibration absorber described in Non-Patent Document 1 is known. In this parallel multiple dynamic vibration absorber, n (n = 2, 3,...) Additional systems are installed in parallel on a structure to be damped as a main system. In addition, Non-Patent Document 2 describes a series dynamic vibration absorber as another dynamic vibration absorber. In this series dynamic vibration absorber, two additional systems are installed in series on a structure to be damped as a main system. According to these multiple dynamic vibration absorbers, it is possible to increase the effect of suppressing the vibration of the structure to be damped, which is the main system, as compared with the case where only one additional system is used.
[0004]
[Non-patent document 1]
Keiji Kamiya and three others, "Optimal Design Method for Multiple Dynamic Vibration Absorbers", Transactions of the Japan Society of Mechanical Engineers (C), September 1996, Vol. 62, No. 601
[Non-patent document 2]
Satoshi Fujita and 5 others, "Study on Mass Damper for Building Damping with Secondary Mass", Transactions of the Japan Society of Mechanical Engineers (C Edition), July 1995, Vol. 61, No. 587
[0005]
[Problems to be solved by the invention]
However, in the parallel multiple dynamic vibration absorber described in Non-Patent Document 1, setting of additional system parameters such as mass and spring constant is very complicated, and it is difficult to actually use it. Further, in the series dynamic vibration absorber described in Non-Patent Document 2, the parameters of the additional system have not been studied in detail, and the vibration of the structure to be damped cannot be sufficiently suppressed.
[0006]
Therefore, an object of the present invention is to provide a dynamic vibration absorber in which parameter setting is relatively simple and the effect of suppressing vibration of the structure to be damped is large.
[0007]
[Means for Solving the Problems]
The dynamic vibration absorber of the present invention includes a first additional mass body connected to the structure to be damped via an elastic body, and a second additional mass body connected to the first additional mass body via another elastic body. And an additional mass body. Then, the natural frequency of the first additional mass body as a single system is set to a higher natural frequency than the natural frequency of the vibration suppression target structure, and the single system of the second additional mass body is set. Is set to a natural frequency lower than the natural frequency of the structure to be damped (claim 1).
[0008]
That is, the natural frequency of the structure to be damped is f_M, The natural frequency of the first additional mass body as a single system is f_m1, The natural frequency of the second additional mass body as a single system is f_m2And when
f_m1> F_MAnd f_m2<F_M
Is set to be Such setting can be realized relatively easily by adjusting the mass and the spring constant of the first and second additional mass bodies, and as will be understood from the embodiments described later, the compliance of vibration (a function of displacement response to input: compliance, acceleration (function of acceleration response to input: accelerance) or mobility (function of speed response to input: mobility) can be sufficiently reduced, and the effect of suppressing vibration of the structure to be damped is large.
[0009]
Note that the direction of the vibration may be any of the XYZ axial directions, or may be the rotation direction around any of the axes.
[0010]
In the dynamic vibration absorber according to the present invention, the damping ratio of the second additional mass body is set such that at least one of compliance, acceleration, and mobility of vibration of the structure to be damped is optimized. (Claim 2). According to this, it is possible to sufficiently reduce at least one of the compliance, the acceleration, and the mobility of the vibration of the structure to be damped, and to obtain the effect of suppressing the vibration of the structure to be damped.
[0011]
Further, in the dynamic vibration absorber according to the present invention, the attenuation ratio of the second additional mass body is ＝ 2 = a × u^bWhen represented by -c, it is preferable that a> 0.80, b> 0.32, and c <0.08 (claim 3). Here, u is a ratio (total mass ratio) of the mass of the first and second additional mass bodies to the mass of the damping target structure.
[0012]
According to this, an approximate expression of the damping ratio ζ2 of the second additional mass body according to the damping of the damping target structure is shown, so that the optimum damping ratio ζ2 can be calculated and selected. As a result, an optimal value of a parameter that can sufficiently reduce at least one of vibration compliance, acceleration, and mobility is obtained.
[0013]
In the present invention, the first and second additional mass bodies are each capable of natural vibration in two or more different directions same as the vibration damping target structure, and the first additional mass body is a single system of the first additional mass body. The two or more natural frequencies are each set to a higher natural frequency than the corresponding natural frequency of the vibration suppression target structure, and the two or more natural frequencies as a single system of the second additional mass body May be set to natural frequencies lower than the corresponding natural frequencies of the structure to be damped (claim 4). In this case, the same vibration damping effect as described above can be obtained in each direction.
[0014]
In addition, the direction of vibration may be two or more axial directions of XYZ, may be a rotational direction around two or more axes, or may be an axial direction and a rotational direction around the axis. They may be combined.
[0015]
In another aspect, the dynamic vibration absorber according to the present invention includes a first additional mass body connected to the vibration damping target structure via an elastic body and the first additional mass body via another elastic body. A second additional mass body is connected, and a third additional mass body is further connected to the second additional mass body via another elastic body. The natural frequency of the first additional mass body as a single system is set to a higher natural frequency than the natural frequency of the structure to be damped, and the second additional mass body as a single system is set as a single system. The natural frequency of the first additional mass body is set to a higher natural frequency than the natural frequency of the single additional mass body as a single system, and the natural frequency of the third additional mass body as a single system is the vibration control target. The natural frequency is set to be lower than the natural frequency of the structure (claim 5).
[0016]
That is, the number of additional mass bodies connected in series is not limited to two, but may be three. At this time, the natural frequency of the structure to be damped is f_M, The natural frequency of the first additional mass body as a single system is f_m1, The natural frequency of the second additional mass body as a single system is f_m2, The natural frequency of the third additional mass body as a single system is f_m3, And
f_m1> F_M, F_m1<F_m2And f_m3<F_M
Is set to be Such a setting is relatively simple, and the effect of suppressing the vibration of the damping target structure is greater when the number of the additional mass bodies is three than when the number is two.
[0017]
In the present invention, the first to third additional mass bodies are each capable of natural vibration in two or more different directions same as the vibration suppression target structure, and the first additional mass body is a single system of the first additional mass body. The two or more natural frequencies are respectively set to higher natural frequencies than the corresponding natural frequencies of the vibration suppression target structure, and the two or more natural frequencies as a single system of the second additional mass body are The first additional mass body is set to a higher natural frequency than a corresponding natural frequency as a single system, and the two or more natural frequencies as a single system of the third additional mass body are the same as the above. The natural frequencies may be set to lower natural frequencies than the corresponding natural frequencies of the structure to be damped (claim 6). In this case, the same vibration damping effect as described above can be obtained in each direction.
[0018]
Note that, similarly to the case where the number of the additional mass bodies is two, the vibration direction may be two or more axial directions of XYZ, a rotation direction about two or more axes, or The directional vibration and the rotational vibration around the axis may be combined.
[0019]
Further, in the dynamic vibration absorber of the present invention, it is preferable that substantially no damping action is exerted between the structure to be damped and the first additional mass body. According to this, the damping effect is further increased.
[0020]
In the present invention, it is preferable that the mass of the first additional mass is larger than the mass of the second additional mass. According to this, the vibration damping effect is further increased, and the adjustment becomes easy.
[0021]
In another aspect, a dynamic vibration absorber according to the present invention is a parallel dynamic vibration absorber including the two dynamic vibration absorbers described above, wherein one of the first additional mass bodies of one of the dynamic vibration absorbers is a single system. Is set to a natural frequency lower than the natural frequency of the structure to be damped, and the natural frequency of the other dynamic vibration absorber as a single system of the first additional mass body is controlled by the natural frequency. The natural frequency is set to be higher than the natural frequency of the structure to be vibrated (claim 9).
[0022]
That is, a parallel dynamic vibration absorber in which the above-described dynamic vibration absorbers in which the additional mass bodies are connected in series are connected in parallel may be used. At this time, the natural frequency of the structure to be damped is f_M, The natural frequency of one of the first additional mass bodies as a single system is f_m21, The natural frequency of the other first additional mass body as a single system is f_m11, And
f_m11> F_M, F_m21<F_M
Is set to be Such a setting is relatively simple, and the effect of suppressing the vibration of the target structure is large.
[0023]
<Optimal design: Series double dynamic vibration absorber>
FIG. 1 is a schematic view of a dynamic vibration absorber in the case where the number of additional mass bodies according to the present invention is two. In FIG. 1, the structure to be damped (mass M) is supported on the ground via a spring (spring constant K) and a damper (damping coefficient C) in a state capable of vibrating in the vertical direction (displacement x). Further, the first additional mass body (mass m1) is supported by the damping target structure via a spring (spring constant k1) and a damper (damping coefficient c1) in a state capable of vibrating in the vertical direction (displacement y1). The second additional mass body (mass m2) is connected to the first additional mass body via a spring (spring constant k2) and a damper (damping coefficient c2) in a state where it can vibrate in the vertical direction (displacement y2). Supported. In other words, two dynamic vibration absorbers (the first dynamic vibration absorber close to the main system and the second dynamic vibration absorber connected to this) are connected in two stages in series with the structure to be damped. Has become.
[0024]
In the following description, as shown in equations (1) to (3), the total mass ratio (ratio of mass (m1 + m2) to mass M) is u, and the mass ratio of masses m1 and m2 to mass M is u1. , U2 (u = u1 + u2).
[0025]
(Equation 1)

[0026]
The equations of motion of the damping target structure and the first and second additional mass bodies shown in FIG. 1 indicate that the external force acting on the main system is represented by f (= F₀sin ωt) are expressed as in the following equations (4) to (6).
[0027]
(Equation 2)

[0028]
By the way, the design of the dynamic vibration absorber is to determine the mass, the spring constant, and the damping coefficient of the dynamic vibration absorber. In the case of a dynamic vibration absorber having only one ordinary additional system, when the mass of the dynamic vibration absorber (mass ratio to the main system) is determined, two parameters of a spring constant and a damping coefficient may be determined. In the series double dynamic vibration absorber, after determining the total mass ratio described above, the internal mass ratio (u1 / u) between the first dynamic vibration absorber and the second dynamic vibration absorber, the spring constant and the damping coefficient of each dynamic vibration absorber Must be obtained.
[0029]
As one method of optimally determining these parameters, a method of finding a parameter that minimizes the maximum value of the compliance of the structure to be damped, which is the main system, is used. However, since such optimized parameters cannot be determined as analytical solutions of equations (4) to (6), the total mass ratio is in the range of 0.02 to 0.2 (just the practical range). Table 1 shows the results obtained as numerical calculation solutions in the above range. The parameters to be obtained are the mass ratio (mass ratio ratio) u1 / u of m1 to m1 + m2 when the total mass ratio is determined, the spring constant and the damping coefficient of each dynamic vibration absorber.
[0030]
In Table 1, the natural frequency f in the vertical direction as a single system of the first and second additional mass bodies is used instead of the spring constant and the damping coefficient of each additional mass body._m1, F_m2And the natural frequency f in the vertical direction as a single system of the damping target structure_MPi (p1, p2: each represented by the formula (7)) and the damping ratio ζi (ζ1, ζ2: each represented by the formula (8)) as a single system of the first and second additional mass bodies. Is performed).
[0031]
[Table 1]

[0032]
(Equation 3)

[0033]
As can be seen from Table 1, when the total mass ratio is in the range of 0.02 to 0.2, the optimum natural frequency ratio p1 is slightly larger than 1 (p1> 1), and the optimum natural frequency ratio p2 is Slightly smaller than 1 (p2 <1), the optimum damping ratio ζ1 is substantially zero. Also, the optimum mass ratio u1 / u decreases as the total mass ratio increases. FIG. 2 is a graph for explaining the characteristics shown in Table 1, and FIG. 2A shows how the optimum mass ratio u1 / u decreases as the total mass ratio increases. . FIG. 2B shows how the optimum mass ratios u1 and u2 increase as the total mass ratio increases. FIG. 2C shows how the optimum ratio p1 increases and the ratio p2 decreases and the optimum damping ratio ζ2 increases as the total mass ratio increases.
[0034]
It should be noted that a similar result can be obtained as a parameter characteristic even when the optimum parameter is determined under the condition that the maximum values of the acceleration and the mobility are minimized.
[0035]
<Vibration control performance>
Normal dynamic absorber with only one additional system (single dynamic absorber), parallel dynamic absorber with two additional systems (parallel double dynamic absorber), parallel dynamic absorber with four additional systems (parallel) For each of the quadruple dynamic vibration absorber, the parallel dynamic vibration absorber with six additional systems (parallel hexadynamic vibration absorber), and the series double dynamic vibration absorber shown in FIG. The maximum value of the compliance of the structure to be damped when the parameters are optimized such that the maximum value of the compliance is minimized under the condition that the total mass ratio is in the range of 0.02 to 0.2 is obtained by numerical calculation. Table 2 shows the results. As can be seen from Table 2, according to the series double dynamic vibration absorber shown in FIG. 1, the compliance can be suppressed to a value equal to or higher than that of the parallel six dynamic vibration absorber. The vibration damping effect of the series double dynamic vibration absorber at a total mass ratio of 5% is equivalent to the vibration damping effect of a single dynamic vibration absorber at a mass ratio of 8.25%, and the series double vibration absorber at a total mass ratio of 10%. The vibration damping effect of the dynamic vibration absorber corresponds to the vibration damping effect of a single dynamic vibration absorber at a mass ratio of 16.5%. Thus, the series dynamic vibration absorber of the present invention has an excellent vibration damping effect.
[0036]
[Table 2]

[0037]
<Comparative Example 1>
FIG. 3 is an example of the compliance curve of the main system when the parameter determined under the above-described optimization condition of minimizing the maximum value of compliance (total mass ratio: 5%). At this time, as shown in FIG. 3, the compliance curve has three maximum values corresponding to the three degrees of freedom of the main system and the two additional systems, and these maximum values are equal. In FIG. 3, Frequency Ratio (frequency ratio) 1 corresponds to the natural frequency of the main system.
[0038]
Next, when only the natural frequency ratios p1 and p2 fluctuate from the optimum state (that is, p1 <1 and p2> 1, p1 <1 and p2 = 1, p1 = 1 and p2 = 1 or p1 = 1 and p2> 1 (when other parameters do not change), how the compliance curve changes will be described. Table 3 shows the parameters at this time.
[0039]
[Table 3]

[0040]
As a result of the numerical calculation, the compliance curves in each case shown in Table 3 were as shown in FIGS. 4 (a) is p1 <1 and p2> 1, FIG. 4 (b) is p1 <1 and p2 = 1, FIG. 4 (c) is p1 = 1 and p2 = 1, and FIG. 4 (d) is 9 is a diagram illustrating compliance curves when p1 = 1 and p2> 1. As can be seen from this result, when p1> 1 and p2 <1 are not satisfied, the maximum value of the compliance cannot be sufficiently reduced, and the vibration damping effect of the series double dynamic vibration absorber decreases. .
[0041]
<Comparative Example 2>
Next, when the ratios p1 and p2 fluctuate from the optimal state and other parameters can be re-optimized accordingly (that is, p1 <1 (p1 = 0.975) and p2> due to the existence of the optimal state). 1 (p2 = 1.025), p1 <1 (p1 = 0.975) and p2 = 1, p1 = 1 and p2 = 1, p1 = 1 and p2> 1 (p2 = 1.025) and other parameters Is re-optimized), how the compliance curve changes.
[0042]
As a result of the numerical calculation, other parameters are re-optimized as shown in Table 4. Note that if p1 <1 (p1 = 0.975) and p2> 1 (p2 = 1.025), re-optimization cannot be performed, so p1 = 0.959 and p2 = 1.005 Parameters were re-optimized. In each case, the compliance curves were as shown in FIGS. 5 (a) to 5 (d). 5 (a) is p1 <1 and p2> 1, FIG. 5 (b) is p1 <1 and p2 = 1, FIG. 5 (c) is p1 = 1 and p2 = 1, and FIG. 9 is a diagram illustrating compliance curves when p1 = 1 and p2> 1.
[0043]
As can be seen from this result, when p1> 1 and p2 <1 are not satisfied, even if other parameters can be reoptimized, the maximum value of the compliance can be sufficiently improved although it is improved as compared with the case of FIG. It cannot be reduced in size, and the vibration damping effect of the series double dynamic vibration absorber is reduced.
[0044]
[Table 4]

[0045]
<Acceleration>
For each of the single dynamic damper, parallel double dynamic damper, parallel quadruple dynamic damper, and series double dynamic damper shown in Fig. 1, the maximum acceleration is provided under the condition that the damping of the structure to be damped is zero. Table 5 shows the maximum value of the acceleration of the damping target structure obtained by numerical calculation in the case where the total mass ratio is in the range of 0.02 to 0.2 when the parameter is optimized to minimize the value. It is.
[0046]
As can be seen from Table 5, according to the series double dynamic vibration absorber shown in FIG. 1, the acceleration can be suppressed to a value equal to or more than that of the parallel quadruple dynamic vibration absorber. In addition, when the vibration damping effect of the series dynamic damper at a total mass ratio of 5% is compared with the vibration damping effect of the single dynamic damper, the resonance peak value is reduced by 20.32%.
[0047]
[Table 5]

[0048]
<Impulse response>
FIG. 6 shows the respective impulse responses when the single dynamic vibration absorber, the parallel double dynamic vibration absorber, and the series double dynamic vibration absorber shown in FIG. 1 are used when the total mass ratio is 5%. 6A corresponds to the main system, FIG. 6B corresponds to the first dynamic vibration absorber, and FIG. 6C corresponds to the second dynamic vibration absorber. Referring to FIG. 6A, in the impulse response of the main system, although the vibration damping effect in the first cycle of the series double dynamic vibration absorber is hardly observed, two cycles of the series double dynamic vibration absorber are used. The subsequent vibration waveform has a more remarkable vibration damping effect than the parallel double dynamic vibration absorber.
[0049]
Referring to FIG. 6B, the impulse response of the first dynamic vibration absorber of the series double dynamic vibration absorber is not much different from other dynamic vibration absorbers, and referring to FIG. It can be seen that the impulse response of the second dynamic vibration absorber is larger than that of the parallel double dynamic vibration absorber. Thus, it can be said that the increase in the motion of the additional system indicates the effect of the series double dynamic vibration absorber according to the present invention.
[0050]
<Adjustment of dynamic vibration absorber>
Generally, when the natural frequency of the main system changes, the spring coefficient and the damping coefficient of the dynamic vibration absorber must be adjusted in order to maintain the optimal effect of the dynamic vibration absorber. As described above, in the case of the series double dynamic vibration absorber according to the present invention, since the damping ratio of the first dynamic vibration absorber is set to be extremely small, no special damping performance is required. It is easier to adjust than the parallel double dynamic vibration absorber and the parallel quadruple vibration absorber. Further, the series double dynamic vibration absorber according to the present invention also has a feature that when the natural frequency of the main system changes, the optimum state can be restored only by adjusting the second dynamic vibration absorber. In an optimal state, the mass of the second dynamic vibration absorber is considerably smaller than the mass of the first dynamic vibration absorber, so that only the parameters of the second dynamic vibration absorber need to be adjusted greatly reduces the actual work load.
[0051]
The fact that the optimum state can be restored only by adjusting the second dynamic vibration absorber will be described with reference to data below. Table 6 shows the results when only the parameters relating to the second dynamic vibration absorber were adjusted without changing the parameters relating to the first dynamic vibration absorber when the natural frequency of the main system changed from 0.90 to 1.02. . FIG. 7 compares the compliance curves of the main system before and after the adjustment.
[0052]
[Table 6]

[0053]
From Table 6 and FIG. 7, it can be seen that, as the natural frequency of the main system becomes smaller than the original frequency, good results can be obtained in which the vibration damping effect hardly changes by increasing the mass of the second dynamic vibration absorber. I understand. However, when the natural frequency of the main system becomes higher than the original frequency, the mass ratio of the second dynamic vibration absorber must be reduced, and the vibration damping effect at this time is slightly deteriorated. If the natural frequency of the main system becomes higher than the frequency of the first dynamic vibration absorber, there is a possibility that a sufficient vibration damping effect cannot be obtained only by adjusting the parameters relating to the second dynamic vibration absorber.
[0054]
<Comparison between the case where the damping of the damping target structure is zero and the case where there is damping>
In the above-described series double dynamic vibration absorber, the compliance and the acceleration of the damping target structure when the parameters are optimized under the condition that the damping of the damping target structure is zero have been described. When there is attenuation in the target structure, the three extreme values in the compliance curve do not become substantially equal as shown in FIG. In other words, when a parameter optimized under the condition that the damping of the damping target structure is zero is adopted for a damping target structure having a damping of 5%, for example, a compliance curve as shown in FIG. The three extrema in the curve are not equal, and the optimized parameters are not optimal for the structure to be damped where there is damping.
[0055]
<Compliance optimization>
Next, a description will be given of the optimization of compliance in the case where damping is present in the structure to be damped. The damping of a general structure to be damped for which a series double dynamic vibration absorber is to be installed is small, and the effect of adding damping is high because the damping of the structure to be damped is about 6% or less. Considered an area. Therefore, for the compliance optimization when the attenuation existing in the damping target structure is changed from 0 to 6%, the change range of the parameter of the series double dynamic vibration absorber is calculated.
[0056]
FIG. 9 shows the characteristics of the parameters of each mass body in the compliance optimization when the damping of the structure to be damped changes from 0 to 6%, and (a) shows the first additional mass body and It is an example of the change curve of each mass ratio of a 2nd additional mass body, (b) is an example of the change curve of the ratio of each natural frequency of a 1st additional mass body and a 2nd additional mass body. (C) is an example of a change curve of the attenuation ratio of the second additional mass body. The change range of the change curve in FIG. 9 is shown in the range of 0.005 to 0.2 in terms of the total mass ratio.
[0057]
As shown in FIG. 9A, in each of the change curves, as the attenuation of the structure to be damped increases, the mass ratio u1 of the first additional mass body tends to decrease, and the mass ratio u1 of the second additional mass body increases. The mass ratio u2 tends to increase. Equation (9) of the change curve of the mass ratio u2 of the second additional mass body is obtained as an approximate equation from FIG. 9A, and the parameter of the mass ratio u2 of the second additional mass body is obtained from Equation (9). , The mass ratio u1 of the first additional mass body can be obtained from u1 = u−u2. Here, ζ is the damping ratio of the structure to be damped.
[0058]
(Equation 4)

[0059]
As shown in FIG. 9B, in each of the change curves, as the damping of the structure to be damped increases, the ratio p1 of the natural frequency of the first additional mass body tends to decrease, and the second additional mass The natural frequency ratio p2 of the mass body also tends to decrease. Equations (10) and (11) of the change curves of the first and second additional mass bodies are similarly obtained as approximate equations from FIG. 9B, and the first and second equations are obtained from Equations (10) and (11). The parameters of the ratios p1 and p2 of the natural frequencies of the two additional mass bodies are obtained.
[0060]
(Equation 5)

[0061]
As shown in FIG. 9C, in each of the change curves, as the attenuation of the structure to be damped increases, the attenuation ratio ζ2 of the second additional mass body increases. The attenuation ratio ζ1 of the first additional mass body is substantially zero as described above. Equation (12) of the change curve of the attenuation ratio ζ2 of the second additional mass body is similarly obtained as an approximate equation from FIG. 9C, and the attenuation ratio ζ2 of the second additional mass body is obtained from Equation (12). Can be
[0062]
(Equation 6)

[0063]
As shown in FIG. 9, the range of change of the parameters of the series double dynamic vibration absorber when the damping of the structure to be damped changes from 0 to 6% is obtained and an approximate expression is obtained, whereby the damping of the structure to be damped is obtained. It is possible to calculate and select the optimum value of the parameter of the series double dynamic vibration absorber according to the above. For example, it was determined under the optimization condition of minimizing the maximum value of the compliance when the damping ratio の of the structure to be damped is 5% and the total mass ratio u of the series double dynamic vibration absorber is 5%. The parameters are shown in Table 7, and the compliance curve of the main system when the parameters are adopted is shown in FIG. The three extreme values in the compliance curve shown in FIG. 10 are almost equal, and the parameters of the series double dynamic vibration absorber can be said to be optimal values as compared with FIG.
[0064]
[Table 7]

[0065]
<Acceleration optimization>
Subsequently, a change range of the parameter of the series double dynamic vibration absorber is calculated for the optimization of the acceleration when the attenuation existing in the damping target structure is changed from 0 to 6%.
[0066]
11A and 11B show characteristics of parameters of each mass body in the acceleration optimization when the attenuation of the structure to be damped changes from 0 to 6%, and FIG. 11A shows the first additional mass body. FIG. 7B is an example of a change curve of each mass ratio of the first and second additional mass bodies, and FIG. 7B is an example of a change curve of a ratio of each natural frequency of the first additional mass body and the second additional mass body. FIG. 6C is an example of a change curve of the attenuation ratio of the second additional mass body. The change range of the change curve in FIG. 11 is shown in the range of 0.005 to 0.2 in the total mass ratio.
[0067]
As shown in FIG. 11A, in each of the change curves, as the attenuation of the structure to be damped increases, the mass ratio u1 of the first additional mass body tends to decrease, and the mass ratio u1 of the second additional mass body increases. The mass ratio u2 tends to increase. Equation (13) of the change curve of the mass ratio u2 of the second additional mass body is obtained as an approximate equation from FIG. 11A, and the parameter of the mass ratio u2 of the second additional mass body is obtained from Equation (13). , The mass ratio u1 of the first additional mass body can be obtained from u1 = u−u2.
[0068]
(Equation 7)

[0069]
As shown in FIG. 11 (b), in each of the change curves, as the damping of the structure to be damped increases, the ratio p1 of the natural frequency of the first additional mass body tends to increase, and the second additional mass increases. The ratio p2 of the natural frequencies of the mass body also tends to increase. Equations (14) and (15) of the change curves of the first and second additional mass bodies are similarly obtained as approximate equations from FIG. 11B, and the first and second equations are obtained from Equations (14) and (15). The parameters of the ratios p1 and p2 of the natural frequencies of the two additional mass bodies are obtained.
[0070]
(Equation 8)

[0071]
As shown in FIG. 11C, in each of the change curves, as the attenuation of the damping target structure increases, the attenuation ratio ζ2 of the second additional mass body increases. The attenuation ratio ζ1 of the first additional mass body is substantially zero as described above. Equation (16) of the change curve of the attenuation ratio ζ2 of the second additional mass body is similarly obtained as an approximate expression from FIG. 11C, and the attenuation ratio ζ2 of the second additional mass body is obtained from Equation (16). Can be
[0072]
(Equation 9)

[0073]
FIG. 11 shows the range of change of the parameters of the series double dynamic vibration absorber when the damping of the structure to be damped changes from 0 to 6%, and an approximate expression is obtained, whereby the damping of the structure to be damped is obtained. It is possible to calculate and select the optimum value of the parameter of the series double dynamic vibration absorber according to the above. For example, when the damping ratio の of the structure to be damped is 5% and the total mass ratio u of the in-line dual dynamic vibration absorber is 5%, the damping ratio is determined under the optimization condition of minimizing the maximum value of the acceleration. Table 8 shows the parameters obtained, and FIG. 12 shows an acceleration curve of the main system when the parameters are adopted. The three extreme values in the acceleration curve shown in FIG. 12 are almost equal, and the parameters of the series double dynamic vibration absorber can be said to be optimum values.
[0074]
[Table 8]

[0075]
<Mobility optimization>
Subsequently, for mobility optimization when the attenuation existing in the damping target structure is changed from 0 to 6%, a change range of the parameter of the series double dynamic vibration absorber is calculated.
[0076]
FIG. 13 shows the characteristics of the parameters of each mass body in the mobility optimization when the damping of the structure to be damped changes from 0 to 6%. It is an example of the change curve of each mass ratio of a 2nd additional mass body, (b) is an example of the change curve of the ratio of each natural frequency of a 1st additional mass body and a 2nd additional mass body. (C) is an example of a change curve of the attenuation ratio of the second additional mass body. The change range of the change curve in FIG. 13 is shown in the range of 0.005 to 0.2 in total mass ratio.
[0077]
As shown in FIG. 13A, in each of the change curves, as the attenuation of the damping target structure increases, the mass ratio u1 of the first additional mass body tends to decrease, and the mass ratio u1 of the second additional mass body increases. The mass ratio u2 tends to increase. Equation (17) of the change curve of the mass ratio u2 of the second additional mass body is obtained as an approximate equation from FIG. 13A, and the parameter of the mass ratio u2 of the second additional mass body is obtained from Equation (17). , The mass ratio u1 of the first additional mass body can be obtained from u1 = u−u2.
[0078]
(Equation 10)

[0079]
As shown in FIG. 13 (b), in each of the change curves, as the damping of the structure to be damped increases, the ratio p1 of the natural frequency of the first additional mass body tends to increase, and the second additional mass increases. The natural frequency ratio p2 of the mass body tends to decrease. Equations (18) and (19) of the change curves of the first and second additional mass bodies are similarly obtained as approximate equations from FIG. 13B, and the first and second equations are obtained from Equations (18) and (19). The parameters of the ratios p1 and p2 of the natural frequencies of the two additional mass bodies are obtained.
[0080]
(Equation 11)

[0081]
As shown in FIG. 13C, in each of the change curves, as the attenuation of the structure to be damped increases, the attenuation ratio ζ2 of the second additional mass body increases. The attenuation ratio ζ1 of the first additional mass body is substantially zero as described above. Expression (20) of the change curve of the attenuation ratio ζ2 of the second additional mass body is similarly obtained as an approximate expression from FIG. 13C, and the attenuation ratio ζ2 of the second additional mass body is obtained from Expression (20). Can be
[0082]
(Equation 12)

[0083]
As shown in FIG. 13, the range of change of the parameters of the series double dynamic vibration absorber when the attenuation of the structure to be damped changes from 0 to 6% is obtained and an approximate expression is obtained, whereby the attenuation of the structure to be damped is obtained. It is possible to calculate and select the optimum value of the parameter of the series double dynamic vibration absorber according to the above. For example, a parameter determined under the optimization condition of minimizing the maximum value of mobility when the damping ratio の of the damping target structure is 5% and the total mass ratio u of the dual dynamic vibration absorber is 5%. Is shown in Table 9, and the mobility curve of the main system when the parameter is adopted is shown in FIG. The three extreme values in the mobility curve shown in FIG. 14 are almost equal, and the parameters of the series double dynamic vibration absorber can be said to be optimal values.
[0084]
[Table 9]

[0085]
As described above, the first additional mass body and the first additional mass body in three optimizations (compliance optimization, acceleration optimization, and mobility optimization) when the damping of the structure to be damped changes from 0 to 6%. The change tendency of the mass ratios u1 and u2 of the second additional mass body and the attenuation ratio ζ2 of the second additional mass body becomes similar, and the change width (the respective changes in the compliance optimization, the acceleration optimization and the mobility optimization). There is no significant difference in the width due to the deviation of the curve. On the other hand, although the changing tendency of the ratio of the natural frequencies of the first additional mass body and the second additional mass body is different, the ratio of the natural frequencies of the first additional mass body is always larger than 1, and The ratio of the natural frequencies of the additional mass is always less than one.
[0086]
FIG. 15 shows an example of a change curve of the attenuation ratio ζ2 of the second additional mass body in the three optimizations when the attenuation of the structure to be damped changes from 0 to 6%. Within the range surrounded by the change curve, the attenuation ratio ３2 of the second additional mass body by the three optimizations exists. From FIG. 15, an approximate expression (21) for obtaining the damping ratio ζ2 min of the second additional mass body when the damping of the structure to be damped is 0% is obtained. An approximate expression (22) for obtaining the attenuation ratio ζ2max of the additional mass body is obtained. Therefore, it is possible to obtain the attenuation ratio ζ2 of the second additional mass body when the attenuation of the structure to be damped changes from 0 to 6%. In the present invention, the attenuation ratio ζ2 that can sufficiently reduce at least one of the compliance, the acceleration, and the mobility of the main system is determined by the expression (21) or (22) described above. Not limited. For example, the attenuation ratio of the second additional mass body is ζ2 = a × u^bWhen indicated by -c, a is greater than 0.80 (a> 0.80), b is greater than 0.32 (b> 0.32), and c is less than 0.08 (c <0 .08), it is possible to obtain an attenuation ratio ζ2 capable of sufficiently reducing at least one of compliance, acceleration, and mobility of the main system.
[0087]
(Equation 13)

[0088]
<Optimal design: Series triple dynamic vibration absorber>
Subsequently, FIG. 16 is a schematic view of a dynamic vibration absorber in the case where the number of the additional mass bodies according to the present invention is three. In FIG. 16, in a state where the third additional mass body (mass m3) can vibrate in the vertical direction (displacement y3), the above-described series double dynamic vibration absorption is performed via a spring (spring constant k3) and a damper (damping coefficient c3). It is supported by the second additional mass body of the vessel, and is configured to be connected in three stages in series with the structure to be damped. That is, in the series triple dynamic vibration absorber, one dynamic vibration absorber (third dynamic vibration absorber) is connected to the second dynamic vibration absorber of the series double dynamic vibration absorber described above. In addition, about the thing similar to the above-mentioned series double dynamic vibration absorber, the same code | symbol is shown and description is abbreviate | omitted.
[0089]
In the following description, the total mass ratio (the ratio of the mass (m1 + m2 + m3) to the mass M) is u, and the mass ratio of the masses m1, m2, and m3 to the mass M is as shown in Expressions (23) and (24). Let u1, u2, u3 (u = u1 + u2 + u3) respectively.
[0090]
[Equation 14]

[0091]
The equation of motion of the damping target structure, the first, second, and third additional mass bodies shown in FIG. 16 indicates that the external force acting on the main system is represented by f (= F₀(sin ωt) are represented by the above-described equations (4) and (5), and the following equations (25) and (26), respectively.
[0092]
[Equation 15]

[0093]
In the design of the series triple dynamic vibration absorber, after the total mass ratio u is determined as described above, the internal mass ratio (u1 / u, u2 //) of the first dynamic vibration absorber, the second dynamic vibration absorber, and the third dynamic vibration absorber is determined. u), eight parameters must be determined: the spring constant and the damping coefficient of each dynamic vibration absorber.
[0094]
As described above, since the parameter for minimizing the maximum value of the compliance of the structure to be damped, which is the main system, cannot be determined as an analytical solution, the total mass ratio is in the range of 0.02 to 0.2. Table 10 shows the results obtained as numerical calculation solutions. The parameters to be determined are the mass ratio of m1 to m1 + m2 + m3 (mass ratio ratio) u1 / u, the mass ratio of m2 to m1 + m2 + m3 (mass ratio ratio) u2 / u when the total mass ratio is determined, Spring constant and damping coefficient.
[0095]
In Table 10, in place of the spring constant and the damping coefficient of each additional mass body, the vertical natural frequency f as a single system of the first, second, and third additional mass bodies is used._m1, F_m2, F_m3And the natural frequency f in the vertical direction as a single system of the damping target structure_M(P1, p2, p3: each represented by the formula (7)), and the damping ratio ζi (ζ1, ζ2, ζ3: as a single system of the first, second, and third additional mass bodies). (Each represented by equation (8)). Further, the mass ratios (mass ratio ratios) u1 / u and u2 / u are not shown in Table 10.
[0096]
[Table 10]

[0097]
As can be seen from Table 10, when the total mass ratio is in the range of 0.02 to 0.2, the optimum natural frequency ratio p1 is slightly larger than 1 (p1> 1), and the optimum natural frequency ratio p2 is The natural frequency ratio p1 is slightly higher than the natural frequency ratio p1 (p1 <p2), the optimum natural frequency ratio p3 is slightly lower than 1 (p3 <1), and the optimum damping ratios ζ1 and ζ2 are substantially zero. FIG. 17 is a graph for explaining the characteristics shown in Table 10, and FIG. 17A shows how the optimum mass ratios u1, u2, and u3 increase as the total mass ratio increases. ing. FIG. 17B shows how the optimum ratios p1 and p2 increase as the total mass ratio increases, the ratio p3 decreases, and the optimum damping ratio ζ3 increases.
[0098]
Note that, even when the optimum parameter is determined under the condition that the maximum value of the acceleration is minimized, similar results can be obtained as described later as the characteristic of the parameter.
[0099]
<Vibration control performance>
Normal dynamic absorber with only one additional system (single dynamic absorber), parallel dynamic absorber with two additional systems (parallel double dynamic absorber), parallel dynamic absorber with four additional systems (parallel) A quadruple dynamic vibration absorber), a parallel dynamic vibration absorber with six additional systems (parallel hexadynamic vibration absorber), a series double dynamic vibration absorber shown in FIG. 1, and a series triple dynamic vibration absorber shown in FIG. , The maximum value of the compliance of the structure to be damped when the parameter is optimized such that the maximum value of the compliance is minimized under the condition that the attenuation is zero is defined as the total mass ratio in the range of 0.02 to 0.2. Table 11 shows the results obtained by numerical calculation in Table 1. As can be seen from Table 11, the maximum compliance can be suppressed to a smaller value than the serial double dynamic vibration absorber according to the series triple dynamic vibration absorber illustrated in FIG. As described above, the series triple dynamic vibration absorber of the present invention has a more excellent vibration damping effect.
[0100]
[Table 11]

[0101]
<Comparative example>
FIG. 18 is an example of the compliance curve of the main system (total mass ratio 5%) when the parameter determined under the above-described optimization condition of minimizing the maximum value of the compliance is adopted. At this time, as shown in FIG. 18, the compliance curve has four maximum values corresponding to the three degrees of freedom of the main system and the three additional systems, and these maximum values are equal. In addition, it can be seen from FIG. 18 that the series triple dynamic vibration absorber suppresses the maximum compliance to a smaller value as compared with the single dynamic vibration absorber, the parallel double dynamic vibration absorber, and the series double dynamic vibration absorber. In FIG. 18, Frequency Ratio (frequency ratio) 1 corresponds to the natural frequency of the main system.
[0102]
<Acceleration>
Next, the parameter for minimizing the maximum value of the acceleration of the damping target structure, which is the main system, is also obtained as the analytical solution of the equations (4), (5), (25), and (26) in the same manner as described above. Table 12 shows the results obtained as numerical solutions when the total mass ratio is in the range of 0.02 to 0.2. The parameters to be determined are the mass ratio of m1 to m1 + m2 + m3 (mass ratio ratio) u1 / u, the mass ratio of m2 to m1 + m2 + m3 (mass ratio ratio) u2 / u when the total mass ratio is determined, Spring constant and damping coefficient.
[0103]
In Table 12, in place of the spring constant and damping coefficient of each additional mass body, the vertical natural frequency f as a single system of the first, second and third additional mass bodies is used._m1, F_m2, F_m3And the natural frequency f in the vertical direction as a single system of the damping target structure_MAre shown, and the attenuation ratios ζ1 to ζ3 of the first, second and third additional mass bodies as a single system are shown. The mass ratios (mass ratio ratios) u1 / u and u2 / u are not shown in Table 12.
[0104]
[Table 12]

[0105]
FIG. 19 is a graph for explaining the characteristics shown in Table 12, and FIG. 19A shows how the optimum mass ratios u1, u2, and u3 increase as the total mass ratio increases. I have. FIG. 19B shows how the optimum ratios p1 and p2 increase, the ratio p3 decreases, and the optimum damping ratio ζ3 increases as the total mass ratio increases.
[0106]
<Vibration control performance>
Normal dynamic absorber with only one additional system (single dynamic absorber), parallel dynamic absorber with two additional systems (parallel double dynamic absorber), parallel dynamic absorber with four additional systems (parallel) For each of the quadruple dynamic vibration absorber), the series double dynamic vibration absorber shown in FIG. 1, and the series triple dynamic vibration absorber shown in FIG. 16, the maximum value of the acceleration under the condition that the damping of the damping target structure is zero. Table 13 shows the maximum value of the acceleration of the structure to be damped in the case where the parameter is optimized so that the minimum is obtained by numerical calculation in the range of the total mass ratio of 0.02 to 0.2. is there. As can be seen from Table 13, according to the series triple dynamic vibration absorber shown in FIG. 16, the maximum acceleration can be suppressed to a smaller value than that of the series double dynamic vibration absorber. As described above, the series triple dynamic vibration absorber of the present invention has a more excellent vibration damping effect.
[0107]
[Table 13]

[0108]
<Comparative example>
FIG. 20 is an example of the main system compliance curve (total mass ratio: 5%) when the parameter determined under the above-described optimization condition of minimizing the maximum value of the acceleration is adopted. At this time, as shown in FIG. 20, the acceleration curve has four maximum values corresponding to the three degrees of freedom of the main system and the three additional systems, and these maximum values are equal. FIG. 20 shows that the series triple dynamic vibration absorber suppresses the maximum acceleration to a smaller value as compared with the single dynamic vibration absorber, the parallel double dynamic vibration absorber, and the series double dynamic vibration absorber. In FIG. 20, Frequency Ratio (frequency ratio) 1 corresponds to the natural frequency of the main system.
[0109]
<Composition of the dynamic vibration absorber>
Subsequently, FIG. 21 shows a schematic diagram of a parallel dynamic vibration absorber in a case where the above-described series double dynamic vibration absorbers are arranged in parallel. In FIG. 21, the damping target structure (mass M) is supported on the ground via a spring (spring constant K) and a damper (damping coefficient C) in a state capable of vibrating in the vertical direction (displacement x). In addition, the first additional mass body (mass m11) on the left side in FIG. 21 is supported by the damping target structure via a spring (spring constant k11) in a state capable of vibrating in the vertical direction (displacement y11). The second additional mass body (mass m12) is oscillated in the vertical direction (displacement y12) via a spring (spring constant k12) and a damper (damping coefficient c12). It is supported by. Further, the first additional mass body (mass m21) on the right side in FIG. 21 is supported by the damping target structure via a spring (spring constant k21) in a state capable of vibrating in the vertical direction (displacement y21). The second additional mass body (mass m22) is connected to the first additional mass body via a spring (spring constant k22) and a damper (damping coefficient c22) while being vibrated in the vertical direction (displacement y22). Supported. That is, two series double dynamic absorbers (the first series double dynamic absorber 100 and the second series double dynamic absorber 200) are connected in parallel on the upper surface of the structure to be damped. ing. Note that the first dynamic vibration absorber of the above-described series double dynamic vibration absorber is provided with a damper connected to the structure to be damped, but since the damping is substantially zero, the parallel dynamic vibration absorber ( Each of the first dynamic vibration absorbers of the composite dynamic vibration absorber) is not provided with a damper connected to the structure to be damped.
[0110]
<Compliance>
In such a composite dynamic vibration absorber, a parameter for minimizing the maximum value of the compliance of the structure to be damped, which is the main system, cannot be obtained as an analytical solution, so that the total mass ratio is 0.02 to 0. Table 14 shows the results obtained as numerical solution in the range of 0.2.
[0111]
In Table 14, in place of the spring constant and the damping coefficient of each additional mass body, the vertical natural frequency f as a single system of the first and second additional mass bodies of each series double dynamic vibration absorber is shown._m11, F_m12, F_m21, F_m22And the natural frequency f in the vertical direction as a single system of the damping target structure_MAre shown, and the damping ratios ζ12 and ζ22 of the first and second series dynamic vibration absorbers as a single system of the second additional mass body are shown.
[0112]
[Table 14]

[0113]
As can be seen from Table 14, when the total mass ratio is in the range of 0.02 to 0.2, the optimal natural frequency ratio p11 is slightly larger than 1 (p11> 1), and the optimal natural frequency ratio p12 is Slightly smaller than 1 (p12 <1), the optimum natural frequency ratio p21 is slightly smaller than 1 (p21 <1), and the optimum natural frequency ratio p22 is slightly smaller than 1 (p22 <1).
[0114]
FIG. 22 is a graph for explaining the characteristics shown in Table 14, and FIGS. 22 (a) and 22 (b) show the first and second series double dynamic vibration absorption as the total mass ratio increases. It shows that the optimum mass ratios u11, u12, u21, u22 of the vessel become large. FIG. 22 (c) shows how the optimum ratio p11 of the first series double dynamic vibration absorber increases, the ratio p12 decreases, and the optimum damping ratio ζ12 increases as the total mass ratio increases. ing. FIG. 22 (d) shows how the optimum ratios p21 and p22 of the second series double dynamic vibration absorber decrease and the optimum damping ratio ζ22 increases as the total mass ratio increases.
[0115]
It should be noted that a similar result can be obtained as a parameter characteristic when the optimum parameter is determined under the condition that the maximum value of the acceleration is minimized.
[0116]
<Vibration control performance>
Normal dynamic absorber with only one additional system (single dynamic absorber), parallel dynamic absorber with two additional systems (parallel double dynamic absorber), parallel dynamic absorber with four additional systems (parallel) A quadruple dynamic vibration absorber), a parallel dynamic vibration absorber with six additional systems (parallel hexadynamic vibration absorber), a series double dynamic vibration absorber shown in FIG. 1, and a combined dynamic vibration absorber shown in FIG. The maximum value of the compliance of the structure to be damped when the parameter is optimized such that the maximum value of the compliance is minimized under the condition that the damping of the structure to be damped is zero is 0.02 Table 15 shows the values obtained by numerical calculation in the range from to 0.2. As can be seen from Table 15, according to the combined dynamic vibration absorber shown in FIG. 21, the maximum compliance can be suppressed to a smaller value than that of the series double dynamic vibration absorber. As described above, the combined dynamic vibration absorber of the present invention has a more excellent vibration damping effect.
[0117]
[Table 15]

[0118]
<Comparative example>
FIG. 23 is an example of the compliance curve of the main system when the parameter determined under the above-described optimization condition of minimizing the maximum value of compliance (total mass ratio: 5%). At this time, as shown in FIG. 23, the compliance curve has five maximum values corresponding to the five degrees of freedom of the main system and the four additional systems, and these maximum values are equal. Further, it can be seen from FIG. 23 that the combined dynamic vibration absorber suppresses the maximum compliance to a smaller value as compared with the single dynamic vibration absorber, the parallel double dynamic vibration absorber, and the series double dynamic vibration absorber. In FIG. 23, Frequency Ratio (frequency ratio) 1 corresponds to the natural frequency of the main system.
[0119]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings.
[0120]
<First embodiment>
FIG. 24 is a schematic diagram of a house in which the series double dynamic vibration absorber according to the first embodiment of the present invention is installed. FIG. 25 is an enlarged view of FIG. 24 and is a schematic view illustrating a serial double dynamic vibration absorber. As shown in FIG. 24, the series double dynamic vibration absorber 1 according to the present embodiment is installed near the attic of the main house 40. The in-line double dynamic vibration absorber 1 includes a first dynamic vibration absorber 2 installed on an installation surface 40a of an attic, and a second dynamic vibration absorber 3 mounted thereon.
[0121]
As shown in FIG. 25, the first dynamic vibration absorber 2 is provided between the additional mass body 21 and the installation surface 40 a and the additional mass body 21 and supports the additional mass body 21 so as to be capable of vibrating in the vertical direction. Spring element (elastic body) 22. As the spring element 22, for example, a coil spring is used.
[0122]
The second dynamic vibration absorber 3 is arranged between the additional mass body 21 and the additional mass body 31 disposed above the additional mass body 21 and can vibrate the additional mass body 31 in the vertical direction. And a plurality of spring elements (elastic bodies) 32 and a damping element 33 that are supported by the spring. As the spring element 32, for example, a coil spring is used. As the damping element 33, one having an appropriate damping coefficient as a damper is used.
[0123]
In the present embodiment, the masses of the additional mass bodies 21 and 31, the spring constants of the spring elements 22 and 32, and the damping coefficient of the damping element 33 are optimized so as to minimize the maximum value of the compliance or acceleration of the house. (That is, the vertical natural frequency of the additional mass body 21 as a single system is higher than the vertical natural frequency of the house 40, and the vertical natural frequency of the additional mass body 31 as a single system is (A value lower than the vertical natural frequency of the house 40). Further, it is preferable to use a spring element 22 having a damping coefficient as small as possible and close to zero. Further, it is preferable that the mass of the additional mass body 21 is larger than that of the additional mass body 31 and the mass ratio between the two is changed according to the total mass ratio. By doing so, the vertical vibration of the house 40 is sufficiently suppressed.
[0124]
<Second embodiment>
FIG. 26 is a schematic diagram of a series double dynamic vibration absorber according to the second embodiment of the present invention. The dynamic vibration absorber 61 illustrated in FIG. 26 includes a first dynamic vibration absorber 70 installed on the installation surface 90a of the structure to be damped, and a second dynamic vibration absorber 80 mounted thereon. ing.
[0125]
As shown in FIG. 26, the first dynamic vibration absorber 70 is provided between the additional mass body 71 and the installation surface 90 a and the additional mass body 71 and supports the additional mass body 71 so as to be capable of vibrating in the horizontal direction. (Elastic body) 72. As the spring element 72, for example, a laminated rubber in which a synthetic rubber and a thin metal layer are laminated is used.
[0126]
The second dynamic vibration absorber 80 includes an additional mass body 81 disposed above the additional mass body 71, two columns 84 projecting upward from the upper surface of the additional mass body 71, 84 and a plurality of spring elements (elastic bodies) 82 and a damping element 83 that support the additional mass body 81 so as to be able to vibrate in the horizontal direction. As the spring element 82, for example, a coil spring is used. As the damping element 83, one having an appropriate damping coefficient as a damper is used. In addition, wheels 81a are attached to the lower surface of the additional mass body 81 so as not to hinder the horizontal vibration of the additional mass body 81.
[0127]
In the present embodiment, the masses of the additional mass bodies 71 and 81, the spring constants of the spring elements 72 and 82, and the damping coefficient of the damping element 83 are set so as to minimize the maximum value of the compliance or the acceleration of the damping target structure. (That is, the horizontal natural frequency of the additional mass body 71 as a single system is higher than the horizontal natural frequency of the structure to be damped, and the additional mass body 81 The natural frequency of the system is lower than the horizontal natural frequency of the structure to be damped. Further, it is preferable to use a spring element 72 having a damping coefficient as small as possible and close to zero. Further, it is preferable that the mass of the additional mass body 71 be larger than that of the additional mass body 81 and the mass ratio between the two be changed in accordance with the total mass ratio. By doing so, the horizontal vibration of the structure to be damped is sufficiently suppressed.
[0128]
<Third embodiment>
FIG. 27 is a schematic perspective view of a series double dynamic vibration absorber according to the third embodiment of the present invention. The dynamic vibration absorber 101 illustrated in FIG. 27 includes a first dynamic vibration absorber 120 installed on the installation surface 190a of the structure to be damped and four second dynamic vibration absorbers 130 mounted thereon. It is configured.
[0129]
As shown in FIG. 27, the first dynamic vibration absorber 120 is disposed between the additional mass body 121 and the installation surface 190a and the additional mass body 121, and moves the additional mass body 121 in two horizontal directions (x direction, y direction). ), Four spring elements (elastic bodies) 122 for supporting the vibration, a spring element 123 for adjusting the spring constant in the x direction, and a spring element 124 for adjusting the spring constant in the y direction. As the spring element 122, for example, a laminated rubber in which a synthetic rubber and a thin metal layer are laminated is used. As the spring elements 123 and 124, for example, leaf springs are used.
[0130]
Two of the four second dynamic vibration absorbers 130 can vibrate in the x direction, and the other two can vibrate in the y direction. Each of the second dynamic vibration absorbers 130 includes an additional mass body 131 disposed above the additional mass body 121 and two protruding upwards on both sides of each of the additional mass bodies 131 from the upper surface of the additional mass body 121. And a plurality of spring elements (elastic bodies) 132 and damping elements 133 disposed between the additional mass body 131 and the support pillar 134 and supporting the additional mass body 131 so as to be able to vibrate in the x direction or the y direction. Contains. As the spring element 132, for example, a coil spring is used. As the damping element 133, one having an appropriate damping coefficient as a damper is used. Further, wheels 131a are attached to the lower surface of the additional mass body 131 so that the horizontal vibration of the additional mass body 131 is not hindered.
[0131]
In the present embodiment, the masses of the additional mass bodies 121 and 131, the spring constants of the spring elements 122 and 132, and the damping coefficient of the damping element 133 are set such that the maximum value of the compliance or the acceleration of the structure to be damped is minimized. (I.e., the natural frequency in the x and y directions of the additional mass body 121 as a single system is higher than the natural frequency in the x and y directions of the structure to be damped. 131 is a value such that the natural frequency as a single system in the x direction and the y direction is lower than the natural frequency in the x direction and the y direction of the structure to be damped. Further, it is preferable to use a spring element 122 having a damping coefficient as small as possible and close to zero. In addition, it is preferable that the mass of the additional mass body 121 is larger than the sum of the four additional mass bodies 131, and that the mass ratio of both is changed according to the total mass ratio. In this way, the vibrations in the two horizontal directions of the structure to be damped are sufficiently suppressed.
[0132]
<Fourth embodiment>
FIG. 28 is a schematic diagram of a series double dynamic vibration absorber according to a fourth embodiment of the present invention. The dynamic vibration absorber 201 illustrated in FIG. 28 includes a first dynamic vibration absorber 210 installed on the installation surface 240a of the structure to be damped, and a second dynamic vibration absorber 220 mounted thereon. ing.
[0133]
As shown in FIG. 28, the first dynamic vibration absorber 210 includes an additional mass body 211 and a spring disposed between the installation surface 240 a and the additional mass body 211 to support the additional mass body 211 so as to be able to vibrate in the vertical direction. Element 212. As the spring element 212, for example, a coil spring is used.
[0134]
The second dynamic vibration absorber 220 includes an additional mass body 221 disposed above the additional mass body 211, and is disposed between the additional mass body 211 and the additional mass body 221 so that the additional mass body can vibrate in the vertical direction. The supporting spring element (elastic body) 222 and the damping element 223, and the support 224 extending horizontally from both sides of the additional mass body 221 and the installation surface 240a, respectively, are arranged to vertically move the additional mass body 221. And a plurality of spring elements 225 that are supported so as to be able to vibrate. As the spring elements 222 and 225, for example, a coil spring is used. As the damping element 223, one having an appropriate damping coefficient as a damper is used.
[0135]
In the present embodiment, the masses of the additional mass bodies 211 and 221, the spring constants of the spring elements 212, 222 and 225, and the damping coefficient of the damping element 223 minimize the maximum value of the compliance or the acceleration of the damping target structure. (That is, the vertical natural frequency of the additional mass body 211 as a single system is higher than the vertical natural frequency of the structure to be damped, and the single mass of the additional mass body 221 is (A value such that the natural frequency in the vertical direction is lower than the natural frequency in the vertical direction of the structure to be damped). It is preferable to use a spring element 212 having a damping coefficient as small as possible and close to zero. Further, it is preferable that the mass of the additional mass body 211 be larger than that of the additional mass body 221 and that the mass ratio between the two be changed in accordance with the total mass ratio. By doing so, the vertical vibration of the target structure is sufficiently suppressed.
[0136]
<Fifth embodiment>
FIG. 29 is a schematic diagram of a series double dynamic vibration absorber according to a fifth embodiment of the present invention. The dynamic vibration absorber 250 illustrated in FIG. 29 includes a first dynamic vibration absorber 260 installed on the installation surface 290a of the structure to be damped, and a second dynamic vibration absorber 270 mounted thereon. ing.
[0137]
As shown in FIG. 29, the first dynamic vibration absorber 260 includes an additional mass body 261, and a spring disposed between the installation surface 290 a and the additional mass body 261 to support the additional mass body 261 so as to be able to vibrate vertically. Element 262. As the spring element 262, for example, a coil spring is used.
[0138]
The second dynamic vibration absorber 270 is disposed between the additional mass body 271 and the additional mass body 271 and is disposed between the additional mass body 261 and the additional mass body 271 so as to vibrate the additional mass body 271 in the vertical direction. (Elastic body) 272, which is supported between the support 275 and the support 275 extending horizontally from both sides of the additional mass 271 and the installation surface 290a so that the additional mass 271 can vibrate in the vertical direction. A supporting spring element 273 and a damping element 274. As the spring elements 272 and 273, for example, a coil spring is used. As the damping element 274, one having an appropriate damping coefficient as a damper is used.
[0139]
In the present embodiment, the masses of the additional mass bodies 261 and 271, the spring constants of the spring elements 262, 272 and 273, and the damping coefficient of the damping element 274 minimize the maximum value of the compliance or the acceleration of the damping target structure. (Ie, the vertical natural frequency of the additional mass body 261 as a single system is higher than the vertical natural frequency of the structure to be damped, and (A value such that the natural frequency in the vertical direction is lower than the natural frequency in the vertical direction of the structure to be damped). Further, it is preferable to use a spring element 262 having a damping coefficient as small as possible and close to zero. In addition, it is preferable that the mass of the additional mass body 261 be larger than that of the additional mass body 271 and the mass ratio between the two be changed according to the total mass ratio. By doing so, the vertical vibration of the target structure is sufficiently suppressed.
[0140]
<Sixth Embodiment>
FIG. 30 is a schematic diagram of a series double dynamic vibration absorber according to a sixth embodiment of the present invention. The dynamic vibration absorber 301 illustrated in FIG. 30 includes a first dynamic vibration absorber 310 installed on the installation surface 340a of the structure to be damped, and a second dynamic vibration absorber 320 mounted thereon. ing.
[0141]
As shown in FIG. 30, the first dynamic vibration absorber 310 includes an additional mass body 311, and a spring disposed between the installation surface 340 a and the additional mass body 311 to support the additional mass body 311 so as to be able to vibrate vertically. Element 312. As the spring element 312, for example, a coil spring is used.
[0142]
The second dynamic vibration absorber 320 is disposed between the additional mass body 321 and the additional mass body 321 above the additional mass body 311, and is capable of vertically vibrating the additional mass body 321. (A resilient body) 322 and a damping element 323 that are supported by the support member 324, and a support 324 that extends horizontally from both sides of the additional mass body 321 and an installation surface 340a. A spring element 325 and a damping element 326 for supporting the vibration element 325 in a vibrating manner. As the spring elements 322 and 325, for example, a coil spring is used. As the damping elements 323 and 326, those having an appropriate damping coefficient as dampers are used.
[0143]
In the present embodiment, the masses of the additional mass bodies 311 and 321, the spring constants of the spring elements 312, 322 and 325, and the damping coefficients of the damping elements 323 and 326 determine the maximum value of the compliance or the acceleration of the damping target structure. The value optimized to be minimized (that is, the vertical natural frequency of the additional mass body 311 as a single system is higher than the vertical natural frequency of the structure to be damped, This is a value such that the vertical natural frequency of the independent system is lower than the vertical natural frequency of the structure to be damped. Further, it is preferable to use a spring element 312 having a damping coefficient as small as possible and close to zero. Further, it is preferable that the mass of the additional mass body 311 is larger than that of the additional mass body 321 and the mass ratio between the two is changed according to the total mass ratio. By doing so, the vertical vibration of the target structure is sufficiently suppressed.
[0144]
<Seventh embodiment>
FIG. 31 is a schematic view of a series triple dynamic vibration absorber according to a seventh embodiment of the present invention. The dynamic vibration absorber 351 illustrated in FIG. 31 includes a first dynamic vibration absorber 360 installed on the installation surface 390a of the structure to be damped, and a second dynamic vibration absorber mounted on the first dynamic vibration absorber 360. It comprises a vibration absorber 370 and a third dynamic vibration absorber mounted on the second dynamic vibration absorber 370.
[0145]
As shown in FIG. 31, the first dynamic vibration absorber 360 includes an additional mass body 361, and a spring disposed between the installation surface 390 a and the additional mass body 361 to support the additional mass body 361 so as to vibrate vertically. Element 362. As the spring element 362, for example, a coil spring is used.
[0146]
The second dynamic vibration absorber 370 is disposed between the additional mass body 361 and the additional mass body 371, and is disposed between the additional mass body 361 and the additional mass body 371, and can vibrate the additional mass body 371 in the vertical direction. And a spring element (elastic body) 372 supported by the spring. As the spring element 372, for example, a coil spring is used.
[0147]
The third dynamic vibration absorber 380 is provided between the additional mass body 371 and the additional mass body 381, and can vibrate the additional mass body 381 in the vertical direction. A spring element (elastic body) 382 and a damping element 383 supported by the first and second members. As the spring element 382, for example, a coil spring is used. As the damping element 383, one having an appropriate damping coefficient as a damper is used.
[0148]
In the present embodiment, the masses of the additional mass bodies 361, 371, 381, the spring constants of the spring elements 362, 372, 382, and the damping coefficient of the damping element 383 indicate the maximum value of the compliance or the acceleration of the structure to be damped. The value optimized to be minimized (that is, the vertical natural frequency of the additional mass body 361 as a single system is higher than the vertical natural frequency of the structure to be damped, The vertical natural frequency of the additional mass body 361 as a single system is higher than the vertical natural frequency of the additional mass body 361, and the vertical natural frequency of the additional mass body 381 as a single system is vertical to the structure to be damped. (A value lower than the natural frequency). Further, it is preferable to use spring elements 362 and 372 having a damping coefficient as small as possible and close to zero. Further, it is preferable that the mass of the additional mass body 361 is made larger than that of the additional mass bodies 371 and 381, and the mass ratio of the three is changed according to the total mass ratio. By doing so, the vertical vibration of the target structure is sufficiently suppressed.
[0149]
<Eighth Embodiment>
FIG. 32 is a schematic diagram of a house in which the combined dynamic vibration absorber according to the eighth embodiment of the present invention is installed. 33 is an enlarged view of FIG. 32, in which (a) is a front view of the combined dynamic vibration absorber, and (b) is a side view of the combined dynamic vibration absorber. As shown in FIG. 32, a house 400 is provided with a ceiling 399 and a floor 398 on each floor. A vertical beam 397 is arranged between the ceiling 399 and the floor 398 and connects them. The composite dynamic vibration absorber 401 according to the present embodiment is installed on the beam 397. As shown in FIGS. 33A and 33B, the composite dynamic vibration absorber 401 includes two sets of first dynamic vibration absorbers 410 and 420 fixed to a fixing portion 396 provided at a center position of the beam 397. And four second dynamic vibration absorbers 430 mounted thereon.
[0150]
As shown in FIG. 33A, the two sets of first dynamic vibration absorbers 410 and 420 are fixed at both end surfaces 396a of the fixing portion 396 and are arranged so as to be symmetrical with each other. Body) 412, 422 and four additional mass bodies 411, 421 provided at both ends of the spring elements 412, 422, respectively. That is, as shown in FIG. 33 (b), two additional mass bodies 421 are disposed at both ends of one spring element 422, respectively, and constitute one set of the first dynamic vibration absorber 420. Further, two additional mass bodies 411 are also arranged at both ends of the other spring element 412, respectively, and constitute one set of the first dynamic vibration absorber 410. By fixing the two spring elements 412 and 422 in parallel with the fixing portion 396, the first dynamic vibration absorbers 410 and 420 are arranged in parallel. Further, the four additional mass bodies 411 and 421 are fixed so as to sandwich the ends of the spring elements 412 and 422 at the corresponding positions. Further, the two spring elements 412 and 422 support the respective additional mass bodies 411 and 421 so as to be able to vibrate in the vertical direction. As the spring elements 412 and 422, for example, a leaf spring is used.
[0151]
The four second dynamic vibration absorbers 430 are disposed between the additional mass bodies 431 and 421, respectively, and between the additional mass bodies 411 and 421 and the additional mass bodies 431. It includes a plurality of spring elements (elastic bodies) 432 and damping elements 433 that support each additional mass body 431 so as to be capable of vibrating in the vertical direction. As the plurality of spring elements 432, for example, a coil spring is used. As the plurality of damping elements 433, those having an appropriate damping coefficient as a damper are used.
[0152]
In the present embodiment, the masses of the additional mass bodies 411, 421, 431, the spring constants of the spring elements 412, 422, 432, and the damping coefficient of the damping element 433 minimize the maximum value of the compliance or acceleration of the house 400. The value optimized as described above (that is, the vertical natural frequency of the additional mass body 411 as a single system is higher than the vertical natural frequency of the house 400, and the vertical Is lower than the vertical natural frequency of the house 400, and the vertical natural frequency of the additional mass body 431 as a single system is lower than the vertical natural frequency of the house 400. ). Further, it is preferable to use spring elements 412 and 422 having a damping coefficient as small as possible and close to zero. Further, it is preferable that the mass of each of the four additional mass bodies 411 and 421 be larger than the mass of each of the four additional mass bodies 431, and that the mass ratio of the two be changed in accordance with the total mass ratio. By doing so, the vertical vibration of the house 400 is sufficiently suppressed.
[0153]
<Ninth embodiment>
FIGS. 34A and 34B are schematic diagrams of a combined dynamic vibration absorber according to a ninth embodiment of the present invention, where FIG. 34A is a front view and FIG. 34B is a side view. The composite type dynamic vibration absorber 451 depicted in FIG. 34A is disposed between the ceiling 449 and the floor 448 of the structure to be damped in the same manner as described above, and is installed at the center of the beam 447 connected to them. ing. The composite dynamic vibration absorber 451 includes two sets of first dynamic vibration absorbers 460 and 470 fixed to a fixing portion 446 provided at the center position of the beam 447 as shown in FIGS. And four second dynamic vibration absorbers 480 mounted thereon.
[0154]
As shown in FIG. 34A, the two sets of first dynamic vibration absorbers 460 and 470 are fixed at both end surfaces 446a of the fixing portion 446 and are arranged so as to be symmetrical with each other. Body) 462, 472, and four additional mass bodies 461, 471 provided at both ends of the spring elements 462, 472, respectively. That is, as shown in FIG. 34B, two additional mass bodies 471 are arranged at both ends of one spring element 472, respectively, and constitute one set of the first dynamic vibration absorber 470. Further, two additional mass bodies 461 are also arranged at both ends of the other spring element 462, respectively, and constitute one set of the first dynamic vibration absorber 460. Then, by fixing the two spring elements 462 and 472 in parallel with the fixing portion 446, the first dynamic vibration absorbers 460 and 470 are arranged in parallel. The four additional mass bodies 461 and 471 are fixed so as to sandwich the ends of the spring elements 462 and 472 at the corresponding positions. The two spring elements 462, 472 support the respective additional mass bodies 461, 471 so as to be able to vibrate in the vertical direction. As the spring elements 462 and 472, for example, leaf springs are used.
[0155]
The four second dynamic vibration absorbers 480 include an additional mass body 481 disposed above each of the additional mass bodies 461 and 471, and a single one that protrudes upward from the upper surface of each of the additional mass bodies 461 and 471. A support 484, and a plurality of spring elements (elastic bodies) 482 arranged to be connected from the center of the support 484 to the lower surface of the additional mass 481 and supporting the additional mass 481 in a vertically oscillating manner, and It includes a spring element 482 connected to the lower surface of the mass body 481 and a damping element 483 disposed between the additional mass bodies 461 and 471. As the spring element 482, for example, a leaf spring is used. As the damping element 483, an elastomer (viscoelastic body) having an appropriate damping coefficient is used as a damper.
[0156]
In the present embodiment, the masses of the additional mass bodies 461, 471, 481, the spring constants of the spring elements 462, 472, 482, and the damping coefficient of the damping element 483 determine the maximum value of the compliance or the acceleration of the damping target structure. The value optimized so as to be minimized (that is, the vertical natural frequency of the additional mass body 461 as a single system is higher than the vertical natural frequency of the structure to be damped, The vertical natural frequency as a single system is lower than the vertical natural frequency of the structure to be damped, and the vertical natural frequency of the additional mass body 481 as a single system is vertical to the structure to be damped. Value lower than the natural frequency in the direction). Also, it is preferable to use spring elements 462 and 472 having a damping coefficient as small as possible and close to zero. In addition, it is preferable that the mass of each of the four additional mass bodies 461 and 471 is larger than the mass of each of the four additional mass bodies 481, and that the mass ratio of both is changed according to the total mass ratio. By doing so, the vertical vibration of the target structure is sufficiently suppressed.
[0157]
<Other embodiments>
As described above, the preferred embodiments of the present invention have been described. However, the applicable range of the present invention is wide, and various embodiments can be assumed. Therefore, the present invention is not limited to the above-described embodiment, and various design changes can be made within the scope of the claims. Basically, as in the first or second embodiment described above, the one in which one second dynamic vibration absorber is mounted on the first dynamic vibration absorber is a prototype, but the third embodiment is similar to the first or second embodiment. The second dynamic vibration absorber may be divided and installed in a plurality of units as in the embodiment. Of course, as in the fourth to sixth embodiments, the spring element and the damping element connected to the second dynamic vibration absorber may be connected to the structure to be damped. Further, between the first dynamic vibration absorber and the second dynamic vibration absorber of the third embodiment, a dynamic vibration absorber similar to the first dynamic vibration absorber can be arranged to form a series triple dynamic vibration absorber. It is.
[0158]
Further, a configuration in which a fourth dynamic vibration absorber is further mounted on the third dynamic vibration absorber of the seventh embodiment can be implemented. Further, as in the eighth or ninth embodiment, not only the configuration in which the series double dynamic vibration absorbers are arranged in parallel on one vibration suppression target structure, but also the series triple dynamic vibration absorbers The present invention can also be implemented with a configuration in which the components are arranged in parallel with a structure. Further, the range of the total mass ratio is not limited to the range of 0.02 to 0.2, and the present invention can be applied outside this range.
[0159]
【The invention's effect】
As described above, according to the present invention, it is possible to obtain a series and parallel dynamic vibration absorber in which the parameter setting is relatively simple and the vibration suppression effect of the structure to be damped is large.
[Brief description of the drawings]
FIG. 1 is a schematic view of a dynamic vibration absorber according to the present invention when there are two additional mass bodies.
FIG. 2 is a graph for explaining characteristics of parameters relating to the dynamic vibration absorber of the present invention.
FIG. 3 is a graph illustrating an example of a compliance curve of a main system in the dynamic vibration absorber of the present invention.
FIG. 4 is a graph illustrating an example of a compliance curve of a main system in a dynamic vibration absorber according to a comparative example of the present invention.
FIG. 5 is a graph illustrating an example of a main system compliance curve in a dynamic vibration absorber according to another comparative example of the present invention.
FIG. 6 is a graph illustrating the impulse response characteristics of the dynamic vibration absorber according to the present invention and the prior art.
FIG. 7 illustrates a compliance curve of the main system before and after adjustment when only the parameters related to the second dynamic vibration absorber are adjusted without changing the parameters related to the first dynamic vibration absorber when the natural frequency of the main system changes. FIG.
FIG. 8 is a graph illustrating an example of a compliance curve in a case where the dynamic vibration absorber according to the present invention, which is optimized on the condition that the damping of the main system is zero with respect to the main system having the damping, is used.
FIG. 9 is a graph for explaining characteristics of parameters relating to the dynamic vibration absorber according to the present invention when compliance is optimized under a condition in which damping exists in the main system, wherein (a) is a first additional mass body; FIG. 7B is an example of a change curve of each mass ratio of the first and second additional mass bodies, and FIG. 7B is an example of a change curve of a ratio of each natural frequency of the first additional mass body and the second additional mass body. (C) is an example of a change curve of the attenuation ratio of the second additional mass body.
FIG. 10 is a graph illustrating an example of a compliance curve of a main system in the dynamic vibration absorber of the present invention.
FIG. 11 is a graph for explaining characteristics of parameters relating to the dynamic vibration absorber according to the present invention when acceleration is optimized under a condition in which damping exists in the main system, and (a) is a first additional mass; It is an example of the change curve of each mass ratio of a body and a 2nd additional mass body, (b) is an example of the change curve of the ratio of each natural frequency of a 1st additional mass body and a 2nd additional mass body. (C) is an example of a change curve of the attenuation ratio of the second additional mass body.
FIG. 12 is a graph illustrating an example of an acceleration curve of a main system in the dynamic vibration absorber of the present invention.
13A and 13B are graphs for explaining characteristics of parameters relating to the dynamic vibration absorber of the present invention when mobility is optimized under the condition where damping exists in the main system, and FIG. 13A is a first additional mass body. FIG. 7B is an example of a change curve of each mass ratio of the first and second additional mass bodies, and FIG. 7B is an example of a change curve of a ratio of each natural frequency of the first additional mass body and the second additional mass body. (C) is an example of a change curve of the attenuation ratio of the second additional mass body.
FIG. 14 is a graph illustrating an example of a mobility curve of a main system in the dynamic vibration absorber of the present invention.
FIG. 15 is a graph showing a change range of a damping ratio of a second additional mass body in the dynamic vibration absorber of the present invention in the main system compliance optimization, acceleration optimization, and mobility optimization.
FIG. 16 is a schematic view of a dynamic vibration absorber according to the present invention when there are three additional mass bodies.
FIG. 17 is a graph for explaining characteristics of parameters relating to the dynamic vibration absorber of the present invention in the main system compliance optimization.
FIG. 18 is a graph illustrating an example of a compliance curve of a main system in the single dynamic vibration absorber, the parallel double dynamic vibration absorber, and the series double dynamic vibration absorber and the series triple dynamic vibration absorber of the present invention.
FIG. 19 is a graph for explaining characteristics of parameters related to the dynamic vibration absorber of the present invention in optimizing the main system acceleration.
FIG. 20 is a graph illustrating an example of an acceleration curve of a main system in the single dynamic vibration absorber, the parallel double dynamic vibration absorber, and the series double dynamic vibration absorber and the series triple dynamic vibration absorber of the present invention.
FIG. 21 is a schematic view of a parallel dynamic vibration absorber according to the present invention in which two dynamic vibration absorbers in which two additional mass bodies are arranged in series are arranged in parallel.
FIG. 22 is a graph for explaining characteristics of parameters relating to the parallel dynamic vibration absorber of the present invention.
FIG. 23 is a graph illustrating a compliance curve of a main system in the single dynamic vibration absorber, the parallel double dynamic vibration absorber, and the series double dynamic vibration absorber and the parallel dynamic vibration absorber of the present invention.
FIG. 24 is a schematic diagram of a house in which the series double dynamic vibration absorber according to the first embodiment of the present invention is installed.
FIG. 25 is an enlarged view of FIG. 24, and is a schematic view illustrating a series double dynamic vibration absorber according to the first embodiment of the present invention.
FIG. 26 is a schematic diagram of a series double dynamic vibration absorber according to a second embodiment of the present invention.
FIG. 27 is a schematic perspective view of a serial double dynamic vibration absorber according to a third embodiment of the present invention.
FIG. 28 is a schematic view of a series double dynamic vibration absorber according to a fourth embodiment of the present invention.
FIG. 29 is a schematic diagram of a series double dynamic vibration absorber according to a fifth embodiment of the present invention.
FIG. 30 is a schematic view of a series double dynamic vibration absorber according to a sixth embodiment of the present invention.
FIG. 31 is a schematic view of a series triple vibration damper according to a seventh embodiment of the present invention.
FIG. 32 is a schematic diagram of a house provided with a combined dynamic vibration absorber according to an eighth embodiment of the present invention.
33 is an enlarged view of FIG. 32, (a) is a front view of the combined dynamic vibration absorber, and (b) is a side view of the combined dynamic vibration absorber.
34A and 34B are schematic views of a combined dynamic vibration absorber according to a ninth embodiment of the present invention, wherein FIG. 34A is a front view and FIG. 34B is a side view.
[Explanation of symbols]
1 series double dynamic vibration absorber
2 first dynamic vibration absorber
3 Second dynamic vibration absorber
21 Additional mass body (first additional mass body)
22 Spring element
31 additional mass body (second additional mass body)
32 spring element
33 damping element

Claims (9)

A first additional mass body connected to the damping target structure via the elastic body;
A second additional mass body connected to the first additional mass body via another elastic body,
The natural frequency of the first additional mass body as a single system is set to a higher natural frequency than the natural frequency of the target structure, and the natural frequency of the second additional mass body as a single system is set. A dynamic vibration absorber having a frequency set to a natural frequency lower than a natural frequency of the structure to be damped. The damping ratio of the second additional mass body is set so that at least one of compliance, acceleration, and mobility of vibration of the structure to be damped is optimized. The dynamic vibration absorber according to the above. When the damping ratio of the second additional mass body is indicated by ^{ζ2 = a × u b -c,} a> 0.80, b> 0.32, and characterized in that it is a c <0.08 The dynamic vibration absorber according to claim 2.
(However, u is a ratio (total mass ratio) of the mass of the first and second additional mass bodies to the mass of the structure to be damped). The first and second additional mass bodies are each capable of natural vibration in the same two or more different directions as the structure to be damped,
The two or more natural frequencies of the first additional mass body as a single system are each set to a higher natural frequency than the corresponding natural frequency of the vibration damping target structure, and the second additional mass 4. The natural frequency according to claim 1, wherein the two or more natural frequencies of the body as a single system are respectively set to lower natural frequencies than a corresponding natural frequency of the structure to be damped. The dynamic vibration absorber according to claim 1 or 2. A first additional mass body connected to the damping target structure via the elastic body;
A second additional mass connected to the first additional mass via another elastic body;
And a third additional mass body connected to the second additional mass body via another elastic body.
The natural frequency of the first additional mass body as a single system is set to a higher natural frequency than the natural frequency of the target structure, and the natural vibration of the second additional mass body as a single system. The number is set to a higher natural frequency than the natural frequency of the first additional mass body as a single system, and the natural frequency of the third additional mass body as a single system is the vibration-damping target structure. A dynamic vibration absorber is set to a lower natural frequency than the natural frequency of the dynamic vibration absorber. The first to third additional mass bodies are each capable of natural vibration in the same two or more different directions as the vibration suppression target structure,
The two or more natural frequencies of the first additional mass body as a single system are each set to a higher natural frequency than the corresponding natural frequency of the vibration damping target structure, and the second additional mass body The two or more natural frequencies of the third additional mass body are respectively set to be higher than the corresponding natural frequencies of the first additional mass body as a single system. The dynamic vibration absorber according to claim 5, wherein the two or more natural frequencies as a single system are respectively set to lower natural frequencies than corresponding natural frequencies of the structure to be damped. . The dynamic vibration absorber according to any one of claims 1 to 6, wherein substantially no damping action is applied between the structure to be damped and the first additional mass body. The dynamic vibration absorber according to any one of claims 1 to 7, wherein a mass of the first additional mass body is larger than a mass of the second additional mass body. It is provided with two dynamic vibration absorbers according to any one of claims 1 to 8,
The natural frequency of one dynamic vibration absorber as a single system of the first additional mass body is set to a natural frequency lower than the natural frequency of the structure to be damped, and the other dynamic vibration absorber A parallel dynamic vibration absorber characterized in that a natural frequency of the first additional mass body as a single system is set to a higher natural frequency than a natural frequency of the structure to be damped.

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