JP6390046B2 - Method for estimating natural frequency of structure and program for estimating natural frequency of structure - Google Patents

Method for estimating natural frequency of structure and program for estimating natural frequency of structure Download PDF

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JP6390046B2
JP6390046B2 JP2015133467A JP2015133467A JP6390046B2 JP 6390046 B2 JP6390046 B2 JP 6390046B2 JP 2015133467 A JP2015133467 A JP 2015133467A JP 2015133467 A JP2015133467 A JP 2015133467A JP 6390046 B2 JP6390046 B2 JP 6390046B2
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恵一 後藤
恵一 後藤
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本発明は、車両が走行している状態における桁などの構造物の固有振動数を推定できる構造物の固有振動数推定方法および構造物の固有振動数推定プログラムに関する。   The present invention relates to a structure natural frequency estimation method and a structure natural frequency estimation program capable of estimating the natural frequency of a structure such as a girder when a vehicle is traveling.

車両が桁などの構造物上を走行する場合、構造物の固有振動数と走行する列車による加振振動数とが一致すると共振が発生し、構造物の動的な応答が増大している。
車両が走行する構造物を設計する際には、構造物が車両の質量に対する構造物の質量の比率が比較的大きいコンクリート構造などの場合は、車両の質量の影響を考慮せずにその強度が設計されている（例えば、非特許文献１参照）。これに対し、構造物が車両の質量に対する構造物の質量の比率が比較的小さい鋼構造などの場合は、構造物に車両の質量に対応する等分布質量が載荷されていると相当してその強度が設計されている（例えば、非特許文献２参照）。 When a vehicle travels on a structure such as a girder, resonance occurs when the natural frequency of the structure matches the vibration frequency of the traveling train, and the dynamic response of the structure increases.
When designing a structure on which a vehicle travels, if the structure is a concrete structure in which the ratio of the mass of the structure to the mass of the vehicle is relatively large, the strength of the structure is not considered without considering the effect of the mass of the vehicle. It is designed (for example, refer nonpatent literature 1). On the other hand, when the structure is a steel structure or the like in which the ratio of the mass of the structure to the mass of the vehicle is relatively small, it is assumed that the structure is loaded with an evenly distributed mass corresponding to the mass of the vehicle. The strength is designed (for example, see Non-Patent Document 2).

「鉄道構造物等設計標準・同解説 コンクリート構造物、国土交通省鉄道局監修、鉄道総合技術研究所編」、丸善株式会社、平成１６年４月"Railway structure design standards / comment concrete structure, supervised by the Ministry of Land, Infrastructure, Transport and Tourism, Railway Bureau, Railway Technical Research Institute", Maruzen Co., Ltd., April 2004 「鉄道構造物等設計標準・同解説 鋼・合成構造物、国土交通省鉄道局監修、鉄道総合技術研究所編」、丸善株式会社、平成２１年７月"Railway structure design standards / commentary steel / composite structure, supervised by the Railway Bureau of the Ministry of Land, Infrastructure, Transport and Tourism, Railway Technical Research Institute", Maruzen Co., Ltd., July 2009

このように、走行する車両の質量や挙動による構造物への影響については、定量的な評価が行われておらず、車両の質量に対する構造物の質量の比率が比較的小さい鋼構造など構造物では、共振が発生する振動数を小さく設定し、その強度が過剰となる傾向があった。   As described above, the influence on the structure due to the mass and behavior of the traveling vehicle has not been quantitatively evaluated, and the structure such as a steel structure in which the ratio of the mass of the structure to the mass of the vehicle is relatively small. Then, the frequency at which resonance occurs is set small, and the strength tends to be excessive.

そこで、本発明は、適切な強度の構造物を設計することができる構造物の固有振動数推定方法および構造物の固有振動数推定プログラムを提供することを目的とする。   Therefore, an object of the present invention is to provide a structure natural frequency estimation method and a structure natural frequency estimation program capable of designing a structure having an appropriate strength.

上記目的を達成するため、本発明に係る構造物の固有振動数推定方法は、車両が走行する際の構造物の固有振動数を推定する構造物の固有振動数推定方法であって、前記構造物の単位長さあたりの質量と前記車両の前記単位長さあたりの質量との質量比を求めるステップと、前記質量比および前記構造物の支持スパン毎に、前記車両の走行速度と該走行速度で前記車両が走行することにより前記構造物に生じるたわみ量との関係を、走行する前記車両の質量および挙動を考慮した場合と、走行する前記車両の質量および挙動を考慮せずに前記車両の質量に相当する荷重が前記構造物上を前記走行速度で移動しているものとした場合と、のそれぞれにおいて求めるステップと、前記質量比および前記構造物の支持スパン毎に、走行する前記車両の質量および挙動を考慮した場合の前記車両が走行する際の前記構造物の固有振動数と、走行する前記車両の質量および挙動を考慮せずに前記車両の質量に相当する荷重が前記構造物上を前記走行速度で移動しているものとした場合の前記車両が走行する際の前記構造物の固有振動数と、の固有振動数比を求めるステップと、前記質量比、前記構造物の支持スパンおよび前記固有振動数比の関係を求めるステップと、を有することを特徴とする。   In order to achieve the above object, a natural frequency estimating method for a structure according to the present invention is a natural frequency estimating method for a structure for estimating a natural frequency of a structure when a vehicle travels. A step of obtaining a mass ratio of a mass per unit length of an object to a mass per unit length of the vehicle; a traveling speed of the vehicle and a traveling speed for each mass ratio and a support span of the structure; The relationship between the amount of deflection generated in the structure when the vehicle travels in the case where the mass and behavior of the traveling vehicle are taken into consideration, and the mass and behavior of the traveling vehicle are not considered. The vehicle that travels for each of the mass ratio and the support span of the structure when the load corresponding to the mass is moving on the structure at the traveling speed The natural frequency of the structure when the vehicle travels in consideration of the mass and behavior, and a load corresponding to the mass of the vehicle without considering the mass and behavior of the vehicle traveling on the structure. The natural frequency of the structure when the vehicle travels when the vehicle is traveling at the travel speed, the mass ratio, the support span of the structure And obtaining the relationship of the natural frequency ratio.

また、本発明に係る構造物の固有振動数推定プログラムは、車両が走行する際の構造物の固有振動数を推定するコンピュータに、前記構造物の単位長さあたりの質量と前記車両の前記単位長さあたりの質量との質量比を求めるステップと、前記質量比および前記構造物の支持スパン毎に、前記車両の走行速度と該走行速度で前記車両が走行することにより前記構造物に生じるたわみ量との関係を、走行する前記車両の質量および挙動を考慮した場合と、走行する前記車両の質量および挙動を考慮せずに前記車両の質量に相当する荷重が前記構造物上を前記走行速度で移動しているものとした場合と、のそれぞれにおいて求めるステップと、前記質量比および前記構造物の支持スパン毎に、走行する前記車両の質量および挙動を考慮した場合の前記車両が走行する際の前記構造物の固有振動数と、走行する前記車両の質量および挙動を考慮せずに前記車両の質量に相当する荷重が前記構造物上を前記走行速度で移動しているものとした場合の前記車両が走行する際の前記構造物の固有振動数と、の固有振動数比を求めるステップと、前記質量比、前記構造物の支持スパンおよび前記固有振動数比の関係を求めるステップと、を実行させることを特徴とする。   Further, the program for estimating the natural frequency of the structure according to the present invention includes a computer for estimating the natural frequency of the structure when the vehicle travels, a mass per unit length of the structure, and the unit of the vehicle. A step of obtaining a mass ratio with respect to a mass per length, and a deflection generated in the structure by the traveling speed of the vehicle and the traveling of the vehicle at the traveling speed for each of the mass ratio and the support span of the structure; The load corresponding to the mass of the vehicle without considering the mass and behavior of the traveling vehicle takes into account the traveling speed on the structure when the mass and behavior of the traveling vehicle are considered. And the step of obtaining in each of the above, the mass ratio and the support span of the structure, and the mass and behavior of the traveling vehicle are taken into account for each support span of the structure. The load corresponding to the mass of the vehicle moves on the structure at the traveling speed without considering the natural frequency of the structure when the vehicle travels and the mass and behavior of the traveling vehicle. A step of obtaining a natural frequency ratio of the structure when the vehicle travels, and a relationship between the mass ratio, a support span of the structure, and the natural frequency ratio. And a step of obtaining

本発明では、走行する車両の質量および挙動を考慮した場合の車両が走行する際の構造物の固有振動数と、走行する車両の質量および挙動を考慮せずに車両の質量に相当する荷重が構造物上を走行速度で移動しているものとした場合の車両が走行する際の構造物の固有振動数と、の固有振動数比が質量比および構造物の支持スパン毎に求められることにより、車両の走行による構造物への影響を定量的に評価することができる。
これにより、比較的質量比の小さい鋼構造などの構造物を過剰な強度の構造とせずに適度な強度に設計することができる。 In the present invention, the natural frequency of the structure when the vehicle travels in consideration of the mass and behavior of the traveling vehicle, and the load corresponding to the mass of the vehicle without considering the mass and behavior of the traveling vehicle. When the natural frequency of the structure and the natural frequency ratio of the vehicle when traveling on the structure at a traveling speed are determined for each mass ratio and structure support span In addition, it is possible to quantitatively evaluate the influence of the traveling of the vehicle on the structure.
As a result, a structure such as a steel structure having a relatively small mass ratio can be designed to have an appropriate strength without using an excessively strong structure.

本発明によれば、比較的質量比の小さい鋼構造などの構造物を過剰な強度の構造とせずに適度な強度に設計することができる。   According to the present invention, it is possible to design a structure such as a steel structure having a relatively small mass ratio to an appropriate strength without using an excessively strong structure.

本発明の実施形態による構造物の固有振動数推定方法および構造物の固有振動数推定プログラムの一例をフローチャートである。It is a flowchart of an example of the natural frequency estimation method of a structure and the natural frequency estimation program of a structure by embodiment of this invention. 桁に作用する車両の荷重を説明する図である。It is a figure explaining the load of the vehicle which acts on a girder. 桁の支持スパンと単位長さあたりの質量との関係を示すグラフである。It is a graph which shows the relationship between the support span of a girder, and the mass per unit length. （ａ）は質量比αが３、桁の支持スパンが１０ｍの場合の走行速度と桁のたわみ量との関係を示すグラフ、（ｂ）は質量比αが５、桁の支持スパンが１０ｍの場合の走行速度と桁のたわみ量との関係を示すグラフ、（ｃ）は質量比αが１０、桁の支持スパンが１０ｍの場合の走行速度と桁のたわみ量との関係を示すグラフ、（ｄ）は質量比αが２０、桁の支持スパンが１０ｍの場合の走行速度と桁のたわみ量との関係を示すグラフである。(A) is a graph showing the relationship between the traveling speed and the deflection amount of the girder when the mass ratio α is 3 and the support span of the girder is 10 m, and (b) is a graph of the mass ratio α is 5 and the support span of the girder is 10 m (C) is a graph showing the relationship between the running speed and the deflection of the girder when the mass ratio α is 10 and the support span of the girder is 10 m. d) is a graph showing the relationship between the traveling speed and the amount of deflection of the beam when the mass ratio α is 20 and the support span of the beam is 10 m. （ａ）は質量比αが３、桁の支持スパンが２０ｍの場合の走行速度と桁のたわみ量との関係を示すグラフ、（ｂ）は質量比αが５、桁の支持スパンが２０ｍの場合の走行速度と桁のたわみ量との関係を示すグラフ、（ｃ）は質量比αが１０、桁の支持スパンが２０ｍの場合の走行速度と桁のたわみ量との関係を示すグラフ、（ｄ）は質量比αが２０、桁の支持スパンが２０ｍの場合の走行速度と桁のたわみ量との関係を示すグラフである。(A) is a graph showing the relationship between the traveling speed and the deflection amount of the girder when the mass ratio α is 3 and the support span of the girder is 20 m, and (b) is a graph of the mass ratio α is 5 and the support span of the girder is 20 m (C) is a graph showing the relationship between the running speed and the deflection of the girder when the mass ratio α is 10 and the support span of the girder is 20 m. d) is a graph showing the relationship between the traveling speed and the amount of deflection of the beam when the mass ratio α is 20 and the support span of the beam is 20 m. （ａ）は質量比αが３、桁の支持スパンが２５ｍの場合の走行速度と桁のたわみ量との関係を示すグラフ、（ｂ）は質量比αが５、桁の支持スパンが２５ｍの場合の走行速度と桁のたわみ量との関係を示すグラフ、（ｃ）は質量比αが１０、桁の支持スパンが２５ｍの場合の走行速度と桁のたわみ量との関係を示すグラフ、（ｄ）は質量比αが２０、桁の支持スパンが２５ｍの場合の走行速度と桁のたわみ量との関係を示すグラフである。(A) is a graph showing the relationship between the traveling speed and the deflection amount of the girder when the mass ratio α is 3 and the support span of the girder is 25 m, and (b) is a graph where the mass ratio α is 5 and the support span of the girder is 25 m. (C) is a graph showing the relationship between the traveling speed and the amount of deflection of the digit when the mass ratio α is 10 and the support span of the digit is 25 m. d) is a graph showing the relationship between the traveling speed and the amount of deflection of the beam when the mass ratio α is 20 and the support span of the beam is 25 m. （ａ）は質量比αが３、桁の支持スパンが２５ｍの場合の走行速度と桁のたわみ量との関係を示すグラフ、（ｂ）は質量比αが５、桁の支持スパンが２５ｍの場合の走行速度と桁のたわみ量との関係を示すグラフ、（ｃ）は質量比αが１０、桁の支持スパンが２５ｍの場合の走行速度と桁のたわみ量との関係を示すグラフ、（ｄ）は質量比αが２０、桁の支持スパンが２５ｍの場合の走行速度と桁のたわみ量との関係を示すグラフである。(A) is a graph showing the relationship between the traveling speed and the deflection amount of the girder when the mass ratio α is 3 and the support span of the girder is 25 m, and (b) is a graph where the mass ratio α is 5 and the support span of the girder is 25 m (C) is a graph showing the relationship between the traveling speed and the amount of deflection of the digit when the mass ratio α is 10 and the support span of the digit is 25 m. d) is a graph showing the relationship between the traveling speed and the amount of deflection of the beam when the mass ratio α is 20 and the support span of the beam is 25 m. 桁の支持スパン毎の固有振動数、１〜３次共振速度、および走行する車両の質量および挙動を考慮せずに車両の質量に相当する荷重が桁上を走行速度で移動しているものとした場合における共振速度を示す表である。The load corresponding to the mass of the vehicle is moving at the running speed on the girder without considering the natural frequency for each support span of the girder, the first to third resonance speeds, and the mass and behavior of the running vehicle. It is a table | surface which shows the resonant speed in the case where it did. 桁の支持スパン毎の質量比αと固有振動数との関係を説明する図である。It is a figure explaining the relationship between mass ratio (alpha) for every support span of a girder, and a natural frequency.

以下、本発明の実施形態による構造物の固有振動数推定方法および構造物の固有振動数推定プログラムについて、図１乃至図９に基づいて説明する。
図１に示す本実施形態による構造物の固有振動数推定方法は、図２に示す車両１が桁（構造物）２上を走行する際の桁２の固有振動数を推定するための方法である。構造物の固有振動数推定プログラムは、コンピュータに構造物の固有振動数推定方法を実行させて、車両１が走行する際の桁２の固有振動数を推定するプログラムである。 Hereinafter, a natural frequency estimation method and a natural frequency estimation program for a structure according to an embodiment of the present invention will be described with reference to FIGS.
The method for estimating the natural frequency of the structure according to this embodiment shown in FIG. 1 is a method for estimating the natural frequency of the girder 2 when the vehicle 1 travels on the girder (structure) 2 shown in FIG. is there. The natural frequency estimation program for a structure is a program that causes a computer to execute a natural frequency estimation method for a structure to estimate the natural frequency of the digit 2 when the vehicle 1 travels.

まず、車両１が走行する桁２の支持スパンＬｂおよび質量を設定する（Ｓ−１）。
続いて、桁２の単位長さあたりの質量Ｗｔと車両１の単位長さあたりの質量Ｗｔとの質量比αを求める（Ｓ−２）。本実施形態では、車両１の単位長さあたりの質量Ｗｓに対する桁２の単位長さあたりの質量Ｗｔの比率を求める。
図３には、桁２の支持スパンＬｂと桁２の単位長さあたりの質量Ｗｔとの関係を示している。ここでは、車両１の単位長さあたりの質量ｗｔを２０ｋＮ／ｍとしている。 First, the support span Lb and mass of the beam 2 where the vehicle 1 travels are set (S-1).
Subsequently, a mass ratio α between the mass W t per unit length of the digit 2 and the mass W t per unit length of the vehicle 1 is obtained (S-2). In the present embodiment, the ratio of the mass W t per unit length of the girder 2 to the mass Ws per unit length of the vehicle 1 is obtained.
FIG. 3 shows the relationship between the support span L b of the beam 2 and the mass W t per unit length of the beam 2. Here, the mass w t per unit length of the vehicle 1 is set to 20 kN / m.

続いて、質量比αおよび桁２の支持スパンＬｂ毎に、車両１の走行速度と車両１が走行することにより桁２に生じるたわみ量との関係を求める（Ｓ−３，Ｓ−４）。このとき、走行する車両１の質量および挙動を考慮した場合の車両１の走行速度と車両１が走行することにより桁２に生じるたわみ量との関係を求める（Ｓ−３）とともに、走行する車両１の質量および挙動を考慮せずに車両１の質量に相当する荷重が桁２上を走行速度で移動しているものとした場合の車両１の走行速度と走行速度で車両１が走行することにより桁２に生じるたわみ量との関係を求める（Ｓ−４）。 Subsequently, each support span L b weight ratio α and the digit 2 to determine the relationship between the deflection amount occurring digit 2 by the traveling speed and the vehicle 1 of the vehicle 1 is traveling (S-3, S-4 ) . At this time, the relationship between the travel speed of the vehicle 1 in consideration of the mass and behavior of the traveling vehicle 1 and the amount of deflection generated in the beam 2 by the traveling of the vehicle 1 is obtained (S-3) and the traveling vehicle The vehicle 1 travels at the traveling speed and the traveling speed of the vehicle 1 when the load corresponding to the mass of the vehicle 1 is moving on the beam 2 at the traveling speed without considering the mass and behavior of the vehicle 1. To obtain the relationship with the deflection amount generated in the digit 2 (S-4).

走行する車両１の質量および挙動を考慮した場合とは、走行する車両１の振動や、車両１の車輪３と桁２に設けられたレール（不図示）との間の荷重移動などを考慮した場合としている。
また、走行する車両１の質量および挙動を考慮せずに車両１の質量に相当する荷重が桁２上を走行速度で移動しているものとした場合では、車両１の質量が車輪３から桁２に作用し、車輪３それぞれから桁２に作用する車両１の質量は、車両１の質量を車輪３の数で割った値としている。
本実施形態では、車両１には車輪３が走行方向（桁２の長さ方向）に４つ設けられており、車両１が４点支持されているものとしている。 When considering the mass and behavior of the traveling vehicle 1, the vibration of the traveling vehicle 1 and the load movement between the wheel 3 of the vehicle 1 and the rail (not shown) provided on the beam 2 are considered. If you are.
In addition, when the load corresponding to the mass of the vehicle 1 is moving on the girder 2 at the traveling speed without considering the mass and behavior of the traveling vehicle 1, the mass of the vehicle 1 is changed from the wheel 3 to the girder. The mass of the vehicle 1 acting on the wheel 2 and acting on the beam 2 from each of the wheels 3 is a value obtained by dividing the mass of the vehicle 1 by the number of the wheels 3.
In the present embodiment, the vehicle 1 is provided with four wheels 3 in the traveling direction (length direction of the beam 2), and the vehicle 1 is supported at four points.

図４乃至図７に、質量比αおよび桁２の支持スパンＬｂ毎の車両１の走行速度と車両１が走行することにより桁２に生じるたわみ量との関係を示している。図４乃至図７では、点線が走行する車両１の質量および挙動を考慮した場合を示し、実線が走行する車両１の質量および挙動を考慮せずに車両１の質量に相当する荷重が桁２上を走行速度で移動しているものとした場合を示している。
図４乃至図７より、質量比が大きくなるに従って、走行する車両１の質量および挙動を考慮した場合の桁２のたわみ量と、走行する車両１の質量および挙動を考慮せずに車両１の質量が桁２上を走行速度で移動しているものとした場合の桁２のたわみ量との差が小さくなることがわかる。また、桁２の支持スパンＬｂが大きくなるに従って、走行する車両１の質量および挙動を考慮した場合の桁２のたわみ量と、走行する車両１の質量および挙動を考慮せずに車両１の質量に相当する荷重が桁２上を走行速度で移動しているものとした場合の桁２のたわみ量との差が大きくなることがわかる。 4 to 7 show the relationship between the deflection amount occurring digit 2 by the traveling speed and the vehicle 1 of the vehicle 1 in each support span L b weight ratio α and column 2 is traveling. 4 to 7 show a case where the mass and behavior of the vehicle 1 traveling in dotted lines are taken into consideration, and the load corresponding to the mass of the vehicle 1 without the consideration of the mass and behavior of the vehicle 1 traveling along the solid line is two digits. The case where it is assumed that the vehicle is moving at a traveling speed is shown.
4 to 7, as the mass ratio increases, the deflection amount of the girder 2 when the mass and behavior of the traveling vehicle 1 are taken into account and the vehicle 1 without considering the mass and behavior of the traveling vehicle 1. It can be seen that the difference from the deflection amount of the digit 2 when the mass is moving on the digit 2 at the traveling speed becomes small. Further, as the support span Lb of the girder 2 increases, the deflection amount of the girder 2 when the mass and behavior of the traveling vehicle 1 are taken into account, and the mass of the vehicle 1 without considering the mass and behavior of the traveling vehicle 1. It can be seen that the difference from the deflection amount of the girder 2 becomes larger when the load corresponding to is moving on the girder 2 at the traveling speed.

続いて、共振が生じる際に桁２たわみ量がピークとなることから、走行する車両１の質量および挙動を考慮した場合、および走行する車両１の質量および挙動を考慮せずに車両１の質量に相当する荷重が桁２上を走行速度で移動しているものとした場合それぞれにおいて、たわみ量がピークとなる走行速度もとに固有振動数を求め、これらの固有振動数の比率（固有振動数比）を求める（Ｓ−５）。
本実施形態では、固有振動数比は、走行する車両１の質量および挙動を考慮せずに車両１の質量に相当する荷重が桁２上を走行速度で移動しているものとした場合の桁２の固有振動数に対する走行する車両１の質量および挙動を考慮した場合の桁２の固有振動数の比率としている。
なお、桁２の固有振動数ｆは以下の式で求める。 Subsequently, since the deflection amount of the girder 2 peaks when resonance occurs, the mass and behavior of the vehicle 1 are taken into consideration when considering the mass and behavior of the traveling vehicle 1 and without considering the mass and behavior of the traveling vehicle 1. In each case, the natural frequency is obtained based on the traveling speed at which the deflection amount reaches a peak, and the ratio of these natural frequencies (natural vibration) is assumed. (Number ratio) is obtained (S-5).
In the present embodiment, the natural frequency ratio is a digit when the load corresponding to the mass of the vehicle 1 is moving at the traveling speed on the digit 2 without considering the mass and behavior of the traveling vehicle 1. The ratio of the natural frequency of the digit 2 when considering the mass and behavior of the traveling vehicle 1 with respect to the natural frequency of 2.
The natural frequency f of the digit 2 is obtained by the following formula.

Figure 0006390046
Figure 0006390046

図８では、支持スパンＬｂごとの桁２の固有振動数、１〜３次共振が生じる車両１の走行速度、および走行する車両１の質量および挙動を考慮せずに車両１の質量に相当する荷重が桁２上を走行速度で移動しているものとした場合の共振が生じる走行速度と、を表に示している。 In Figure 8, the natural frequency of the digits 2 per support span L b, corresponding to the mass of the vehicle 1 without considering the mass and behavior of the vehicle 1 to 3 primary resonance traveling speed of the vehicle 1 occurs, and travels The table shows the traveling speed at which resonance occurs when the load to be moved is moving on the beam 2 at the traveling speed.

続いて、質量比α、桁２の支持スパンＬｂおよび固有振動数比の関係を求める（Ｓ−６）。図９では、質量比α、桁２の支持スパンＬｂおよび固有振動数比の関係を示している。
図９より、質量比αが小さくなるに従って固有振動数比が小さくなり、質量比αが大きくなるに従って固有振動数比が大きくなり１に近付くことがわかる。
このため、質量比αが小さくなる鋼構造などの場合では、固有振動数として、走行する車両１の質量および挙動を考慮せずに車両１の質量に相当する荷重が桁２上を走行速度で移動しているものとした場合の桁２の固有振動数を採用すると、走行する車両１の質量および挙動を考慮した場合の桁２の固有振動数よりも小さくなり、桁２の設計を行う際に過剰な強度となる。これに対し、固有振動数として走行する車両１の質量および挙動を考慮した場合の桁２の固有振動数を採用することで適切な強度の桁２を設計することができる。 Subsequently, the relationship between the mass ratio α, the support span L b of the girder 2 and the natural frequency ratio is obtained (S-6). FIG. 9 shows the relationship among the mass ratio α, the support span L b of the girder 2, and the natural frequency ratio.
FIG. 9 shows that the natural frequency ratio decreases as the mass ratio α decreases, and the natural frequency ratio increases and approaches 1 as the mass ratio α increases.
For this reason, in the case of a steel structure or the like in which the mass ratio α is small, the load corresponding to the mass of the vehicle 1 is the traveling speed on the girder 2 without considering the mass and behavior of the traveling vehicle 1 as the natural frequency. When the natural frequency of the digit 2 when it is assumed to be moving is adopted, it becomes smaller than the natural frequency of the digit 2 when the mass and behavior of the traveling vehicle 1 are taken into consideration. Excessive strength. On the other hand, by adopting the natural frequency of the girder 2 when the mass and behavior of the vehicle 1 traveling as the natural frequency are taken into account, the girder 2 with appropriate strength can be designed.

桁２の設計を行う際には、質量比α、桁２の支持スパンＬｂおよび固有振動数比の関係から、固有振動数として走行する車両１の質量および挙動を考慮した場合の桁２の固有振動数を容易に割り出すことができる。
なお、質量比αが大きくなるに従って、走行する車両１の質量および挙動を考慮せずに車両１の質量に相当する荷重が桁２上を走行速度で移動しているものとした場合の桁２の固有振動数と、走行する車両１の質量および挙動を考慮した場合の桁２の固有振動数との値が略等しくなるため、梁の設計の際に、固有振動数を走行する車両１の質量および挙動を考慮せずに車両１の質量に相当する荷重が桁２上を走行速度で移動しているものとした場合の桁２の固有振動数を採用する場合と、固有振動数を走行する車両１の質量および挙動を考慮せずに車両１の質量に相当する荷重が桁２上を走行速度で移動しているものとした場合の桁２の固有振動数から固有振動数として走行する車両１の質量および挙動を考慮した場合の桁２の固有振動数を割り出して採用する場合との質量比αの閾値を設定してもよい。 When performing design digit 2, the weight ratio alpha, the relationship of the support span L b and the natural frequency ratio of the digits 2, digit 2 in consideration of the mass and behavior of the vehicle 1 that travels as natural frequency The natural frequency can be easily determined.
As the mass ratio α increases, the digit 2 in the case where the load corresponding to the mass of the vehicle 1 is moving at the traveling speed on the digit 2 without considering the mass and behavior of the traveling vehicle 1. And the natural frequency of the digit 2 when the mass and behavior of the traveling vehicle 1 are taken into consideration are substantially equal to each other. The case where the natural frequency of the girder 2 is adopted when the load corresponding to the mass of the vehicle 1 is moving on the girder 2 at the traveling speed without considering the mass and the behavior, and the natural frequency is traveled. The vehicle 1 travels as the natural frequency from the natural frequency of the digit 2 when the load corresponding to the mass of the vehicle 1 is moving on the digit 2 at the traveling speed without considering the mass and behavior of the vehicle 1 The natural frequency of girder 2 considering the mass and behavior of vehicle 1 It may set the threshold value of the weight ratio α of the case of employed Eject and.

次に、上述した固有振動数推定方法および構造物の固有振動数推定プログラムの作用・効果について図面を用いて説明する。
上述した本実施形態による固有振動数推定方法および構造物の固有振動数推定プログラムでは、走行する車両１の質量および挙動を考慮した場合の車両１が走行する際の桁２の固有振動数と、走行する車両１の質量および挙動を考慮せずに車両１の質量に相当する荷重が桁２上を走行速度で移動しているものとした場合の車両１が走行する際の桁２の固有振動数と、の固有振動数比が質量比αおよび桁２の支持スパンＬｂ毎に求められることにより、車両１の走行による桁２への影響を定量的に評価することができる。
これにより、比較的質量比の小さい鋼構造などの桁２を過剰な強度の構造とせずに適度な強度に設計することができる。 Next, the operation and effect of the above-described natural frequency estimation method and structure natural frequency estimation program will be described with reference to the drawings.
In the natural frequency estimating method and the natural frequency estimating program for a structure according to the above-described embodiment, the natural frequency of the digit 2 when the vehicle 1 travels in consideration of the mass and behavior of the traveling vehicle 1, The natural vibration of the girder 2 when the vehicle 1 travels when the load corresponding to the mass of the vehicle 1 is moving on the girder 2 at a traveling speed without considering the mass and behavior of the traveling vehicle 1. The natural frequency ratio of the number 1 is obtained for each mass ratio α and the support span Lb of the girder 2, so that the influence of the traveling of the vehicle 1 on the girder 2 can be quantitatively evaluated.
Thereby, the girder 2 such as a steel structure having a relatively small mass ratio can be designed to have an appropriate strength without making the structure of excessive strength.

以上、本発明による固有振動数推定方法および構造物の固有振動数推定プログラムの実施形態について説明したが、本発明は上記の実施形態に限定されるものではなく、その趣旨を逸脱しない範囲で適宜変更可能である。
例えば、上記の実施形態では、走行する車両１の質量および挙動を考慮した場合とは、走行する車両１の振動や、車両１の車輪３と桁２に設けられたレールとの間の荷重移動などを考慮した場合としているが、その他の条件を考慮してもよい。
また、車両１および桁２の形態は適宜設定されてよい。 As mentioned above, although the embodiment of the natural frequency estimation method and the natural frequency estimation program for a structure according to the present invention has been described, the present invention is not limited to the above-described embodiment, and may be appropriately selected without departing from the scope of the present invention. It can be changed.
For example, in the above embodiment, when the mass and behavior of the traveling vehicle 1 are taken into account, the vibration of the traveling vehicle 1 and the load movement between the wheel 3 of the vehicle 1 and the rail provided on the beam 2 are described. However, other conditions may be considered.
Moreover, the form of the vehicle 1 and the girder 2 may be set as appropriate.

１ 車両
２ 桁（構造物） 1 vehicle 2 digits (structure)

Claims (2)

車両が走行する際の構造物の固有振動数を推定する構造物の固有振動数推定方法であって、
前記構造物の単位長さあたりの質量と前記車両の前記単位長さあたりの質量との質量比を求めるステップと、
前記質量比および前記構造物の支持スパン毎に、前記車両の走行速度と該走行速度で前記車両が走行することにより前記構造物に生じるたわみ量との関係を、走行する前記車両の質量および挙動を考慮した場合と、走行する前記車両の挙動を考慮せずに前記車両の質量が前記構造物上を前記走行速度で移動しているものとした場合と、のそれぞれにおいて求めるステップと、
前記質量比および前記構造物の支持スパン毎に、走行する前記車両の質量および挙動を考慮した場合の前記車両が走行する際の前記構造物の固有振動数と、走行する前記車両の質量および挙動を考慮せずに前記車両の質量に相当する荷重が前記構造物上を前記走行速度で移動しているものとした場合の前記車両が走行する際の前記構造物の固有振動数と、の固有振動数比を求めるステップと、
前記質量比、前記構造物の支持スパンおよび前記固有振動数比の関係を求めるステップと、を有することを特徴とする構造物の固有振動数推定方法。 A method for estimating the natural frequency of a structure for estimating the natural frequency of the structure when the vehicle travels,
Obtaining a mass ratio between the mass per unit length of the structure and the mass per unit length of the vehicle;
For each of the mass ratio and the support span of the structure, the relationship between the traveling speed of the vehicle and the amount of deflection generated in the structure when the vehicle travels at the traveling speed is determined. And the step of obtaining each in the case where the mass of the vehicle is moving on the structure at the traveling speed without considering the behavior of the traveling vehicle,
The natural frequency of the structure when the vehicle travels and the mass and behavior of the traveling vehicle when the mass and behavior of the traveling vehicle are taken into account for each mass ratio and the support span of the structure. The natural frequency of the structure when the vehicle travels when the load corresponding to the mass of the vehicle is moving on the structure at the travel speed without considering the Obtaining a frequency ratio;
Obtaining a relationship between the mass ratio, a support span of the structure, and the natural frequency ratio, and a method for estimating the natural frequency of the structure. 車両が走行する際の構造物の固有振動数を推定するコンピュータに、
前記構造物の単位長さあたりの質量と前記車両の前記単位長さあたりの質量との質量比を求めるステップと、
前記質量比および前記構造物の支持スパン毎に、前記車両の走行速度と該走行速度で前記車両が走行することにより前記構造物に生じるたわみ量との関係を、走行する前記車両の質量および挙動を考慮した場合と、走行する前記車両の質量および挙動を考慮せずに前記車両の質量に相当する荷重が前記構造物上を前記走行速度で移動しているものとした場合と、のそれぞれにおいて求めるステップと、
前記質量比および前記構造物の支持スパン毎に、走行する前記車両の質量および挙動を考慮した場合の前記車両が走行する際の前記構造物の固有振動数と、走行する前記車両の質量および挙動を考慮せずに前記車両の質量に相当する荷重が前記構造物上を前記走行速度で移動しているものとした場合の前記車両が走行する際の前記構造物の固有振動数と、の固有振動数比を求めるステップと、
前記質量比、前記構造物の支持スパンおよび前記固有振動数比の関係を求めるステップと、を実行させることを特徴とする構造物の固有振動数推定プログラム。 A computer that estimates the natural frequency of the structure when the vehicle travels,
Obtaining a mass ratio between the mass per unit length of the structure and the mass per unit length of the vehicle;
For each of the mass ratio and the support span of the structure, the relationship between the traveling speed of the vehicle and the amount of deflection generated in the structure when the vehicle travels at the traveling speed is determined. And a case where a load corresponding to the mass of the vehicle is moving on the structure at the traveling speed without considering the mass and behavior of the traveling vehicle. Seeking steps,
The natural frequency of the structure when the vehicle travels and the mass and behavior of the traveling vehicle when the mass and behavior of the traveling vehicle are taken into account for each mass ratio and the support span of the structure. The natural frequency of the structure when the vehicle travels when the load corresponding to the mass of the vehicle is moving on the structure at the travel speed without considering the Obtaining a frequency ratio;
And a step of obtaining a relationship between the mass ratio, the support span of the structure, and the natural frequency ratio.
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