JP4148793B2 - Dynamic vibration absorber - Google Patents

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（＝Ｆ₀ｓｉｎωｔ）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（＝Ｆ₀ｓｉｎωｔ）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]
BACKGROUND OF THE INVENTION
The present invention relates to a dynamic vibration absorber used for suppressing vibration of a structure to be controlled.
[0002]
[Prior art]
A dynamic vibration absorber has an additional mass added to a structure to be controlled as a main system, and is used to suppress vibrations of many structures such as buildings, bridges, machines, vehicles, and ships. It is used. In general, a dynamic vibration absorber is obtained by adding an additional mass body, a spring, and a damper as an additional system to a structure to be controlled 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 controlled as a main system. As another dynamic vibration absorber, Non-Patent Document 2 describes a series dynamic vibration absorber. In this series dynamic vibration absorber, two additional systems are installed in series on a structure to be controlled as a main system. According to these multiple dynamic vibration absorbers, it is possible to increase the vibration suppression effect of the structure to be controlled that is the main system, compared to the case where there is only one additional system.
[0004]
[Non-Patent Document 1]
Shinji Kamiya, 3 others, “Optimum Design Method for Multiple Dynamic Absorbers”, Transactions of the Japan Society of Mechanical Engineers (C), September 1996, Vol. 62, No. 601
[Non-Patent Document 2]
Satoshi Fujita, 5 others, "Study on mass damper for building vibration control with secondary mass", Transactions of the Japan Society of Mechanical Engineers (C), July 1995, Vol. 61, No. 587
[0005]
[Problems to be solved by the invention]
However, the parallel multiple dynamic vibration absorber described in Non-Patent Document 1 is very complicated to set additional parameters such as mass and spring constant, and is difficult to use in practice. Further, the series dynamic vibration absorber described in Non-Patent Document 2 has not been studied in detail for the parameters of the additional system, and cannot sufficiently suppress the vibration of the structure to be controlled.
[0006]
Therefore, an object of the present invention is to provide a dynamic vibration absorber that has a relatively simple parameter setting and has a large vibration suppressing effect on the structure to be controlled.
[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 controlled via an elastic body and a second additional mass body connected to the first additional mass body via another elastic body. Additional mass bodies. 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 controlled, and the single system of the second additional mass body The natural frequency is set to a natural frequency lower than the natural frequency of the structure to be controlled (claim 1).
[0008]
In other words, the natural frequency of the structure to be controlled 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 f_m2When
f_m1> F_MAnd f_m2<F_M
Is set to be Such a setting can be realized relatively easily by adjusting the masses and the spring constants of the first and second additional mass bodies, and as can be seen from the examples described later, the vibration compliance (function of displacement response to the input: compliance), acceleration (function of acceleration response to input: acceleration) or mobility (function of velocity response to input: mobility) can be sufficiently reduced, and the vibration suppressing effect of the structure to be controlled is great.
[0009]
Note that the direction of vibration may be any axial direction of XYZ, or may be a rotational direction around any axis.
[0010]
In the dynamic vibration absorber of the present invention, the damping ratio of the second additional mass body is set so that at least one of vibration compliance, acceleration, and mobility of the structure to be controlled is optimized. (Claim 2). According to this, at least one of vibration compliance, acceleration, and mobility of the vibration suppression target structure can be sufficiently reduced, and the vibration suppression effect of the vibration suppression target structure can be obtained.
[0011]
In the dynamic vibration absorber of the present invention, the damping ratio of the second additional mass body is ζ2 = a × u^bWhen represented by -c, it is preferable that a> 0.80, b> 0.32, and c <0.08 (claim 3). In addition, u is a ratio (total mass ratio) of the mass which added the 1st and 2nd additional mass body with respect to the mass of the structure for damping | damping.
[0012]
According to this, since the approximate expression of the damping ratio ζ2 of the second additional mass body according to the damping of the structure to be controlled is shown, the optimum damping ratio ζ2 can be calculated and selected. As a result, an optimum 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 capable of natural vibration in the same two or more different directions as the structure to be damped, respectively, and the first additional mass body as a single system The natural frequency of 2 or more is set to a natural frequency higher than the corresponding natural frequency of the structure to be controlled, and the natural frequency of 2 or more as a single system of the second additional mass body May be set to a natural frequency lower than the corresponding natural frequency of the structure to be damped (Claim 4). In this case, the same vibration damping effect as described above for each direction can be obtained.
[0014]
The direction of vibration may be two or more axial directions of XYZ, may be rotational directions around two or more axes, and the vibration in the axial direction and the vibration in the rotational direction around the axis may be It may be combined.
[0015]
In another aspect, the dynamic vibration absorber of the present invention is connected to the first additional mass body connected to the structure to be controlled via an elastic body and the first additional mass body via another elastic body. A second additional mass body connected thereto, and a third additional mass body connected to the second additional mass body via another elastic 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 structure to be controlled, and the second additional mass body as a single system. The natural frequency is set to be higher 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 suppression target. The natural frequency is set 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, and may be three. At this time, the natural frequency of the structure to be controlled is expressed as 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 f_m2, The natural frequency of the third additional mass body as a single system f_m3, And
f_m1> F_M, F_m1<F_m2And f_m3<F_M
Is set to be Such setting is relatively simple, and the vibration suppression effect of the structure to be controlled is greater when the number of additional mass bodies is three than when the number is two.
[0017]
In the present invention, the first to third additional mass bodies are capable of natural vibration in the same two or more different directions as the structure to be damped, and the first additional mass body as a single system. Two or more natural frequencies are set to higher natural frequencies than the corresponding natural frequencies of the structure to be controlled, and the two or more natural frequencies as a single system of the second additional mass body are The natural frequency is set higher than the corresponding natural frequency of the first additional mass body as a single system, and the two or more natural frequencies as the single system of the third additional mass body are The natural frequency may be set to be lower than the corresponding natural frequency of the structure to be controlled (claim 6). In this case, the same vibration damping effect as described above for each direction can be obtained.
[0018]
As in the case of the two additional mass bodies described above, the direction of vibration may be two or more axial directions of XYZ, may be a rotational direction around two or more axes, The vibration in the direction and the vibration in the rotational direction around the axis may be combined.
[0019]
In the dynamic vibration absorber of the present invention, it is preferable that a damping action does not substantially act between the structure to be damped and the first additional mass body (Claim 7). According to this, the vibration control effect is further increased.
[0020]
Moreover, in this invention, it is preferable that the mass of the 1st addition mass body is larger than the mass of the 2nd addition mass body (Claim 8). According to this, the vibration control effect is further increased and adjustment is facilitated.
[0021]
In another aspect, the dynamic vibration absorber of the present invention is a parallel dynamic vibration absorber having two of the above-described dynamic vibration absorbers, as a single system of the first additional mass body of one dynamic vibration absorber. Is set to a natural frequency lower than the natural frequency of the structure to be controlled, and the natural frequency of the other dynamic vibration absorber as the single system of the first additional mass body is the above-mentioned natural frequency. The natural frequency is set to be higher than the natural frequency of the structure to be oscillated (claim 9).
[0022]
That is, the parallel dynamic vibration absorber which connected in parallel the dynamic vibration absorber to which the additional mass bodies as mentioned above were connected in series may be sufficient. At this time, the natural frequency of the structure to be controlled is expressed as f_M, The natural frequency of one of the first additional mass bodies as a single system is f_m21, And the natural frequency of the other first additional mass body as a single system f_m11, And
f_m11> F_M, F_m21<F_M
Is set to be Such setting is relatively simple and increases the vibration suppression effect of the structure to be controlled.
[0023]
<Optimum design: Series double dynamic vibration absorber>
FIG. 1 shows a schematic diagram of a dynamic vibration absorber when there are two additional mass bodies according to the present invention. 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 where it can vibrate in the vertical direction (displacement x). Further, the first additional mass body (mass m1) is supported by the structure to be controlled via a spring (spring constant k1) and a damper (damping coefficient c1) in a state where it can vibrate 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). It is supported. In other words, two dynamic vibration absorbers (the first dynamic vibration absorber on the side close to the main system and the second dynamic vibration absorber connected thereto) are connected in series in two stages to the structure to be controlled. It 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 ratios of mass m1 and m2 to mass M are u1. , U2 (u = u1 + u2).
[0025]
[Expression 1]

[0026]
The equation of motion of the vibration suppression target structure shown in FIG. 1 and the first and second additional mass bodies indicates the external force acting on the main system as f (= F₀sinωt) is expressed as the following equations (4) to (6), respectively.
[0027]
[Expression 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 with respect to the main system) is determined, two parameters, a spring constant and a damping coefficient, may be determined. In the series double dynamic vibration absorber, after determining the above total mass ratio, 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 The following five parameters must be obtained.
[0029]
As one method for optimally determining these parameters, a method is used in which a parameter that minimizes the maximum compliance value of the main structure to be damped is used. However, since such optimized parameters cannot be obtained as analytical solutions of equations (4) to (6), the total mass ratio is in the range of 0.02 to 0.2 (simply a practical range). Table 1 shows the results obtained as a numerical calculation solution. 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, instead of the spring constant and damping coefficient of each additional mass body, the natural frequency f in the vertical direction as a single system of the first and second additional mass bodies is shown._m1, F_m2And the natural frequency f in the vertical direction as a single system of the structure subject to vibration suppression_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 shown).
[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 optimal natural frequency ratio p1 is slightly larger than 1 (p1> 1), and the optimal natural frequency ratio p2 is Slightly smaller than 1 (p2 <1), the optimum damping ratio ζ1 is substantially zero. Further, 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]
Even when the optimum parameter is determined under the condition that the maximum values of acceleration and mobility are minimized, the same result can be obtained as the parameter characteristics.
[0035]
<Vibration control performance>
Dynamic vibration absorber with only one additional system (single dynamic vibration absorber), parallel dynamic vibration absorber with two additional systems (parallel double dynamic vibration absorber), parallel dynamic vibration absorber with four additional systems (parallel) The damping of the vibration control target structure is zero for each of the quadruple vibration absorber), the parallel vibration absorber having six additional systems (parallel six vibration absorber), and the series double vibration absorber shown in FIG. When the parameters are optimized so that the maximum compliance value is minimized under the condition of the above, the maximum compliance value of the structure subject to vibration suppression is calculated numerically in the range of the total mass ratio of 0.02 to 0.2 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 small value as much as or more than that of the parallel six dynamic vibration absorber. Moreover, the damping effect of the series double dynamic vibration absorber at the total mass ratio of 5% corresponds to the vibration suppression effect of the single dynamic vibration absorber at the mass ratio of 8.25%, and the series double vibration absorber at the 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 with a mass ratio of 16.5%. Thus, the series dynamic vibration damper of the present invention has an excellent vibration damping effect.
[0036]
[Table 2]

[0037]
<Comparative Example 1>
FIG. 3 shows 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 compliance is adopted. At this time, as shown in FIG. 3, the compliance curve has three maximum values corresponding to 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 change 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 and 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, in each case shown in Table 3, the compliance curves 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 The compliance curves in the case of p1 = 1 and p2> 1 are respectively drawn. As can be seen from this result, when p1> 1 and p2 <1 are not satisfied, the maximum value of compliance cannot be sufficiently reduced, and the damping effect of the series double dynamic vibration absorber is reduced. .
[0041]
<Comparative example 2>
Next, if the ratios p1, p2 vary from the optimal state and other parameters can be reoptimized accordingly (ie, p1 <1 (p1 = 0.975) and p2> 1 (p2 = 1.005), p1 <1 (p1 = 0.975) and p2 = 1, p1 = 1 and p2 = 1, p1 = 1 and p2> 1 (p2 = 1.005) Will explain how the compliance curve changes).
[0042]
As a result of the numerical calculation, other parameters are re-optimized as shown in Table 4. If p1 <1 (p1 = 0.975) and p2> 1 (p2 = 1.005), re-optimization cannot be performed, so that p1 = 0.993, p2 = 1.005, etc. The parameters were reoptimized. And about these cases, the compliance curve became like FIG. 5 (a)-(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. 5 (d) is The compliance curves in the case of p1 = 1 and p2> 1 are respectively drawn.
[0043]
As can be seen from this result, if p1> 1 and p2 <1 are not satisfied, the maximum value of the compliance can be sufficiently increased even if other parameters can be re-optimized. It cannot be made small, and the damping effect of the series double dynamic vibration absorber will be small.
[0044]
[Table 4]

[0045]
<Acceleration>
For each of the single dynamic vibration absorber, parallel double dynamic vibration absorber, parallel quadruple vibration vibration absorber, and series double dynamic vibration absorber shown in Fig. 1, the maximum acceleration is obtained under the condition that the damping of the structure to be controlled is zero. Table 5 shows the maximum value of the acceleration of the structure to be damped when the parameters are optimized so that the value is minimized. It is.
[0046]
As can be seen from Table 5, according to the series double dynamic vibration absorber shown in FIG. 1, it is possible to suppress the acceleration to a small value to the same extent or more than that of the parallel four dynamic vibration absorber. Further, when the damping effect of the series double dynamic vibration absorber and the vibration suppression effect of the single dynamic vibration absorber at the total mass ratio of 5% are compared, the resonance peak value is reduced by 20.32%.
[0047]
[Table 5]

[0048]
<Impulse response>
FIG. 6 shows impulse responses when the total mass ratio is 5% 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. 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, the vibration effect of the first cycle by the series double dynamic vibration absorber hardly shows the vibration suppression effect, but two cycles by the serial double dynamic vibration absorber. In the subsequent vibration waveforms, the vibration suppression effect is more remarkable than that of the parallel double dynamic absorber.
[0049]
Referring to FIG. 6 (b), the impulse response of the first dynamic vibration absorber of the series double dynamic vibration absorber is not significantly different from that of other dynamic vibration absorbers. It can be seen that the impulse response of the second dynamic vibration absorber is larger than that of the parallel double vibration vibration absorber. Thus, it can be said that the increase in the motion of the additional system shows 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 damping coefficient of the dynamic vibration absorber must be adjusted in order to maintain the optimum 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 attenuation ratio of the first dynamic vibration absorber is set to be extremely small, no special attenuation performance is required. However, the adjustment is easier than in the case of the parallel double dynamic vibration absorber and the parallel quadruple vibration vibration absorber. In addition, the series double dynamic vibration absorber according to the present invention 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 the optimum state, the mass of the second dynamic vibration absorber is considerably smaller than the mass of the first dynamic vibration absorber, so that it is only necessary to adjust the parameters of the second dynamic vibration absorber, which greatly reduces the actual work load.
[0051]
The point that the optimum state can be restored simply by adjusting the second dynamic vibration absorber will be described below with reference to data. Table 6 shows the results 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 from 0.90 to 1.02. . FIG. 7 shows a comparison of the compliance curves of the main system before and after adjustment.
[0052]
[Table 6]

[0053]
From Table 6 and FIG. 7, it can be seen that by increasing the mass of the second dynamic absorber as the natural frequency of the main system becomes smaller than the original frequency, good results with almost no change in the damping effect can be obtained. 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 from the original one. When 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 damping effect cannot be obtained only by adjusting the parameters related to the second dynamic vibration absorber.
[0054]
<Comparison between the case where the damping target structure has zero damping and the case where damping exists>
In the above-described series double dynamic vibration absorber, the compliance and the acceleration of the structure to be damped when the parameters are optimized under the condition that the damping of the structure to be damped is zero have been described. When attenuation exists in the target structure, the three extreme values in the compliance curve are not substantially equal as shown in FIG. In other words, if a parameter optimized under the condition that the damping target structure has zero attenuation is employed for the damping target structure having 5% damping, for example, a compliance curve as shown in FIG. The three extreme values in the curve are not equal and the optimized parameters are not optimal for the structure to be dampened where damping exists.
[0055]
<Compliance optimization>
Next, the optimization of compliance in the case where damping exists in the vibration suppression target structure will be described. It should be noted that the attenuation of a general structure subject to vibration suppression to which a series double dynamic vibration absorber is to be installed is small, and the effect of adding attenuation is high when the attenuation of the structure to be controlled is about 6% or less. Considered an area. Therefore, the parameter change range of the series double dynamic vibration absorber is calculated for compliance optimization when the damping existing in the vibration suppression target structure is changed from 0 to 6%.
[0056]
FIG. 9 shows the parameter characteristics of each mass body in compliance optimization when the damping of the structure to be controlled changes from 0 to 6%. (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 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 damping ratio of the second additional mass body. In addition, the change range of the change curve in FIG. 9 is shown in the range of 0.005-0.2 by total mass ratio.
[0057]
As shown in FIG. 9A, in each change curve, when the damping of the structure to be controlled increases, the mass ratio u1 of the first additional mass body tends to decrease, and the second additional mass body The mass ratio u2 tends to increase. Expression (9) of the change curve of the mass ratio u2 of the second additional mass body is obtained as an approximate expression from FIG. 9A, and the parameter of the mass ratio u2 of the second additional mass body is obtained from the expression (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 controlled.
[0058]
[Expression 4]

[0059]
As shown in FIG. 9B, in each change curve, when the damping of the structure to be controlled increases, the ratio p1 of the natural frequency of the first additional mass body tends to decrease, and the second addition The ratio p2 of the natural frequency of the mass body tends to be small. Similarly, equations (10) and (11) of the change curves of the first and second additional mass bodies are obtained as approximate equations from FIG. 9 (b), and the first and second equations are obtained from equations (10) and (11). The parameters of the natural frequency ratios p1 and p2 of the additional mass body 2 are obtained.
[0060]
[Equation 5]

[0061]
As shown in FIG. 9C, in each change curve, when the damping of the structure to be controlled increases, the damping ratio ζ2 of the second additional mass body increases. Note that the damping ratio ζ1 of the first additional mass body is substantially zero as described above. Similarly, the equation (12) of the change curve of the damping ratio ζ2 of the second additional mass body is obtained as an approximate expression from FIG. 9C, and the damping ratio ζ2 of the second additional mass body is obtained from the equation (12). It is done.
[0062]
[Formula 6]

[0063]
In this way, when the attenuation of the structure to be controlled changes from 0 to 6%, the change range of the parameters of the series double dynamic vibration absorber is shown in FIG. It is possible to calculate and select the optimum value of the parameters of the series double dynamic vibration absorber according to the above. For example, when the damping ratio ζ of the structure to be controlled is 5% and the total mass ratio u of the series double dynamic vibration absorber is 5%, the maximum compliance value is determined to be minimized. Table 7 shows the parameters, and FIG. 10 shows the compliance curve of the main system when the parameters are adopted. The three extreme values in the compliance curve shown in FIG. 10 are substantially equal, and the parameters of the series double dynamic vibration absorber can be said to be optimum values as compared with FIG.
[0064]
[Table 7]

[0065]
<Optimization of acceleration>
Subsequently, the parameter change range of the series double dynamic vibration absorber is calculated for the optimization of the acceleration when the attenuation existing in the structure to be controlled is changed from 0 to 6%.
[0066]
FIG. 11 shows the parameter characteristics of each mass body in the acceleration optimization when the damping of the structure to be controlled varies from 0 to 6%. FIG. 11A shows the first additional mass body. And (b) is an example of a change curve of the ratio of the natural frequencies of the first additional mass body and the second additional mass body. Yes, (c) is an example of a change curve of the damping ratio of the second additional mass body. In addition, the change range of the change curve in FIG. 11 is shown in the range of 0.005-0.2 by total mass ratio.
[0067]
As shown in FIG. 11A, in each change curve, when the damping of the structure to be damped increases, the mass ratio u1 of the first additional mass body tends to decrease, and the second additional mass body The mass ratio u2 tends to increase. Expression (13) of the change curve of the mass ratio u2 of the second additional mass body is obtained as an approximate expression from FIG. 11A, and the parameter of the mass ratio u2 of the second additional mass body is obtained from the expression (13). The mass ratio u1 of the first additional mass body can be obtained from u1 = u−u2.
[0068]
[Expression 7]

[0069]
As shown in FIG. 11B, in each change curve, when the damping of the structure to be controlled increases, the ratio p1 of the natural frequency of the first additional mass body tends to increase, and the second addition The natural frequency ratio p2 of the mass body also tends to increase. Similarly, equations (14) and (15) of the change curves of the first and second additional mass bodies are also obtained as approximate equations from FIG. 11 (b), and the first and first equations are obtained from equations (14) and (15). The parameters of the natural frequency ratios p1 and p2 of the additional mass body 2 are obtained.
[0070]
[Equation 8]

[0071]
As shown in FIG. 11 (c), in each change curve, when the damping of the structure to be controlled increases, the damping ratio ζ2 of the second additional mass body increases. Note that the damping ratio ζ1 of the first additional mass body is substantially zero as described above. Similarly, equation (16) of the change curve of the damping ratio ζ2 of the second additional mass body is obtained as an approximate expression from FIG. 11C, and the damping ratio ζ2 of the second additional mass body is obtained from equation (16). It is done.
[0072]
[Equation 9]

[0073]
In this way, when the attenuation of the structure to be controlled changes from 0 to 6%, the change range of the parameters of the series double dynamic vibration absorber is shown in FIG. It is possible to calculate and select the optimum value of the parameters of the series double dynamic vibration absorber according to the above. For example, when the damping ratio ζ of the structure to be controlled is 5% and the total mass ratio u of the series double dynamic vibration absorber is 5%, it is determined under the optimization condition of minimizing the maximum value of the acceleration. The parameters shown in Table 8 are shown in FIG. 12, and the acceleration curve of the main system when the parameters are adopted is shown in FIG. The three extreme values in the acceleration curve shown in FIG. 12 are substantially equal, and the parameters of the series double dynamic vibration absorber are optimum values.
[0074]
[Table 8]

[0075]
<Mobility optimization>
Subsequently, a parameter change range of the series double dynamic vibration absorber is calculated for mobility optimization in a case where the attenuation existing in the vibration suppression target structure is changed from 0 to 6%.
[0076]
FIG. 13 shows the parameter characteristics of each mass body in mobility optimization when the damping of the structure to be controlled changes from 0 to 6%. (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 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 damping ratio of the second additional mass body. In addition, the change range of the change curve in FIG. 13 is shown in the range of 0.005-0.2 by total mass ratio.
[0077]
As shown in FIG. 13 (a), in each change curve, when the damping of the structure to be controlled increases, the mass ratio u1 of the first additional mass body tends to decrease, and the second additional mass body The mass ratio u2 tends to increase. Expression (17) of the change curve of the mass ratio u2 of the second additional mass body is obtained as an approximate expression from FIG. 13A, and the parameter of the mass ratio u2 of the second additional mass body is obtained from Expression (17). The mass ratio u1 of the first additional mass body can be obtained from u1 = u−u2.
[0078]
[Expression 10]

[0079]
As shown in FIG. 13B, in each change curve, when the damping of the structure to be controlled increases, the ratio p1 of the natural frequency of the first additional mass body tends to increase, and the second addition The natural frequency ratio p2 of the mass body tends to decrease. Similarly, equations (18) and (19) of the change curves of the first and second additional mass bodies are obtained as approximate equations from FIG. 13 (b), and the first and first equations are obtained from equations (18) and (19). The parameters of the natural frequency ratios p1 and p2 of the additional mass body 2 are obtained.
[0080]
[Expression 11]

[0081]
As shown in FIG. 13C, in each change curve, when the damping of the structure to be controlled increases, the damping ratio ζ2 of the second additional mass body increases. Note that the damping ratio ζ1 of the first additional mass body is substantially zero as described above. Similarly, equation (20) of the change curve of the damping ratio ζ2 of the second additional mass body is obtained as an approximate expression from FIG. 13C, and the damping ratio ζ2 of the second additional mass body is obtained from equation (20). It is done.
[0082]
[Expression 12]

[0083]
In this way, when the attenuation of the structure to be controlled changes from 0 to 6%, the change range of the parameters of the series double dynamic vibration absorber is shown in FIG. It is possible to calculate and select the optimum value of the parameters of the series double dynamic vibration absorber according to the above. For example, the parameter determined under the optimization condition of minimizing the maximum value of mobility when the damping ratio ζ of the structure to be controlled is 5% and the total mass ratio u of the double dynamic vibration absorber is 5%. Is shown in Table 9, and the mobility curve of the main system when the parameters are adopted is shown in FIG. The three extreme values in the mobility curve shown in FIG. 14 are substantially equal, and the parameters of the series double dynamic vibration absorber can be said to be optimum values.
[0084]
[Table 9]

[0085]
As described above, the first additional mass body and the first mass in the three optimizations (compliance optimization, acceleration optimization, and mobility optimization) when the damping of the structure to be controlled changes from 0 to 6%. The change trends of the mass ratios u1 and u2 of the additional mass body 2 and the damping ratio ζ2 of the second additional mass body are the same, and the change width (respective changes in compliance optimization, acceleration optimization, and mobility optimization) There is no significant difference in the width 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 frequency of the first additional mass body is always larger than 1, The ratio of the natural frequency of the additional mass is always less than 1.
[0086]
FIG. 15 shows an example of a change curve of the damping ratio ζ2 of the second additional mass body in the three optimizations when the damping of the structure to be controlled changes from 0 to 6%. Within the range surrounded by the change curve, the damping ratio ζ2 of the second additional mass body by three optimizations exists. From FIG. 15, the approximate expression (21) for obtaining the damping ratio ζ2min of the second additional mass when the damping target structure is 0% is obtained, and the second equation when the damping target structure is 6% is obtained. An approximate expression (22) for obtaining the damping ratio ζ2max of the additional mass is obtained. Therefore, it is possible to obtain the damping ratio ζ2 of the second additional mass body when the damping of the structure to be controlled changes from 0 to 6%. In the present invention, the damping ratio ζ2 that can sufficiently reduce at least one of compliance, acceleration, and mobility of the main system is expressed by the above-described equations (21) and (22). It is not limited. For example, the damping ratio of the second additional mass body is ζ2 = a × u^bAs 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 0.08), it is possible to obtain the damping ratio ζ2 that can sufficiently reduce at least one of compliance, acceleration, and mobility of the main system.
[0087]
[Formula 13]

[0088]
<Optimum design: Series triple motion vibration absorber>
Next, FIG. 16 shows a schematic diagram of a dynamic vibration absorber when there are three additional mass bodies according to the present invention. In FIG. 16, the above-described series double dynamic vibration absorption is performed via the spring (spring constant k3) and the damper (damping coefficient c3) in a state where the third additional mass body (mass m3) can vibrate in the vertical direction (displacement y3). It is supported by the second additional mass body of the container, and is configured to be connected in series in three stages to the structure to be controlled. That is, this series triple dynamic vibration absorber is obtained by connecting one dynamic vibration absorber (third dynamic vibration absorber) to the above-described second dynamic vibration absorber of the series double dynamic vibration absorber. In addition, about the thing similar to the series double dynamic vibration absorber mentioned above, it shows with the same symbol and abbreviate | omits description.
[0089]
In the following description, as shown in equations (23) and (24), the total mass ratio (ratio of mass (m1 + m2 + m3) to mass M) is u, and the mass ratio of mass m1, m2, and m3 to mass M is the mass ratio. U1, u2, and u3 (u = u1 + u2 + u3), respectively.
[0090]
[Expression 14]

[0091]
The equation of motion of the structure to be controlled shown in FIG. 16 and the first, second, and third additional mass bodies is expressed as f (= F₀sinωt) is expressed as the above-described equations (4) and (5) and the following equations (25) and (26), respectively.
[0092]
[Expression 15]

[0093]
In the design of the series triple vibration absorber, after determining the total mass ratio u as described above, the internal mass ratios of the first dynamic vibration absorber, the second dynamic vibration absorber, and the third dynamic vibration absorber (u1 / u, u2 / u) Eight parameters, spring constant and damping coefficient of each dynamic vibration absorber must be obtained.
[0094]
As described above, since the parameter that minimizes the maximum compliance value of the structure to be controlled that is the main system cannot be obtained 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 obtained are the mass ratio (mass ratio ratio) u1 / u of m1 to m1 + m2 + m3 when the total mass ratio is determined, the mass ratio (mass ratio ratio) u2 / u of m2 to m1 + m2 + m3, Spring constant and damping coefficient.
[0095]
In Table 10, instead of the spring constant and damping coefficient of each additional mass body, the natural frequency f in the vertical direction as a single system of the first, second, and third additional mass bodies is shown._m1, F_m2, F_m3And the natural frequency f in the vertical direction as a single system of the structure subject to vibration suppression_MPi (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 formula (8)). Further, 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 larger (p1 <p2), the optimum natural frequency ratio p3 is slightly smaller 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. 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 and the ratio p3 decreases and the optimum damping ratio ζ3 increases as the total mass ratio increases.
[0098]
Even when the optimum parameter is determined under the condition that the maximum value of the acceleration is minimized, the same result can be obtained as described later as the parameter characteristics.
[0099]
<Vibration control performance>
Dynamic vibration absorber with only one additional system (single dynamic vibration absorber), parallel dynamic vibration absorber with two additional systems (parallel double dynamic vibration absorber), parallel dynamic vibration absorber with four additional systems (parallel) Quadruple vibration absorbers), parallel dynamic vibration absorbers with six additional systems (parallel six-motion vibration absorbers), series double-motion vibration absorbers shown in FIG. 1, and series triple-motion vibration absorbers shown in FIG. In the case where the parameter is optimized so that the maximum compliance value is minimized under the condition that the attenuation is zero, the maximum compliance value of the structure subject to vibration suppression is in the range of 0.02 to 0.2 in total mass ratio. Table 11 shows the values obtained by numerical calculation. As can be seen from Table 11, according to the series triple motion vibration absorber shown in FIG. 16, the maximum compliance can be suppressed to a smaller value than the series double motion vibration absorber. Thus, the series triple motion vibration absorber of the present invention has a more excellent vibration damping effect.
[0100]
[Table 11]

[0101]
<Comparative example>
FIG. 18 is an example (total mass ratio 5%) 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 is adopted. At this time, as shown in FIG. 18, the compliance curve has four maximum values corresponding to three degrees of freedom of the main system and the three additional systems, and these maximum values are equal. Moreover, it can be seen from FIG. 18 that the series triple dynamic vibration absorber suppresses the maximum compliance to a smaller value compared to the single dynamic vibration absorber, the parallel double dynamic vibration absorber, and the serial double dynamic vibration absorber. In FIG. 18, Frequency Ratio 1 corresponds to the natural frequency of the main system.
[0102]
<Acceleration>
Next, the parameter that minimizes the maximum value of the acceleration of the damping target structure that is the main system is also obtained as an analytical solution of the equations (4), (5), (25), and (26) in the same manner as described above. Table 12 shows the results obtained as a numerical calculation solution when the total mass ratio is in the range of 0.02 to 0.2. The parameters to be obtained are the mass ratio (mass ratio ratio) u1 / u of m1 to m1 + m2 + m3 when the total mass ratio is determined, the mass ratio (mass ratio ratio) u2 / u of m2 to m1 + m2 + m3, Spring constant and damping coefficient.
[0103]
In Table 12, instead of the spring constant and damping coefficient of each additional mass body, the natural frequency f in the vertical direction as a single system of the first, second, and third additional mass bodies is shown._m1, F_m2, F_m3And the natural frequency f in the vertical direction as a single system of the structure subject to vibration suppression_MAnd the damping ratios ζ1 to ζ3 as a single system of the first, second and third additional mass bodies are shown. Further, 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. Yes. FIG. 19B shows how the optimum ratios p1 and p2 increase and the ratio p3 decreases and the optimum damping ratio ζ3 increases as the total mass ratio increases.
[0106]
<Vibration control performance>
Dynamic vibration absorber with only one additional system (single dynamic vibration absorber), parallel dynamic vibration absorber with two additional systems (parallel double dynamic vibration absorber), parallel dynamic vibration absorber with four additional systems (parallel) Quadruple vibration absorber), series double dynamic vibration absorber shown in FIG. 1, and series triple dynamic vibration absorber shown in FIG. 16, the maximum value of acceleration under the condition that the damping of the structure to be controlled is zero Table 13 shows the maximum value of the acceleration of the structure to be damped when the parameters are optimized so as to minimize the total mass ratio in the range of 0.02 to 0.2 by numerical calculation. is there. As can be seen from Table 13, according to the series triple motion vibration absorber shown in FIG. 16, the maximum acceleration can be suppressed to a smaller value than in the series double motion vibration absorber. Thus, the series triple motion 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 a compliance curve of the main system (total mass ratio of 5%) when the parameter determined under the above-described optimization condition of minimizing the maximum value of acceleration is adopted. At this time, as shown in FIG. 20, the acceleration curve has four maximum values corresponding to 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. 20 that the series triple dynamic absorber suppresses the maximum acceleration to a smaller value compared to the single dynamic absorber, the parallel double dynamic absorber, and the series double dynamic absorber. In FIG. 20, Frequency Ratio (frequency ratio) 1 corresponds to the natural frequency of the main system.
[0109]
<Configuration of combined dynamic vibration absorber>
Next, FIG. 21 shows a schematic diagram of a parallel dynamic vibration absorber when the above-described series double dynamic vibration absorbers are arranged in parallel. In FIG. 21, 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 where it can vibrate in the vertical direction (displacement x). Further, the first additional mass body (mass m11) on the left side in FIG. 21 is supported by the structure to be damped through a spring (spring constant k11) in a state where it can vibrate in the vertical direction (displacement y11). The second additional mass body (mass m12) is capable of vibrating in the vertical direction (displacement y12) through the spring (spring constant k12) and the damper (damping coefficient coefficient c12). It is supported by. In addition, the first additional mass body (mass m21) on the right side in FIG. 21 is supported by the structure to be controlled via a spring (spring constant k21) in a state where it can vibrate in the vertical direction (displacement y21). The second additional mass body (mass m22) is oscillated in the vertical direction (displacement y22) to the first additional mass body via a spring (spring constant k22) and a damper (damping coefficient c22). It is supported. That is, two series double dynamic vibration absorbers (first serial double dynamic vibration absorber 100 and second serial double dynamic vibration absorber 200) are connected in parallel on the upper surface of the structure to be controlled. ing. In addition, although the damper connected to the structure to be controlled is provided in the first dynamic vibration absorber of the above-described series double dynamic vibration absorber, 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 controlled.
[0110]
<Compliance>
In such a composite dynamic vibration absorber, the parameter that minimizes the maximum compliance value of the main structure to be damped 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 calculation solutions in the range of .2.
[0111]
In Table 14, instead of the spring constant and damping coefficient of each additional mass body, the natural frequency f in the vertical direction as the single system of the first and second additional mass bodies of each series double dynamic vibration absorber_m11, F_m12, F_m21, F_m22And the natural frequency f in the vertical direction as a single system of the structure subject to vibration suppression_MP11, p12, p21, and p22, and damping ratios ζ12 and ζ22 as individual systems of the second additional mass bodies of the first and second series dynamic vibration absorbers.
[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 optimum natural frequency ratio p11 is slightly larger than 1 (p11> 1), and the optimum natural frequency ratio p12 is It 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. FIGS. 22 (a) and 22 (b) show the first and second series double dynamic vibration absorptions as the total mass ratio increases. It shows how the optimum mass ratio u11, u12, u21, u22 of the vessel increases. FIG. 22 (c) shows how the optimum ratio p11 of the first series double dynamic vibration absorber increases and 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 ratio p21, p22 of the second series double dynamic vibration absorber decreases and the optimum damping ratio ζ22 increases as the total mass ratio increases.
[0115]
Even when the optimum parameter is determined under the condition that the maximum value of the acceleration is minimized, the same result is obtained as the parameter characteristic.
[0116]
<Vibration control performance>
Dynamic vibration absorber with only one additional system (single dynamic vibration absorber), parallel dynamic vibration absorber with two additional systems (parallel double dynamic vibration absorber), parallel dynamic vibration absorber with four additional systems (parallel) Quadruple vibration absorbers), parallel dynamic vibration absorbers having six additional systems (parallel six dynamic vibration absorbers), series double dynamic vibration absorbers shown in FIG. 1, and composite dynamic vibration absorbers shown in FIG. In the case where the parameter is optimized so that the maximum compliance value is minimized under the condition that the damping of the structure to be damped is zero, the total mass ratio is 0.02 Table 15 shows the values obtained by numerical calculation within the range of 0.2 to 0.2. As can be seen from Table 15, according to the composite dynamic vibration absorber shown in FIG. 21, the maximum compliance can be suppressed to a smaller value than in the series double dynamic vibration absorber. Thus, the composite 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 (total mass ratio 5%) when the parameter determined under the above-described optimization condition of minimizing the maximum value of compliance is adopted. At this time, as shown in FIG. 23, the compliance curve has five maximum values corresponding to 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 composite 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 1 corresponds to the natural frequency of the main system.
[0119]
DETAILED DESCRIPTION OF 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 view of a house in which a 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 diagram depicting a series double dynamic vibration absorber. As shown in FIG. 24, the series double dynamic vibration absorber 1 according to the present embodiment is installed in the vicinity of the attic of the house 40 which is the main system. The series double dynamic vibration absorber 1 includes a first dynamic vibration absorber 2 installed on an installation surface 40a on the attic and a second dynamic vibration absorber 3 placed on the first dynamic vibration absorber 2.
[0121]
As shown in FIG. 25, the first dynamic vibration absorber 2 is disposed between the additional mass body 21 and the installation surface 40a and the additional mass body 21 and supports the additional mass body 21 so as to vibrate in the vertical direction. The spring element (elastic body) 22 is included. For example, a coil spring is used as the spring element 22.
[0122]
The second dynamic vibration absorber 3 is arranged between the additional mass body 31 disposed above the additional mass body 21 and between the additional mass body 21 and the additional mass body 31, and can vibrate the additional mass body 31 in the vertical direction. And a plurality of spring elements (elastic body) 32 and damping elements 33 supported by the actuator. As the spring element 32, for example, a coil spring is used. As the damping element 33, a damper having an appropriate damping coefficient 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 housing compliance or tolerance. (That is, the vertical natural frequency of the additional mass body 21 as a single system is higher than the natural frequency of the house 40 in the vertical direction, and the vertical natural frequency of the additional mass body 31 as a single system is The value is lower than the natural frequency in the vertical direction 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. Moreover, it is preferable to make the mass of the additional mass body 21 larger than that of the additional mass body 31 and to change the mass ratio between them according to the total mass ratio. By doing in this way, the vibration of the house 40 in the vertical direction 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 depicted in FIG. 26 includes a first dynamic vibration absorber 70 installed on the installation surface 90a of the structure to be controlled, and a second dynamic vibration absorber 80 mounted thereon. ing.
[0125]
As shown in FIG. 26, the first dynamic vibration absorber 70 is disposed between the additional mass body 71 and the installation surface 90a and the additional mass body 71, and supports the additional mass body 71 so as to vibrate in the horizontal direction. The spring element (elastic body) 72 is included. 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, and the additional mass body 81 and the column. And a plurality of spring elements (elastic bodies) 82 and damping elements 83 that are respectively disposed between them and support the additional mass body 81 so as to vibrate in the horizontal direction. As the spring element 82, for example, a coil spring is used. As the damping element 83, a damper having an appropriate damping coefficient is used. A wheel 81a is attached to the lower surface of the additional mass body 81 so that the horizontal vibration of the additional mass body 81 is not hindered.
[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 compliance or acceleration of the structure to be controlled. (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 controlled, and the additional mass body 81 in the horizontal direction alone). The natural frequency as the system is a value that is lower than the natural frequency in the horizontal direction of the structure to be controlled. Further, it is preferable to use a spring element 72 having a damping coefficient as small as possible and close to zero. Moreover, it is preferable that the mass of the additional mass body 71 is made larger than that of the additional mass body 81 and the mass ratio between the two is changed according to the total mass ratio. By doing in this way, the horizontal vibration of the structure to be controlled 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 depicted 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 placed 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 so that the additional mass body 121 is placed in two horizontal directions (x direction, y direction). ), Four spring elements (elastic bodies) 122 that are supported so as to vibrate, 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. Further, 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 remaining 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 pieces projecting upward from both sides of each additional mass body 131 from the upper surface of the additional mass body 121. A plurality of spring elements (elastic bodies) 132 and damping elements 133 that are arranged between the additional mass body 131 and the additional mass body 131 and the support pillar 134 to support the additional mass body 131 so as to vibrate in the x direction or the y direction. Is included. As the spring element 132, for example, a coil spring is used. As the damping element 133, a damper having an appropriate damping coefficient is used. Further, wheels 131 a 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 so as to minimize the maximum value of compliance or acceleration of the structure to be controlled. (That is, 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 controlled, and the additional mass body 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 controlled. Further, it is preferable to use a spring element 122 having a damping coefficient as small as possible and close to zero. Moreover, it is preferable that the mass of the additional mass body 121 is made larger than the sum of the four additional mass bodies 131 and the mass ratio between the two is changed according to the total mass ratio. By doing so, vibrations in the two horizontal directions of the structure to be controlled are sufficiently suppressed.
[0132]
<Fourth embodiment>
FIG. 28 is a schematic diagram of a series double dynamic vibration absorber according to the fourth embodiment of the present invention. The dynamic vibration absorber 201 depicted in FIG. 28 includes a first dynamic vibration absorber 210 installed on the installation surface 240a of the structure to be controlled, and a second dynamic vibration absorber 220 placed thereon. ing.
[0133]
As shown in FIG. 28, the first dynamic vibration absorber 210 is disposed between the additional mass body 211 and the installation surface 240a and the additional mass body 211, and supports the additional mass body 211 so as 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 is disposed between the additional mass body 221 disposed above the additional mass body 211 and 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 additional mass body 221 is arranged in the vertical direction by being arranged between the supporting spring element (elastic body) 222 and the damping element 223, and the support surface 240a extending horizontally from both sides of the additional mass body 221 and the installation surface 240a. And a plurality of spring elements 225 that are oscillatingly supported. As the spring elements 222, 225, for example, coil springs are used. As the damping element 223, a damper having an appropriate damping coefficient 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 compliance or acceleration of the structure to be controlled. (I.e., the natural frequency in the vertical direction of the additional mass body 211 as a single system is higher than the natural frequency in the vertical direction of the structure to be controlled, and the single system of the additional mass body 221) As the natural frequency in the vertical direction is lower than the natural frequency in the vertical direction of the structure to be controlled. Further, it is preferable to use a spring element 212 having a damping coefficient as small as possible and close to zero. Moreover, it is preferable to make the mass of the additional mass body 211 larger than that of the additional mass body 221 and to change the mass ratio between them according to the total mass ratio. By doing in this way, the vibration in the vertical direction of the structure to be controlled is sufficiently suppressed.
[0136]
<Fifth embodiment>
FIG. 29 is a schematic diagram of a series double dynamic vibration absorber according to the fifth embodiment of the present invention. A dynamic vibration absorber 250 depicted in FIG. 29 includes a first dynamic vibration absorber 260 installed on the installation surface 290a of the structure to be controlled, and a second dynamic vibration absorber 270 placed thereon. ing.
[0137]
As shown in FIG. 29, the first dynamic vibration absorber 260 is disposed between the additional mass body 261 and the installation surface 290a and the additional mass body 261, and supports the additional mass body 261 so as to vibrate in the vertical direction. Element 262. As the spring element 262, for example, a coil spring is used.
[0138]
The second dynamic vibration absorber 270 is arranged between the additional mass body 271 disposed above the additional mass body 261, and between the additional mass body 261 and the additional mass body 271, and can vibrate the additional mass body 271 in the vertical direction. Are arranged between a spring element (elastic body) 272 that is supported by the support member, a support column 275 extending horizontally from both sides of the additional mass body 271 and the installation surface 290a, so that the additional mass body 271 can vibrate in the vertical direction. A supporting spring element 273 and a damping element 274 are included. As the spring elements 272 and 273, for example, coil springs are used. As the damping element 274, a damper having an appropriate damping coefficient is used.
[0139]
In the present embodiment, the mass 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 compliance or acceleration of the structure to be controlled. (I.e., the natural frequency in the vertical direction of the additional mass body 261 as a single system is higher than the natural frequency in the vertical direction of the structure to be controlled, and the single system of the additional mass body 271) As the natural frequency in the vertical direction is lower than the natural frequency in the vertical direction of the structure to be controlled. Further, it is preferable to use a spring element 262 that has a damping coefficient as small as possible and close to zero. Moreover, it is preferable to make the mass of the additional mass body 261 larger than that of the additional mass body 271 and to change the mass ratio between them according to the total mass ratio. By doing in this way, the vibration in the vertical direction of the structure to be controlled is sufficiently suppressed.
[0140]
<Sixth Embodiment>
FIG. 30 is a schematic diagram of a series double dynamic vibration absorber according to the sixth embodiment of the present invention. The dynamic vibration absorber 301 depicted in FIG. 30 includes a first dynamic vibration absorber 310 installed on the installation surface 340a of the structure to be controlled, and a second dynamic vibration absorber 320 mounted thereon. ing.
[0141]
As shown in FIG. 30, the first dynamic vibration absorber 310 is disposed between the additional mass body 311 and the installation surface 340a and the additional mass body 311 and supports the additional mass body 311 so as to vibrate in the vertical direction. Element 312. As the spring element 312, for example, a coil spring is used.
[0142]
The second dynamic vibration absorber 320 is arranged between the additional mass body 321 disposed above the additional mass body 311, and between the additional mass body 311 and the additional mass body 321, and can vibrate the additional mass body 321 in the vertical direction. Are arranged between a spring element (elastic body) 322 and a damping element 323 that are supported on each other, and a column 324 extending horizontally from both sides of the additional mass body 321 and the installation surface 340a, and the additional mass body 321 is disposed in the vertical direction. A spring element 325 and a damping element 326 that are supported so as to vibrate. As the spring elements 322 and 325, for example, coil springs are used. As the damping elements 323 and 326, those having appropriate damping coefficients 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 are the maximum values of compliance or acceleration of the structure to be damped. The value optimized so as to minimize (that is, the natural frequency in the vertical direction as a single system of the additional mass body 311 is higher than the natural frequency in the vertical direction of the structure to be controlled, and the additional mass body 321 The value is such that the natural frequency in the vertical direction as a single system is lower than the natural frequency in the vertical direction of the structure to be controlled. Further, it is preferable to use a spring element 312 having a damping coefficient as small as possible and close to zero. Moreover, it is preferable to make the mass of the additional mass body 311 larger than that of the additional mass body 321 and to change the mass ratio between them according to the total mass ratio. By doing in this way, the vibration in the vertical direction of the structure to be controlled is sufficiently suppressed.
[0144]
<Seventh embodiment>
FIG. 31 is a schematic view of a series triple motion vibration absorber according to the seventh embodiment of the present invention. The dynamic vibration absorber 351 depicted in FIG. 31 includes a first dynamic vibration absorber 360 installed on the installation surface 390a of the structure to be controlled, and a second dynamic vibration absorber 360 mounted on the first dynamic vibration absorber 360. The vibration absorber 370 and a third dynamic vibration absorber mounted on the second dynamic vibration absorber 370 are further configured.
[0145]
As shown in FIG. 31, the first dynamic vibration absorber 360 is disposed between the additional mass body 361 and the installation surface 390a and the additional mass body 361 and supports the additional mass body 361 so as to vibrate in the vertical direction. Element 362. For example, a coil spring is used as the spring element 362.
[0146]
The second dynamic vibration absorber 370 is disposed between the additional mass body 371 disposed above the additional mass body 361, and 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 to be supported. For example, a coil spring is used as the spring element 372.
[0147]
The third dynamic vibration absorber 380 is arranged between the additional mass body 381 disposed above the additional mass body 371, and between the additional mass body 371 and the additional mass body 381, and can vibrate the additional mass body 381 in the vertical direction. And a spring element (elastic body) 382 and a damping element 383. For example, a coil spring is used as the spring element 382. As the damping element 383, a damper having an appropriate damping coefficient 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 compliance or acceleration of the structure to be controlled. The value optimized so as to minimize (that is, the natural frequency in the vertical direction as a single system of the additional mass body 361 is higher than the natural frequency in the vertical direction of the structure to be controlled, and the additional mass body 371 The natural frequency in the vertical direction as a single system is higher than the natural frequency in the vertical direction of the additional mass body 361, and the natural frequency in the vertical direction as a single system of the additional mass body 381 is the vertical direction of the structure to be controlled. It is a value that is lower than the natural frequency). In addition, it is preferable to use spring elements 362 and 372 having a damping coefficient as small as possible and close to zero. Moreover, it is preferable that the mass of the additional mass body 361 is 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 in this way, the vibration in the vertical direction of the structure to be controlled is sufficiently suppressed.
[0149]
<Eighth Embodiment>
FIG. 32 is a schematic diagram of a house in which a composite dynamic vibration absorber according to an eighth embodiment of the present invention is installed. FIG. 33 is an enlarged view of FIG. 32, where (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, the house 400 is provided with a ceiling 399 and a floor 398 on each floor. A vertical beam 397 is disposed between the ceiling 399 and the floor 398 and connects them. The beam 397 is provided with the composite dynamic vibration absorber 401 according to the present embodiment. 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 the center position of the beam 397 as shown in FIGS. It is composed of four second dynamic vibration absorbers 430 placed 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 (elasticity). 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 arranged at both ends of one spring element 422, respectively, and constitute a set of first dynamic vibration absorbers 420. In addition, two additional mass bodies 411 are also arranged at both ends of the other spring element 412 to constitute a set of first dynamic vibration absorbers 410. Then, the two dynamic elements 410 and 420 are arranged in parallel by fixing the two spring elements 412 and 422 in parallel by the fixing portion 396. The four additional mass bodies 411 and 421 are fixed so as to sandwich the end portions of the spring elements 412 and 422 at positions corresponding to the respective additional mass bodies 411 and 421. The two spring elements 412 and 422 support the additional mass bodies 411 and 421 so as to vibrate in the vertical direction. As the spring elements 412, 422, for example, leaf springs are used.
[0151]
The four second dynamic vibration absorbers 430 are disposed between the additional mass bodies 431 disposed above the additional mass bodies 411 and 421, and between the additional mass bodies 411 and 421 and the additional mass bodies 431, respectively. A plurality of spring elements (elastic bodies) 432 and damping elements 433 that support the additional mass bodies 431 so as to vibrate in the vertical direction are included. As the plurality of spring elements 432, for example, coil springs are used. In addition, a plurality of damping elements 433 having an appropriate damping coefficient as a damper are used.
[0152]
In the present embodiment, the masses of the additional mass bodies 411, 421, and 431, the spring constants of the spring elements 412, 422, and 432, and the damping coefficient of the damping element 433 minimize the maximum value of the compliance or acceleration of the house 400. (Ie, the natural frequency in the vertical direction of the additional mass body 411 as a single system is higher than the natural frequency in the vertical direction of the house 400, and the vertical direction as a single system of the additional mass body 421) The natural frequency of the house 400 is lower than the natural frequency in the vertical direction, and the vertical natural frequency of the additional mass body 431 as a single system is lower than the natural frequency of the house 400 in the vertical direction. ). In addition, it is preferable to use spring elements 412 and 422 having a damping coefficient as small as possible and close to zero. Moreover, it is preferable that the mass of each of the four additional mass bodies 411 and 421 is larger than the mass of each of the four additional mass bodies 431, and the mass ratio of the two is changed according to the total mass ratio. By doing in this way, the vibration of the house 400 in the vertical direction is sufficiently suppressed.
[0153]
<Ninth embodiment>
FIG. 34 is a schematic view of a combined dynamic vibration absorber according to a ninth embodiment of the present invention, where (a) is a front view and (b) is a side view. The composite dynamic vibration absorber 451 depicted in FIG. 34A is disposed between the ceiling 449 and the floor 448 of the structure to be controlled in the same manner as described above, and is installed at the center of the beam 447 connected thereto. ing. As shown in FIGS. 34A and 34B, 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. It is composed of four second dynamic vibration absorbers 480 mounted thereon.
[0154]
As shown in FIG. 34 (a), 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 (elasticity). 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. 34 (b), two additional mass bodies 471 are arranged at both ends of one spring element 472, respectively, and constitute a set of first dynamic vibration absorbers 470. In addition, two additional mass bodies 461 are arranged at both ends of the other spring element 462, respectively, and constitute a set of first dynamic vibration absorbers 460. Then, by fixing the two spring elements 462 and 472 in parallel by 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 end portions of the spring elements 462 and 472 at positions corresponding to the respective additional mass bodies 461 and 471. The two spring elements 462 and 472 support the additional mass bodies 461 and 471 so as 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 the additional mass bodies 461 and 471, and a single piece projecting upward from the upper surface of each additional mass body 461 and 471. A support 484, a plurality of spring elements (elastic bodies) 482 arranged to be connected to the lower surface of the additional mass body 481 from the center of the support 484 and supporting the additional mass body 481 so as to vibrate in the vertical direction, and the addition A portion of the 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 are included. As the spring element 482, for example, a leaf spring is used. The damping element 483 is made of an elastomer (viscoelastic material) having a suitable damping coefficient as a damper.
[0156]
In the present embodiment, the masses of the additional mass bodies 461, 471, and 481, the spring constants of the spring elements 462, 472, and 482, and the damping coefficient of the damping element 483 are the maximum values of compliance or acceleration of the structure to be controlled. The value optimized to minimize (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 controlled, and the additional mass body 471 The natural frequency in the vertical direction as a single system is lower than the natural frequency in the vertical direction of the structure to be controlled, and the natural frequency in the vertical direction as the single system of the additional mass body 481 is vertical in the structure to be controlled. The value is lower than the natural frequency in the direction). Further, it is preferable to use spring elements 462 and 472 that have a damping coefficient as small as possible and close to zero. Moreover, it is preferable that the mass of each of the four additional mass bodies 461 and 471 is made larger than the mass of each of the four additional mass bodies 481, and the mass ratio between the two is changed in accordance with the total mass ratio. By doing in this way, the vibration in the vertical direction of the structure to be controlled is sufficiently suppressed.
[0157]
<Other embodiments>
Although the preferred embodiments of the present invention have been described above, the scope of the present invention is wide and various embodiments can be assumed. Therefore, the present invention is not limited to the above-described embodiments, and various design changes can be made as long as they are described in the claims. Basically, the first dynamic vibration absorber is mounted on the first dynamic vibration absorber as in the first or second embodiment described above, but the prototype is the third embodiment. The 2nd dynamic vibration absorber may be divided and installed in multiple units like the form of this. 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 controlled. In addition, it is possible to implement a series triple motion vibration absorber by disposing a dynamic vibration absorber similar to the first dynamic vibration absorber between the first dynamic vibration absorber and the second dynamic vibration absorber of the third embodiment. It is.
[0158]
Further, the fourth dynamic vibration absorber may be further mounted on the third dynamic vibration absorber of the seventh embodiment. Further, as in the eighth or ninth embodiment, not only the configuration in which the series double vibration absorber is arranged in parallel to one structure to be damped but also the series triple vibration absorber is one vibration object. It can also be implemented in a configuration in which the structure is arranged in parallel. 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 series and parallel dynamic vibration absorbers that have a relatively simple parameter setting and a large vibration suppression effect of the structure to be controlled.
[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 parameter characteristics according to the dynamic vibration absorber of the present invention;
FIG. 3 is a graph depicting an example of a compliance curve of the main system in the dynamic vibration absorber of the present invention.
FIG. 4 is a graph depicting an example of a compliance curve of a main system in a dynamic vibration absorber of a comparative example of the present invention.
FIG. 5 is a graph depicting an example of a compliance curve of a main system in a dynamic vibration absorber of another comparative example of the present invention.
FIG. 6 is a graph depicting impulse response characteristics in the dynamic vibration absorber of the present invention and the prior art.
FIG. 7 shows 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. It is a graph.
FIG. 8 is a graph depicting an example of a compliance curve in the case where the dynamic vibration absorber of the present invention optimized using a condition in which the attenuation of the main system is zero with respect to the main system in which attenuation exists.
FIG. 9 is a graph for explaining the characteristics of parameters related to the dynamic vibration absorber of the present invention when compliance is optimized under a condition where damping exists in the main system, and (a) is a first additional mass body; And (b) is an example of a change curve of the ratio of the natural frequencies of the first additional mass body and the second additional mass body. (C) is an example of a change curve of the damping ratio of the second additional mass body.
FIG. 10 is a graph depicting an example of a compliance curve of the main system in the dynamic vibration absorber of the present invention.
FIG. 11 is a graph for explaining the characteristic of a parameter related to the dynamic vibration absorber of the present invention when the acceleration is optimized under the condition where the damping exists in the main system, and (a) shows the 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 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 damping ratio of the second additional mass body.
FIG. 12 is a graph depicting an example of an acceleration curve of the main system in the dynamic vibration absorber of the present invention.
FIG. 13 is a graph for explaining characteristics of parameters related to the dynamic vibration absorber of the present invention when mobility is optimized under a condition in which attenuation exists in the main system, where (a) is a first additional mass body; And (b) is an example of a change curve of the ratio of the natural frequencies of the first additional mass body and the second additional mass body. (C) is an example of a change curve of the damping ratio of the second additional mass body.
FIG. 14 is a graph depicting an example of the mobility curve of the 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 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 parameter characteristics according to the dynamic vibration absorber of the present invention in the main system compliance optimization;
FIG. 18 is a graph depicting an example of a compliance curve of a main system in a single dynamic vibration absorber, a parallel double dynamic vibration absorber, and a series double dynamic vibration absorber and a series triple dynamic vibration absorber of the present invention.
FIG. 19 is a graph for explaining parameter characteristics according to the dynamic vibration absorber of the present invention in the optimization of the main system acceleration;
FIG. 20 is a graph depicting an example of an acceleration curve of a main system in a single dynamic vibration absorber, a parallel double dynamic vibration absorber, and a series double dynamic vibration absorber and a series triple dynamic vibration absorber of the present invention.
FIG. 21 is a schematic diagram 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 parameter characteristics according to the parallel dynamic vibration absorber of the present invention;
FIG. 23 is a graph depicting a compliance curve of a main system in a single dynamic vibration absorber, a parallel double dynamic vibration absorber, and a series double dynamic vibration absorber and a parallel dynamic vibration absorber of the present invention.
FIG. 24 is a schematic view of a house provided with a series double dynamic vibration absorber according to the first embodiment of the present invention.
FIG. 25 is an enlarged view of FIG. 24, and is a schematic diagram depicting 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 series double dynamic vibration absorber according to a third embodiment of the present invention.
FIG. 28 is a schematic diagram 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 diagram of a series double dynamic vibration absorber according to a sixth embodiment of the present invention.
FIG. 31 is a schematic diagram of a series triple motion vibration absorber according to a seventh embodiment of the present invention.
FIG. 32 is a schematic view of a house in which a composite dynamic vibration absorber according to an eighth embodiment of the present invention is installed.
33 is an enlarged view of FIG. 32, where (a) is a front view of the combined dynamic vibration absorber, and (b) is a side view of the combined dynamic vibration absorber.
FIG. 34 is a schematic view of a combined dynamic vibration absorber according to a ninth embodiment of the present invention, where (a) is a front view and (b) 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 (first additional mass)
22 Spring element
31 Additional mass (second additional mass)
32 Spring element
33 Damping element

Claims (9)

A first additional mass body connected to the structure to be controlled via an elastic body;
A second additional mass connected to the first additional mass via another elastic body,
The natural frequency of the first additional mass body as a single system is set to a natural frequency higher than the natural frequency of the structure to be damped, and the natural frequency of the second additional mass body as a single system The dynamic vibration absorber is characterized in that the vibration frequency is set to be lower than the natural frequency of the structure to be controlled. The damping ratio of the second additional mass body is set so that at least one of vibration compliance, acceleration, and mobility of the structure to be controlled is optimized. The dynamic vibration absorber described in 1. 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 the 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 capable of natural vibration in two or more different directions, respectively, the same as the structure to be controlled;
The two or more natural frequencies as a single system of the first additional mass body are set to higher natural frequencies than the corresponding natural frequencies of the structure to be controlled, and the second additional mass The natural frequency of 2 or more as a single body system is set to a natural frequency lower than a corresponding natural frequency of the structure to be controlled, respectively. The dynamic vibration absorber of Claim 1. A first additional mass body connected to the structure to be controlled via an elastic body;
A second additional mass body connected to the first additional mass body via another elastic body, and a third additional mass connected to the second additional mass body via another elastic body With a 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 natural vibration of the second additional mass body as a single system. The natural frequency of the third additional mass body as a single system is set to a higher natural frequency than the natural frequency of the first additional mass body as a single system. The dynamic vibration absorber is characterized by being set to a natural frequency lower than the natural frequency. The first to third additional mass bodies are capable of natural vibration in two or more different directions that are the same as the structure to be damped,
The two or more natural frequencies as a single system of the first additional mass body are set to higher natural frequencies than the corresponding natural frequencies of the structure to be controlled, respectively, and the second additional mass body The two or more natural frequencies of the first additional mass body are set to higher natural frequencies than the corresponding natural frequencies of the first additional mass body, respectively, and the third additional mass body 6. The dynamic vibration absorber according to claim 5, wherein the two or more natural frequencies as a single system are set to natural frequencies lower than the corresponding natural frequencies of the structure to be controlled. . The dynamic vibration absorber according to any one of claims 1 to 6, wherein substantially no damping action is exerted between the structure to be damped and the first additional mass body. 8. The dynamic vibration absorber according to claim 1, wherein a mass of the first additional mass body is larger than a mass of the second additional mass body. 9. Two dynamic vibration absorbers according to any one of claims 1 to 8 are provided,
The natural frequency as a single system of the first additional mass body of one dynamic vibration absorber is set to a natural frequency lower than the natural frequency of the structure to be controlled, and the other vibration absorber A parallel dynamic vibration absorber, wherein the natural frequency of the first additional mass body as a single system is set to be higher than the natural frequency of the structure to be damped.

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