JP6289929B2

JP6289929B2 - Structure damping device and specification setting method thereof

Info

Publication number: JP6289929B2
Application number: JP2014027316A
Authority: JP
Inventors: 英範木田
Original assignee: Aseismic Devices Co Ltd
Current assignee: Aseismic Devices Co Ltd
Priority date: 2014-02-17
Filing date: 2014-02-17
Publication date: 2018-03-07
Anticipated expiration: 2034-02-17
Also published as: JP2015151785A

Description

本発明は、建物や橋梁などの構造物に対し、その振動を抑制するための構造物の制振装置及びその諸元設定方法に関する。 The present invention relates to a structure damping device for suppressing vibration of a structure such as a building or a bridge, and a specification setting method thereof.

従来、この種の構造物の制振装置として、例えば本出願人がすでに出願し、特許された特許文献１に開示したものが知られている。この制振装置は、ビルなどの建物の構造物を制振するためのものであり、構造物と同じ高さを有するとともに構造物と別個に設置されたフレームと、構造物とフレームの間に設けられたマスダンパとを備えている。フレームは、Ｈ鋼などから成り、鉛直に延びる一対の柱と、両柱間に水平に延びる複数の梁で構成されたラーメン構造を有している。一方、マスダンパは、回転慣性効果を得るための回転マス、及び減衰効果を得るための粘性要素を有しており、構造物及びフレームのそれぞれの最上部間を連結するように設置されている。 2. Description of the Related Art Conventionally, as a vibration damping device for this type of structure, for example, the one already disclosed by the present applicant and disclosed in Patent Document 1 is known. This vibration damping device is for damping a building structure such as a building, and has a frame that is the same height as the structure and is installed separately from the structure, and between the structure and the frame. And a mass damper provided. The frame is made of H steel or the like, and has a frame structure composed of a pair of vertically extending columns and a plurality of beams extending horizontally between both columns. On the other hand, the mass damper has a rotating mass for obtaining a rotational inertia effect and a viscous element for obtaining a damping effect, and is installed so as to connect the uppermost portions of the structure and the frame.

上記のマスダンパ及びフレームによる制振装置により、主振動系としての構造物に付加されかつその構造物の振動を抑制する付加振動系が構成されている。そして、この付加振動系の固有振動数、具体的には、マスダンパの回転マスの回転慣性質量及びフレームの剛性によって定まる固有振動数が、構造物の固有振動数に同調するように設定されている。これにより、構造物が地震などによって振動すると、マスダンパは、構造物とフレームの間の相対変位を回転マスの回転運動に変換しながら、構造物の振動に共振するように作動し、構造物の振動エネルギーを付加振動系で吸収することによって、構造物の振動を抑制する。 The vibration damping device using the mass damper and the frame constitutes an additional vibration system that is added to the structure as the main vibration system and suppresses the vibration of the structure. The natural frequency of the additional vibration system, specifically, the natural frequency determined by the rotational inertial mass of the rotating mass of the mass damper and the rigidity of the frame is set to be synchronized with the natural frequency of the structure. . As a result, when the structure vibrates due to an earthquake or the like, the mass damper operates to resonate with the vibration of the structure while converting the relative displacement between the structure and the frame into the rotational motion of the rotating mass. The vibration of the structure is suppressed by absorbing the vibration energy by the additional vibration system.

特許第５１８９２１３号公報Japanese Patent No. 5189213

一般に、ビルなどの多層建物の構造物では、それを振動モデルでモデル化すると、層数と同じ数の質点が存在し、例えばｎ個の質点（ｎ自由度）を有する多質点系の振動モデルで表される構造物では、その振動は、ｎ個の固有振動数と固有モード（１〜ｎ次モードの振動の形態）を有している。しかし、上記の制振装置では、付加振動系の１つの固有振動数を構造物の１つの固有振動数に同調するように設定することにより、構造物の振動における単一の固有モード（例えば、１次モード）のみを制御することで、構造物を制振している。つまり、制御される単一の固有モード以外の他の固有モードの振動については何ら制御されない。したがって、上記の制振装置では、構造物の振動の全ての固有モード（以下「全次数モード」という）に対する制御、及びそれによる構造物の制振という点では十分とは言えず、改善の余地がある。 In general, in a multi-layer building structure such as a building, when it is modeled by a vibration model, there are as many mass points as the number of layers, for example, a multi-mass point vibration model having n mass points (n degrees of freedom). In the structure represented by the above, the vibration has n natural frequencies and natural modes (1 to n-order mode vibration forms). However, in the above-described vibration damping device, by setting one natural frequency of the additional vibration system to be synchronized with one natural frequency of the structure, a single natural mode (for example, vibration of the structure) (for example, The structure is controlled by controlling only the primary mode. That is, no control is performed for vibrations of other eigenmodes other than the single eigenmode to be controlled. Therefore, the above-described vibration damping device is not sufficient in terms of control over all the eigenmodes of the vibration of the structure (hereinafter referred to as “all-order mode”) and the vibration damping of the structure, and there is room for improvement. There is.

本発明は、以上のような課題を解決するためになされたものであり、構造物の振動の全次数モードを同調効果により制御し、それにより、構造物の振動を適切に抑制することができる構造物の制振装置を提供することを目的とする。 The present invention has been made to solve the above-described problems, and can control all order modes of vibration of a structure by a tuning effect, thereby appropriately suppressing vibration of the structure. An object of the present invention is to provide a structure damping device.

上記の目的を達成するために、請求項１に係る発明は、所定方向に延びるように設置され、複数の質点を有する振動モデルでモデル化可能な構造物に対し、その振動を抑制するための構造物の制振装置であって、構造物の長さ方向に沿って連続的に延び、構造物と別個に設置されたフレームと、各々が慣性質量要素及び減衰要素を有し、複数の質点にそれぞれ対応するとともに、構造物とフレームの間を連結するように設けられた複数のダンパと、を備え、構造物は、各質点及びそれを支持する支持バネ部である主系支持バネ部を一組とする複数組の質点・支持バネ部によって、主振動系を構成し、制振装置は、各ダンパ、及びそれを支持する支持バネ部である、フレームの付加系支持バネ部を一組とし、複数組の質点・支持バネ部と同数でかつこれらにそれぞれ対応する複数組のダンパ・支持バネ部によって、主振動系の振動を抑制するための付加振動系を構成しており、付加振動系の各組のダンパ・支持バネ部において、慣性質量要素の慣性質量、及び付加系支持バネ部の剛性の一方は、主振動系の対応する組の質点・支持バネ部における質点の質量、及び主系支持バネ部の剛性の対応する一方に対し、所定倍数に設定され、慣性質量要素の慣性質量及び付加系支持バネ部の剛性の他方は、設定された所定倍数に応じ、主振動系の全次数モードの固有振動数に対して同調するように設定されることを特徴とする。 In order to achieve the above object, an invention according to claim 1 is provided for suppressing vibration of a structure that is installed so as to extend in a predetermined direction and can be modeled by a vibration model having a plurality of mass points. A structure damping device, which extends continuously along the length of the structure and is installed separately from the structure, each having an inertial mass element and a damping element, and having a plurality of mass points And a plurality of dampers provided so as to connect between the structure and the frame, and the structure includes each mass point and a main system support spring part that is a support spring part that supports the mass point. The main vibration system is constituted by a plurality of sets of mass points and support springs, and the vibration damping device is a set of each damper and a support spring part of the frame, which is a support spring part that supports the damper. the same number and a and a plurality of sets of mass-supporting spring part One of a plurality of sets of damper supporting spring part respectively corresponding to these, constitute an additional vibration system for suppressing the vibration of the main vibration system, in each pair of damper supporting spring part of the additional vibration system, inertial One of the inertial mass of the mass element and the rigidity of the additional system support spring part corresponds to one of the corresponding mass point of the main vibration system, the mass of the mass point in the support spring part, and the corresponding rigidity of the main system support spring part. The other of the inertial mass of the inertial mass element and the rigidity of the additional system support spring is tuned to the natural frequency of all the order modes of the main vibration system in accordance with the predetermined multiple that has been set. It is characterized by being set to.

この構成によれば、所定方向に延びるように設置された構造物の振動が、上記フレーム及び複数のダンパを備えた制振装置によって抑制される。上記の構造物は、複数の質点を有する振動モデルでモデル化可能であり、各質点及びそれを支持する主系支持バネ部を一組とする複数組の質点・支持バネ部によって、制振対象としての主振動系を構成する。また、構造物と別個に設置されたフレームは、構造物の長さ方向に沿って連続的に延びており、複数のダンパは、各々が慣性質量要素及び減衰要素を有し、主振動系の複数の質点にそれぞれ対応するとともに、構造物とフレームの間を連結するように設けられている。加えて、制振装置は、各ダンパ及びそれを支持するフレームの付加系支持バネ部を一組とし、主振動系の複数の質点・支持バネ部と同数でかつこれらにそれぞれ対応する複数組のダンパ・支持バネ部によって、主振動系の振動を抑制するための付加振動系を構成する。そして、付加振動系の各組のダンパ・支持バネ部において、その諸元が、主振動系の対応する組の質点・支持バネ部の諸元に対して、以下のように設定される。 According to this configuration, the vibration of the structure installed so as to extend in the predetermined direction is suppressed by the vibration damping device including the frame and the plurality of dampers. The above structure can be modeled with a vibration model having a plurality of mass points, and is subject to vibration suppression by a plurality of sets of mass points / support spring portions each consisting of each mass point and the main system support spring portion supporting it. As the main vibration system. The frame installed separately from the structure extends continuously along the length direction of the structure, and the plurality of dampers each have an inertial mass element and a damping element, and Each of the mass points is provided so as to connect the structure and the frame. In addition, the vibration damping device includes a set of additional support spring portions of each damper and a frame that supports the damper, and the same number as the plurality of mass points / support spring portions of the main vibration system. The damper / support spring portion constitutes an additional vibration system for suppressing vibration of the main vibration system. The specifications of the damper / support spring part of each set of the additional vibration system are set as follows with respect to the specifications of the corresponding mass point / support spring part of the main vibration system.

具体的には、まず、各組のダンパ・支持バネ部における慣性質量要素の慣性質量、及び付加系支持バネ部の剛性の一方は、主振動系の対応する組の質点・支持バネ部における質点の質量、及び主系支持バネ部の剛性の対応する一方に対し、所定倍数に設定され、慣性質量要素の慣性質量及び付加系支持バネ部の剛性の他方は、設定された所定倍数に応じ、主振動系の全次数モードの固有振動数に対して同調するように設定される。以上により、主振動系の各組の質点・支持バネ部に対し、それらを最適に制振するために、付加振動系の各組のダンパ・支持バネ部における慣性質量要素の慣性質量、及び付加系支持バネ部の剛性が、適切に設定される。 Specifically, first, one of the inertial mass of the inertial mass element in each set of damper / support spring part and the rigidity of the additional system support spring part is the mass point of the corresponding set of the main vibration system and the mass of the support spring part. And the corresponding one of the rigidity of the main system support spring part is set to a predetermined multiple, and the other of the inertia mass of the inertial mass element and the rigidity of the additional system support spring part depends on the set predetermined multiple, It is set to be tuned to the natural frequency of all the order modes of the main vibration system. As described above, in order to optimally control the mass points / support springs of each set of the main vibration system, the inertia mass of the inertia mass element in the damper / support spring part of each set of the additional vibration system, and the addition The rigidity of the system support spring is set appropriately.

前述したように、例えばｎ個の質点を有する振動モデルで表される構造物は、ｎ個の固有振動数と固有モードを有しており、それにより、構造物が振動する際には、１〜ｎ次モードの振動が発生する。本発明では、主振動系の複数組の質点・支持バネ部にそれぞれ対応し、かつ諸元が適切に設定された、主振動系と同じ自由度を有する付加振動系の複数組のダンパ・支持バネ部により、全ての質点・支持バネ部を適切に制御しながら、主振動系である構造物を制振する。このように、本発明では、構造物の振動の全次数モードを、主振動系と同じ自由度を有する付加振動系の同調効果により制御し、それにより、構造物の振動を適切に抑制することができる。 As described above, for example, a structure represented by a vibration model having n mass points has n natural frequencies and natural modes, and thus, when the structure vibrates, 1 ~ Nth order mode vibration occurs. In the present invention, a plurality of sets of dampers / supports of an additional vibration system having the same degree of freedom as the main vibration system, each corresponding to a plurality of mass points / support spring portions of the main vibration system and having appropriate specifications. The structure that is the main vibration system is damped while appropriately controlling all the mass points / supporting spring portions by the spring portion. As described above, in the present invention, all order modes of the vibration of the structure are controlled by the tuning effect of the additional vibration system having the same degree of freedom as that of the main vibration system, thereby appropriately suppressing the vibration of the structure. Can do.

請求項２に係る発明は、請求項１に記載の構造物の制振装置において、付加振動系の各組のダンパ・支持バネ部における慣性質量要素の慣性質量ｍd(i)が、主振動系の対応する組の質点・支持バネ部における質点の質量Ｍs(i)のβ倍に設定されたときに、主振動系の各組の質点・支持バネ部における主系支持バネ部の剛性Ｋs(i)に対する付加振動系の対応する組のダンパ・支持バネ部における付加系支持バネ部の剛性ｋb(i)の比である剛性比αが、式（１）又は式（２）で設定され、これらにそれぞれ基づき、剛性ｋb(i)が式（３）又は（４）に基づいて設定されることを特徴とする請求項１に記載の構造物の制振装置。

The invention according to claim 2 is the vibration damping device for a structure according to claim 1, wherein the inertia mass md (i) of the inertia mass element in each damper / support spring portion of the additional vibration system is the main vibration system. Is set to β times the mass Ms (i) of the mass point / support spring part of the corresponding pair of the masses, the rigidity Ks ( The stiffness ratio α, which is the ratio of the stiffness kb (i) of the additional system support spring portion of the corresponding damper / support spring portion of the additional vibration system to i), is set by Formula (1) or Formula (2), 2. The structure damping device according to claim 1, wherein the rigidity kb (i) is set based on each of these, based on the formula (3) or (4). 3.

この構成によれば、付加振動系の各組のダンパ・支持バネ部における慣性質量要素の慣性質量ｍd(i)が、主振動系の対応する組の質点・支持バネ部における質点の質量Ｍs(i)のβ倍に設定されたときに、上記の剛性比αが、式（１）又は式（２）で設定される。そして、これらの式にそれぞれ基づき、各組のダンパ・支持バネ部における付加系支持バネ部の剛性ｋb(i)が、式（３）又は（４）に基づいて設定される。式（１）は、主振動系の相対変位応答を、主振動系と同じ自由度を有する付加振動系の同調効果により最小にするよう、定点理論から得られるものであり、したがって、式（３）に基づいて、上記剛性ｋb(i)が最適に設定される。また、式（２）は、主振動系の絶対加速度応答を、主振動系と同じ自由度を有する付加振動系の同調効果により最小にするよう、定点理論から得られるものであり、したがって、式（４）に基づいて、上記剛性ｋb(i)が最適に設定される。以上のように、付加振動系の各組のダンパ・支持バネ部における付加系支持バネ部の剛性ｋb(i)を、定点理論に基づき、最適に設定することができる。
なお、定点理論とは、動吸振器などの制振器の最適設計に適用される理論であり、構造物の応答倍率曲線のピークを最小化するように、最適同調条件（最適同調振動数比、最適減衰定数）を満足する付加振動系の諸元の最適値を求めるための理論である。 According to this configuration, the inertia mass md (i) of the inertia mass element in each of the damper / support spring portions of the additional vibration system is the mass point Ms ( When β is set to β times i), the rigidity ratio α is set by the equation (1) or the equation (2). Based on each of these equations, the rigidity kb (i) of the additional system support spring portion in each set of damper / support spring portion is set based on the equation (3) or (4). Equation (1) is obtained from the fixed point theory so that the relative displacement response of the main vibration system is minimized by the tuning effect of the additional vibration system having the same degree of freedom as the main vibration system. ), The rigidity kb (i) is optimally set. Equation (2) is obtained from the fixed point theory so that the absolute acceleration response of the main vibration system is minimized by the tuning effect of the additional vibration system having the same degree of freedom as that of the main vibration system. Based on (4), the rigidity kb (i) is optimally set. As described above, the rigidity kb (i) of the additional system support spring part in each set of the damper / support spring part of the additional vibration system can be optimally set based on the fixed point theory.
The fixed point theory is a theory applied to the optimal design of vibration dampers such as dynamic vibration absorbers, and the optimal tuning conditions (optimal tuning frequency ratio so as to minimize the peak of the response magnification curve of the structure. This is a theory for obtaining the optimum value of the specifications of the additional vibration system that satisfies the optimum damping constant.

請求項３に係る発明は、請求項１に記載の構造物の制振装置において、付加振動系の各組のダンパ・支持バネ部における付加系支持バネ部の剛性ｋb(i)が、主振動系の対応する組の質点・支持バネ部における主系支持バネ部の剛性Ｋs(i)のα倍に設定されたときに、主振動系の各組の質点・支持バネ部における質点の質量Ｍs(i)に対する付加振動系の対応する組のダンパ・支持バネ部における慣性質量要素の慣性質量ｍd(i)の比である質量比βが、式（５）又は式（６）で設定され、これらにそれぞれ基づき、慣性質量ｍd(i)が式（７）又は式（８）に基づいて設定されることを特徴とする。

According to a third aspect of the present invention, in the structure damping device according to the first aspect, the rigidity kb (i) of the additional system support spring part in each of the damper / support spring parts of the additional vibration system is the main vibration. The mass Ms of the mass point of each set of the main vibration system and the mass of the support spring when set to α times the stiffness Ks (i) of the main system support spring at the mass / support spring of the corresponding set of the system The mass ratio β, which is the ratio of the inertia mass md (i) of the inertia mass elements in the corresponding damper / support spring portion of the additional vibration system to (i), is set by equation (5) or equation (6), Based on these, the inertial mass md (i) is set based on the formula (7) or the formula (8).

この構成によれば、付加振動系の各組のダンパ・支持バネ部における付加系支持バネ部の剛性ｋb(i)が、主振動系の対応する組の質点・支持バネ部における主系支持バネ部の剛性Ｋs(i)のα倍に設定されたときに、上記の質量比βが、式（５）又は式（６）で設定される。そして、これらの式にそれぞれ基づき、各組のダンパ・支持バネ部における慣性質量要素の慣性質量ｍd(i)が、式（７）又は式（８）に基づいて設定される。式（５）は、主振動系の相対変位応答を、主振動系と同じ自由度を有する付加振動系の同調効果により最小にするよう、定点理論から得られるものであり、したがって、式（７）に基づいて、上記慣性質量ｍd(i)が最適に設定される。また、式（６）は、主振動系の絶対加速度応答を、主振動系と同じ自由度を有する付加振動系の同調効果により最小にするよう、定点理論から得られるものであり、したがって、式（８）に基づいて、上記慣性質量ｍd(i)が最適に設定される。以上のように、付加振動系の各組のダンパ・支持バネ部における慣性質量要素の慣性質量ｍd(i)を、定点理論に基づき、最適に設定することができる。 According to this configuration, the rigidity kb (i) of the additional system support spring portion in the damper / support spring portion of each set of the additional vibration system is equal to the main system support spring in the corresponding mass point / support spring portion of the main vibration system. When set to α times the rigidity Ks (i) of the part, the mass ratio β is set by the equation (5) or the equation (6). Then, based on these formulas, the inertia mass md (i) of the inertia mass element in each set of damper / support spring portions is set based on formula (7) or formula (8). Equation (5) is obtained from the fixed point theory so that the relative displacement response of the main vibration system is minimized by the tuning effect of the additional vibration system having the same degree of freedom as the main vibration system. ), The inertial mass md (i) is optimally set. Equation (6) is obtained from fixed point theory so that the absolute acceleration response of the main vibration system is minimized by the tuning effect of the additional vibration system having the same degree of freedom as that of the main vibration system. Based on (8), the inertial mass md (i) is optimally set. As described above, the inertia mass md (i) of the inertia mass element in each damper / support spring portion of the additional vibration system can be optimally set based on the fixed point theory.

請求項４に係る発明は、請求項２又は３に記載の構造物の制振装置において、αの値を用い、式（９）から最適減衰定数ｈdが設定され、これを用い、付加振動系の各組のダンパ・支持バネ部における減衰要素の減衰係数ｃd(i)が、式（１０）に基づいて設定されることを特徴とする。

The invention according to claim 4 is the structure damping device according to

claim

2 or 3, wherein the value of α is used, the optimum damping constant hd is set from equation (9), and this is used to add the additional vibration system. The damping coefficient cd (i) of the damping element in each set of damper / support spring portion is set based on the equation (10).

この構成によれば、前記αの値を用い、最適減衰定数ｈdが、式（９）で設定される。そして、設定された最適減衰定数ｈdを用い、付加振動系の各組のダンパ・支持バネ部における減衰要素の減衰係数ｃd(i)が、式（１０）に基づいて設定される。式（９）は、主振動系の相対変位応答や絶対加速度応答を、主振動系と同じ自由度を有する付加振動系の同調効果により最小にするよう、定点理論から得られるものであり、したがって、式（１０）に基づいて、付加振動系の上記減衰係数ｃd(i)が最適に設定される。以上のように、付加振動系の各組のダンパ・支持バネ部における減衰要素の減衰係数ｃd(i)を、定点理論に基づき、最適に設定することができる。 According to this configuration, the optimum attenuation constant hd is set by the equation (9) using the value of α. Then, using the set optimum damping constant hd, the damping coefficient cd (i) of the damping element in each set of damper / support spring portion of the additional vibration system is set based on the equation (10). Equation (9) is obtained from fixed point theory so that the relative displacement response and absolute acceleration response of the main vibration system are minimized by the tuning effect of the additional vibration system having the same degree of freedom as the main vibration system. Based on the equation (10), the damping coefficient cd (i) of the additional vibration system is optimally set. As described above, it is possible to optimally set the damping coefficient cd (i) of the damping element in the damper / support spring portion of each set of the additional vibration system based on the fixed point theory.

請求項５に係る発明は、所定方向に延びるように設置され、複数の質点を有する振動モデルでモデル化可能な構造物に対し、その振動を抑制するための構造物の制振装置の諸元設定方法であって、制振装置は、構造物の長さ方向に沿って連続的に延び、構造物と別個に設置されたフレームと、各々が慣性質量要素及び減衰要素を有し、複数の質点にそれぞれ対応するとともに、構造物とフレームの間を連結するように設けられた複数のダンパと、を備えており、構造物は、各質点及びそれを支持する支持バネ部である主系支持バネ部を一組とする複数組の質点・支持バネ部によって、主振動系を構成し、制振装置は、各ダンパ、及びそれを支持する支持バネ部である、フレームの付加系支持バネ部を一組とし、複数組の質点・支持バネ部と同数でかつこれらにそれぞれ対応する複数組のダンパ・支持バネ部によって、主振動系の振動を抑制するための付加振動系を構成しており、付加振動系の各組のダンパ・支持バネ部において、慣性質量要素の慣性質量、及び付加系支持バネ部の剛性の一方を、主振動系の対応する組の質点・支持バネ部における質点の質量、及び主系支持バネ部の剛性の対応する一方に対し、所定倍数に設定する第１工程と、慣性質量要素の慣性要素及び付加系支持バネ部の剛性の他方を、設定された所定倍数に応じ、主振動系の全次数モードの固有振動数に対して同調するように設定する第２工程と、を備えていることを特徴とする。 The invention according to claim 5 is a specification of a structure damping device for suppressing vibration of a structure that is installed so as to extend in a predetermined direction and can be modeled by a vibration model having a plurality of mass points. A damping method, wherein the damping device continuously extends along the length direction of the structure, has a frame installed separately from the structure, each includes an inertial mass element and a damping element, A plurality of dampers corresponding to each of the mass points and connected between the structure and the frame, and the structure is supported by the main system, which is each mass point and a support spring portion that supports the mass points. The main vibration system is constituted by a plurality of mass points / support spring portions including one spring portion, and the vibration damping device is an additional system support spring portion of the frame which is each damper and a support spring portion supporting the damper. It was a set, the plurality of sets of mass-supporting spring part In and by a plurality of sets of damper supporting spring part respectively corresponding to these, it constitutes an additional vibration system for suppressing the vibration of the main vibration system, in each pair of damper supporting spring part of the additional vibration system, One of the inertial mass of the inertial mass element and the rigidity of the additional system support spring is set to one of the corresponding mass of the main vibration system, the mass of the mass in the support spring, and the rigidity of the main system support spring. On the other hand, the first step of setting a predetermined multiple, and the other of the inertial element of the inertial mass element and the rigidity of the additional system support spring part are set to the natural frequencies of all the order modes of the main vibration system according to the predetermined multiple set. And a second step of setting to synchronize with each other.

この構成によれば、前述した請求項１と同様、構造物が各質点及び主系支持バネ部を一組とする複数組の質点・支持バネ部によって主振動系を構成し、制振装置が各ダンパ及び付加系支持バネ部を一組とする複数組のダンパ・支持バネ部によって付加振動系を構成する。そして、付加振動系の各組のダンパ・支持バネ部において、その諸元を、主振動系の対応する組の質点・支持バネ部の諸元に対して、以下のように設定する。 According to this configuration, similarly to the above-described claim 1, the structure includes the main vibration system by the plurality of sets of mass points / support spring portions each including the mass points and the main system support spring portion, and the vibration damping device is The additional vibration system is constituted by a plurality of sets of dampers / support springs each including the dampers and the additional system support springs. The specifications of the damper / support spring portion of each set of the additional vibration system are set as follows with respect to the specifications of the corresponding mass point / support spring portion of the main vibration system.

まず、各組のダンパ・支持バネ部における慣性質量要素の慣性質量、及び付加系支持バネ部の剛性の一方を、主振動系の対応する組の質点・支持バネ部における質点の質量、及び主系支持バネ部の剛性の対応する一方に対し、所定倍数に設定する（第１工程）。次いで、慣性質量要素の慣性質量、及び付加系支持バネ部の剛性の他方を、第１工程において設定された所定倍数に応じ、主振動系の全次数モードの固有振動数に対して同調するように設定する（第２工程）。以上により、主振動系の各組の質点・支持バネ部に対し、それらを最適に制振するために、付加振動系の各組のダンパ・支持バネ部における慣性質量要素の慣性質量、及び付加系支持バネ部の剛性が、適切に設定される。これにより、本発明では、前述した請求項１と同様、主振動系と同じ自由度を有する付加振動系の複数組のダンパ・支持バネ部により、主振動系の全ての質点・支持バネ部を適切に制御しながら、すなわち、構造物の振動の全次数モードを、主振動系と同じ自由度を有する付加振動系の同調効果により制御し、それにより、構造物の振動を適切に抑制することができる。 First, one of the inertial mass of the inertial mass element in each set of damper / support spring part and the rigidity of the additional system support spring part, the mass of the corresponding point in the main vibration system, the mass of the mass point in the support spring part, and the main mass A predetermined multiple is set for one of the corresponding stiffnesses of the system support spring (first step). Next, the other of the inertial mass of the inertial mass element and the rigidity of the additional system support spring portion is tuned to the natural frequency of all the order modes of the main vibration system in accordance with the predetermined multiple set in the first step. (Second step). As described above, in order to optimally control the mass points / support springs of each set of the main vibration system, the inertia mass of the inertia mass element in the damper / support spring part of each set of the additional vibration system, and the addition The rigidity of the system support spring is set appropriately. Thus, in the present invention, as in the first aspect, all mass points / support spring parts of the main vibration system are provided by the plurality of sets of dampers / support spring parts of the additional vibration system having the same degree of freedom as the main vibration system. With proper control, that is, to control all order modes of the structure vibration by the tuning effect of the additional vibration system having the same degree of freedom as the main vibration system, thereby appropriately suppressing the vibration of the structure Can do.

請求項６に係る発明は、請求項５に記載の構造物の制振装置の諸元設定方法において、第１工程において、付加振動系の各組のダンパ・支持バネ部における慣性質量要素の慣性質量ｍd(i)を、主振動系の対応する組の質点・支持バネ部における質点の質量Ｍs(i)のβ倍に設定し、第２工程において、主振動系の各組の質点・支持バネ部における主系支持バネ部の剛性Ｋs(i)に対する付加振動系の対応する組のダンパ・支持バネ部における付加系支持バネ部の剛性ｋb(i)の比である剛性比αを、式（１）又は（２）で設定し、これらにそれぞれ基づき、剛性ｋb(i)を式（３）又は（４）に基づいて設定することを特徴とする。

According to a sixth aspect of the present invention, in the method for setting the specifications of the vibration damping device for a structure according to the fifth aspect, in the first step, the inertia of the inertia mass element in the damper / support spring portion of each set of the additional vibration system The mass md (i) is set to β times the mass Ms (i) of the corresponding set of mass points / support springs in the main vibration system, and in the second step, the mass points / support of each set of main vibration systems The rigidity ratio α, which is the ratio of the rigidity kb (i) of the additional system support spring part in the corresponding damper / support spring part of the additional vibration system to the rigidity Ks (i) of the main system support spring part in the spring part, (1) or (2) is set, and based on these, the rigidity kb (i) is set based on the formula (3) or (4).

この構成によれば、第１工程において、付加振動系の各組のダンパ・支持バネ部における慣性質量要素の慣性質量ｍd(i)を、主振動系の対応する組の質点・支持バネ部における質点の質量Ｍs(i)のβ倍に設定する。次いで、第２工程において、上記の剛性比αを、式（１）又は（２）で設定し、これらにそれぞれ基づき、各組のダンパ・支持バネ部における付加系支持バネ部の剛性ｋb(i)を、式（３）又は（４）に基づいて設定する。前述したように、式（１）は、主振動系の相対変位応答を、主振動系と同じ自由度を有する付加振動系の同調効果により最小にするよう、また式（２）は、主振動系の絶対加速度応答を、主振動系と同じ自由度を有する付加振動系の同調効果により最小にするよう、定点理論から得られるものである。したがって、式（３）又は（４）に基づいて、上記剛性ｋb(i)を設定することにより、前述した請求項２と同様、付加振動系の各組のダンパ・支持バネ部における付加系支持バネ部の剛性ｋb(i)を、定点理論に基づき、最適に設定することができる。 According to this configuration, in the first step, the inertia mass md (i) of the inertia mass element in each damper / support spring portion of the additional vibration system is changed to the corresponding mass point / support spring portion of the main vibration system. Set to β times the mass Ms (i) of the mass point. Next, in the second step, the rigidity ratio α is set by the equation (1) or (2), and based on these, the rigidity kb (i of the additional system support spring part in each set of damper / support spring part is set. ) Is set based on the formula (3) or (4). As described above, equation (1) minimizes the relative displacement response of the main vibration system by the tuning effect of the additional vibration system having the same degree of freedom as the main vibration system, and equation (2) It is obtained from the fixed point theory so that the absolute acceleration response of the system is minimized by the tuning effect of the additional vibration system having the same degree of freedom as the main vibration system. Therefore, by setting the rigidity kb (i) based on the formula (3) or (4), the additional system support in the damper / support spring portion of each set of the additional vibration system is set as in the second aspect. The rigidity kb (i) of the spring portion can be optimally set based on the fixed point theory.

請求項７に係る発明は、請求項５に記載の構造物の制振装置の諸元設定方法において、第１工程において、付加振動系の各組のダンパ・支持バネ部における付加系支持バネ部の剛性ｋb(i)を、主振動系の対応する組の質点・支持バネ部における主系支持バネ部の剛性Ｋs(i)のα倍に設定し、第２工程において、主振動系の各組の質点・支持バネ部における質点の質量Ｍs(i)に対する付加振動系の対応する組のダンパ・支持バネ部における慣性質量要素の慣性質量ｍd(i)の比である質量比βを、式（５）又は（６）で設定し、これらにそれぞれ基づき、慣性質量ｍd(i)を式（７）又は（８）に基づいて設定することを特徴とする。

The invention according to claim 7 is the specification setting method of the vibration damping device for a structure according to claim 5, wherein, in the first step, the additional system support spring part in the damper / support spring part of each set of the additional vibration system The rigidity kb (i) of the main vibration system is set to α times the rigidity Ks (i) of the main system support spring part in the corresponding mass point / support spring part of the main vibration system. The mass ratio β, which is the ratio of the inertia mass md (i) of the inertia mass element in the corresponding damper / support spring of the additional vibration system to the mass Ms (i) of the mass in the mass / support spring of the set (5) or (6) is set, and based on these, inertial mass md (i) is set based on Formula (7) or (8), It is characterized by the above-mentioned.

この構成によれば、第１工程において、付加振動系の各組のダンパ・支持バネ部における付加系支持バネ部の剛性ｋb(i)を、主振動系の対応する組の質点・支持バネ部における主系支持バネ部の剛性Ｋs(i)のα倍に設定する。次いで、第２工程において、上記の質量比βを、式（５）又は（６）で設定し、これらにそれぞれ基づき、各組のダンパ・支持バネ部における慣性質量要素の慣性質量ｍd(i)を、式（７）又は（８）に基づいて設定する。前述したように、式（５）は、主振動系の相対変位応答を、主振動系と同じ自由度を有する付加振動系の同調効果により最小にするよう、また式（６）は、主振動系の絶対加速度応答を、主振動系と同じ自由度を有する付加振動系の同調効果により最小にするよう、定点理論から得られるものである。したがって、式（７）又は（８）に基づいて、上記慣性質量ｍd(i)を設定することにより、前述した請求項３と同様、付加振動系の各組のダンパ・支持バネ部における慣性質量要素の慣性質量ｍd(i)を、定点理論に基づき、最適に設定することができる。 According to this configuration, in the first step, the rigidity kb (i) of the additional system support spring part in each set of damper / support spring part of the additional vibration system is set to the corresponding mass point / support spring part of the main vibration system. Is set to α times the rigidity Ks (i) of the main system support spring portion. Next, in the second step, the mass ratio β is set by the equation (5) or (6), and based on each of these, the inertia mass md (i) of the inertia mass element in each set of damper / support spring portion Is set based on the equation (7) or (8). As described above, equation (5) minimizes the relative displacement response of the main vibration system due to the tuning effect of the additional vibration system having the same degree of freedom as the main vibration system, and equation (6) It is obtained from the fixed point theory so that the absolute acceleration response of the system is minimized by the tuning effect of the additional vibration system having the same degree of freedom as the main vibration system. Therefore, by setting the inertial mass md (i) based on the formula (7) or (8), the inertial mass in each set of damper / support spring part of the additional vibration system is the same as in the third aspect. The inertial mass md (i) of the element can be set optimally based on the fixed point theory.

請求項８に係る発明は請求項６又は７に記載の構造物の制振装置の諸元設定方法において、αの値を用い、式（９）から最適減衰定数ｈdを設定し、これを用い、付加振動系の各組のダンパ・支持バネ部における減衰要素の減衰係数ｃd(i)を、式（１０）に基づいて設定することを特徴とする。

The invention according to claim 8 is the specification setting method of the structure damping device according to

claim

6 or 7, wherein the value of α is used to set the optimum damping constant hd from the equation (9), and this is used. The damping coefficient cd (i) of the damping element in each set of damper / support springs of the additional vibration system is set based on the equation (10).

この構成によれば、まず、前記αの値を用い、式（９）から最適減衰定数ｈdを設定する。そして、設定した最適減衰定数ｈdを用い、付加振動系の各組のダンパ・支持バネ部における減衰要素の減衰係数ｃd(i)を、式（１０）に基づいて設定する。前述したように、式（９）は、主振動系の相対変位応答や絶対加速度応答を、主振動系と同じ自由度を有する付加振動系の同調効果により最小にするよう、定点理論から得られるものである。したがって、式（１０）に基づいて、上記減衰係数ｃd(i)を設定することにより、前述した請求項４と同様、付加振動系の各組のダンパ・支持バネ部における減衰要素の減衰係数ｃd(i)を、定点理論に基づき、最適に設定することができる。 According to this configuration, first, the optimum attenuation constant hd is set from Equation (9) using the value of α. Then, using the set optimum damping constant hd, the damping coefficient cd (i) of the damping element in each set of damper / support spring portion of the additional vibration system is set based on the equation (10). As described above, the equation (9) is obtained from the fixed point theory so as to minimize the relative displacement response and the absolute acceleration response of the main vibration system by the tuning effect of the additional vibration system having the same degree of freedom as the main vibration system. Is. Therefore, by setting the damping coefficient cd (i) based on the expression (10), the damping coefficient cd of the damping element in each damper / support spring portion of each set of the additional vibration system is set as in the above-described fourth aspect. (i) can be set optimally based on fixed point theory.

（ａ）は、本発明の第１実施形態による制振装置を、１０層構造物とともに模式的に示す図であり、（ｂ）は、その構造物及び制振装置を振動モデルでモデル化して示す図である。(A) is a figure which shows the damping device by 1st Embodiment of this invention typically with a 10-layer structure, (b) modeled the structure and the damping device with a vibration model. FIG. 制振装置におけるマスダンパの縦断面図である。It is a longitudinal cross-sectional view of the mass damper in a damping device. 図１（ｂ）と同じモデル図であり、主振動系の各組の質点・支持バネ部の諸元と、付加振動系の各組のダンパ・支持バネ部の諸元との対応関係を示す。It is the same model diagram as FIG.1 (b), and shows the correspondence of the specification of the mass point and support spring part of each group of the main vibration system, and the specification of the damper and support spring part of each group of the additional vibration system . ３層構造物及び制振装置を振動モデルでモデル化して示す図である。It is a figure which models and shows a three-layer structure and a damping device with a vibration model. ３層構造物の各層において、地面からの相対変位応答倍率を示す図であり、（ａ）は構造物のみの場合、（ｂ）は制振装置を適用した場合を示す。It is a figure which shows the relative displacement response magnification from the ground in each layer of a three-layer structure, (a) shows the case where only a structure and (b) show the case where a damping device is applied. ３層構造物の各層において、絶対加速度応答倍率を示す図であり、（ａ）は構造物のみの場合、（ｂ）は制振装置を適用した場合を示す。It is a figure which shows an absolute acceleration response magnification in each layer of a 3 layer structure, (a) shows the case where only a structure is applied, (b) shows the case where a damping device is applied. 本発明の第２実施形態を説明するための図であり、（ａ）は制振装置を高層構造物の上半部に適用した状態を模式的に示す図であり、（ｂ）はその構造物及び制振装置を振動モデルでモデル化して示す図である。It is a figure for demonstrating 2nd Embodiment of this invention, (a) is a figure which shows typically the state which applied the damping device to the upper half part of the high-rise structure, (b) is the structure It is a figure which shows a thing and a damping device modeled with a vibration model. 本発明の第３実施形態を説明するための図であり、（ａ）は制振装置のマスダンパを高層構造物の複数層ごとに設置した状態を模式的に示す図であり、（ｂ）はその構造物及び制振装置を振動モデルでモデル化して示す図である。It is a figure for demonstrating 3rd Embodiment of this invention, (a) is a figure which shows typically the state which installed the mass damper of the damping device for every several layers of a high-rise structure, (b) It is the figure which models the structure and the damping device with the vibration model and shows. 本発明の第４実施形態を説明するための図であり、（ａ）は制振装置を橋梁である構造物とともに模式的に示す図であり、（ｂ）は、その構造物及び制振装置を振動モデルでモデル化して示す図である。It is a figure for demonstrating 4th Embodiment of this invention, (a) is a figure which shows a damping device with the structure which is a bridge typically, (b) is the structure and the damping device It is a figure which models by a vibration model.

以下、図面を参照しながら、本発明の好ましい実施形態を詳細に説明する。図１（ａ）は、本発明の第１実施形態による制振装置１を、構造物２とともに模式的に示し、また同図（ｂ）は、その構造物２及び制振装置１を振動モデルでモデル化して示している。同図（ｂ）に示すように、この振動モデルでは、鉛直方向に延びる構造物２が制振対象としての主振動系Ａを構成し、この主振動系Ａの振動を抑制するための制振装置１が付加振動系Ｂを構成している。 Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the drawings. FIG. 1A schematically shows the vibration damping device 1 according to the first embodiment of the present invention together with the structure 2, and FIG. 1B shows the structure 2 and the vibration damping device 1 as a vibration model. Modeled with As shown in FIG. 5B, in this vibration model, the structure 2 extending in the vertical direction constitutes a main vibration system A as a vibration control target, and vibration suppression for suppressing vibration of the main vibration system A is performed. The apparatus 1 constitutes the additional vibration system B.

構造物２は、例えば、鉄骨構造を有し、基礎３上に立設された１０階建てビルなどから成る１０層構造物である。したがって、この構造物２をモデル化した主振動系Ａは、層数と同じ数の１０個（図１（ｂ）では５個のみ図示）の質点４と、各質点４をそれぞれ支持する支持バネ部（以下「主系支持バネ部」という）５で構成されている。また、この主振動系Ａは、各質点４とそれを支持する主系支持バネ部５を一組とする１０組の質点・支持バネ部６Ａで構成されている。なお、図１（ｂ）に示す各主系支持バネ部５において、上側のばね様の記号５ａは、主系支持バネ部５のせん断剛性を表し、下側の渦巻き様の記号５ｂは、主系支持バネ部５の曲げ剛性を表している。 The structure 2 is, for example, a 10-layer structure including a 10-story building standing on the foundation 3 and having a steel structure. Therefore, the main vibration system A in which the structure 2 is modeled is composed of ten mass points 4 (only five are shown in FIG. 1B) as many as the number of layers, and support springs for supporting the mass points 4 respectively. Part (hereinafter referred to as “main system support spring part”) 5. The main vibration system A is composed of 10 sets of mass points / support springs 6A, each of which is composed of each mass point 4 and a main system support spring 5 supporting the same. In each main system support spring portion 5 shown in FIG. 1B, the upper spring-like symbol 5a represents the shear rigidity of the main system support spring portion 5, and the lower spiral-like symbol 5b represents the main spring-like symbol 5b. The bending rigidity of the system support spring part 5 is shown.

制振装置１は、構造物２とは別個に基礎３上に立設され、構造物２とほぼ同じ高さを有するフレーム７と、構造物２とフレーム７の間を連結するように設けられた１０個のマスダンパ８（ダンパ）とを備えている。 The vibration damping device 1 stands on the foundation 3 separately from the structure 2 and is provided so as to connect the frame 7 having substantially the same height as the structure 2 and the structure 2 and the frame 7. And 10 mass dampers 8 (dampers).

フレーム７は、例えば、Ｈ鋼などから成り、構造物２の外側に、その外壁に沿って上下方向に延びる複数の柱、水平に延びる複数の梁、及び斜めに延びるブレースなどで構成されたラーメン構造を有している。なお、フレーム７は、構造物２の複数の外壁（例えば四方の外壁）に沿って配置してもよく、また、構造物２の外側に限らず、その内側に設けることも可能である。 The frame 7 is made of, for example, H steel, and is composed of a plurality of columns extending vertically along the outer wall of the structure 2, a plurality of beams extending horizontally, a brace extending diagonally, and the like. It has a structure. The frame 7 may be arranged along a plurality of outer walls (for example, four outer walls) of the structure 2, and may be provided not only on the outside of the structure 2 but also on the inside thereof.

一方、マスダンパ８は、本発明者が提案し、特許された前記特許文献１に開示されたものと同じであるので、以下、図２を参照しながら簡単に説明する。同図に示すように、マスダンパ８は、内筒１１、ボールねじ１２及び回転マス１３（慣性質量要素）を有している。内筒１１は、鋼材などで構成され、一端部が開口した円筒状のものであり、他端部は、第１フランジ１４に取り付けられている。 On the other hand, the mass damper 8 is the same as that disclosed in Patent Document 1 proposed and patented by the present inventor, and will be briefly described below with reference to FIG. As shown in the figure, the mass damper 8 includes an inner cylinder 11, a ball screw 12, and a rotary mass 13 (inertial mass element). The inner cylinder 11 is made of a steel material or the like, has a cylindrical shape with one end opened, and the other end is attached to the first flange 14.

また、ボールねじ１２は、ねじ軸１２ａと、ねじ軸１２ａに多数のボール１２ｂを介して螺合するナット１２ｃを有している。ねじ軸１２ａの一端部は、内筒１１の開口に収容され、他端部は、第２フランジ１５に取り付けられている。また、ナット１２ｃは、軸受１６を介して、内筒１１に回転自在に支持されている。 The ball screw 12 includes a screw shaft 12a and a nut 12c that is screwed to the screw shaft 12a via a large number of balls 12b. One end of the screw shaft 12 a is accommodated in the opening of the inner cylinder 11, and the other end is attached to the second flange 15. The nut 12 c is rotatably supported by the inner cylinder 11 via the bearing 16.

回転マス１３は、比重の大きな材料、例えば鉄で構成され、円筒状に形成されている。また、回転マス１３は、内筒１１及びボールねじ１２の外側に、これらを覆うように設けられ、軸受１７を介して、内筒１１に回転自在に支持されている。回転マス１３と内筒１１の間の空間は、一対のリング状のシール材１８、１８で密閉されており、この空間には、シリコンオイルで構成された粘性体１９（減衰要素）が充填されている。さらに、このマスダンパ８には、マスダンパ８自体からの過大な反力が構造物２やフレーム７に作用することによるそれらの損傷などを防止するために、マスダンパ８の軸線方向に作用する荷重を制限するための軸力制限機構１０が設けられている。 The rotary mass 13 is made of a material having a large specific gravity, for example, iron, and is formed in a cylindrical shape. The rotating mass 13 is provided outside the inner cylinder 11 and the ball screw 12 so as to cover them, and is rotatably supported by the inner cylinder 11 via a bearing 17. A space between the rotary mass 13 and the inner cylinder 11 is sealed with a pair of ring-shaped sealing materials 18 and 18, and this space is filled with a viscous body 19 (attenuating element) made of silicon oil. ing. Further, the mass damper 8 limits the load acting in the axial direction of the mass damper 8 in order to prevent an excessive reaction force from the mass damper 8 itself from acting on the structure 2 and the frame 7. An axial force limiting mechanism 10 is provided.

以上のように構成されたマスダンパ８は、両端側の第１フランジ１４及び第２フランジ１５の一方が、構造物２の各層の所定位置（質点４に対応する位置）に連結され、他方がフレーム７に連結されている。構造物２とフレーム７の間に相対変位が発生すると、その直線運動が、ボールねじ１２で回転運動に変換された状態で、回転マス１３に伝達されることによって、回転マス１３が回転する。 In the mass damper 8 configured as described above, one of the first flange 14 and the second flange 15 on both ends is connected to a predetermined position (a position corresponding to the mass point 4) of each layer of the structure 2, and the other is a frame. 7 is connected. When a relative displacement occurs between the structure 2 and the frame 7, the linear motion is transmitted to the rotary mass 13 in a state converted into a rotary motion by the ball screw 12, whereby the rotary mass 13 rotates.

以上の構成のマスダンパ８は、前述したように、構造物２の各層とフレーム７の間を連結するように設けられている。したがって、制振装置１をモデル化した付加振動系Ｂは、１０個の質点４にそれぞれ対応する１０個のマスダンパ８と、各マスダンパ８をそれぞれ支持するフレーム７における１０個の支持バネ部（以下「付加系支持バネ部」という）９で構成されている。また、この付加振動系Ｂは、各マスダンパ８とそれを支持する付加系支持バネ部９を一組とする１０組のダンパ・支持バネ部６Ｂで構成されている。なお、図１に示す各付加系支持バネ部９の２つの記号９ａ及び９ｂはそれぞれ、主系支持バネ部５の記号５ａ及び５ｂと同様、付加系支持バネ部９のせん断剛性及び曲げ剛性を表している。 The mass damper 8 having the above-described configuration is provided so as to connect between each layer of the structure 2 and the frame 7 as described above. Therefore, the additional vibration system B that models the vibration damping device 1 includes ten mass dampers 8 corresponding to the ten mass points 4 and ten support spring portions (hereinafter referred to as the frame dampers 7) that respectively support the mass dampers 8. 9) (referred to as “additional system support spring portion”). The additional vibration system B is composed of 10 sets of damper / support spring portions 6B, each of which includes a mass damper 8 and an additional system support spring portion 9 that supports the mass damper 8. In addition, the two symbols 9a and 9b of each additional system support spring portion 9 shown in FIG. 1 respectively indicate the shear rigidity and bending rigidity of the additional system support spring portion 9 in the same manner as the symbols 5a and 5b of the main system support spring portion 5. Represents.

付加振動系Ｂの各組のダンパ・支持バネ部６Ｂは、主振動系Ａの各組の質点・支持バネ部６Ａにそれぞれ対応するように設けられ、諸元も対応する組の質点・支持バネ部６Ａに応じて、以下のように設定される。なお、この諸元の設定方法には、各組のダンパ・支持バネ部６Ｂにおける回転マス１３の回転慣性質量を先に決める方法（以下「方法１」という）と、各組のダンパ・支持バネ部６Ｂにおける付加系支持バネ部９の剛性を先に決める方法（以下「方法２」という）がある。これらの方法１及び２について、図１及び３を参照しながら順に説明する。 The damper / support spring portion 6B of each set of the additional vibration system B is provided so as to correspond to the mass point / support spring portion 6A of each set of the main vibration system A, and the specifications also correspond to the mass point / support spring of the set. It is set as follows according to the part 6A. This specification setting method includes a method of determining the rotational inertia mass of the rotary mass 13 in each set of damper / support spring portion 6B first (hereinafter referred to as “method 1”), and each set of damper / support spring. There is a method (hereinafter referred to as “method 2”) for determining the rigidity of the additional system support spring portion 9 in the portion 6B first. These methods 1 and 2 will be described in order with reference to FIGS.

方法１
この方法１ではまず、ステップ１（第１工程）として、付加振動系Ｂの各組のダンパ・支持バネ部６Ｂにおける回転マス１３の回転慣性質量ｍd(i)を、主振動系Ａの対応する組の質点・支持バネ部６Ａにおける質点４の質量Ｍs(i)のβ倍に設定する。なお、β倍は、例えば５％や１０％（β＝０．０５、０．１０）などが採用される。 Method 1
In this method 1, first, as step 1 (first process), the rotational inertia mass md (i) of the rotary mass 13 in the damper / support spring portion 6B of each set of the additional vibration system B corresponds to the main vibration system A. It is set to β times the mass Ms (i) of the mass point 4 in the mass point / support spring portion 6A of the set. For example, 5% or 10% (β = 0.05, 0.10) or the like is employed as the β-fold.

次いで、ステップ２（第２工程）として、主振動系Ａの各組の質点・支持バネ部６Ａにおける主系支持バネ部５の剛性（せん断剛性Ｋs(i)及び曲げ剛性Ｋsθ(i)）に対する各組のダンパ・支持バネ部６Ｂにおける付加系支持バネ部９の剛性（せん断剛性ｋb(i)及び曲げ剛性ｋbθ(i)）の比である剛性比αを、下式（１）又は（２）に基づいて算出する。なお、主系支持バネ部５及び付加系支持バネ部９の剛性にはいずれも、せん断剛性に加えて曲げ剛性が含まれているが、以下の説明では適宜、せん断剛性及び曲げ剛性をまとめて、主系支持バネ部５の剛性を「Ｋs(i)」で表し、付加系支持バネ部９の剛性を「ｋb(i)」で表すものとする。

Next, as step 2 (second process), the mass (shear stiffness Ks (i) and bending stiffness Ksθ (i)) of the main system support spring portion 5 in each mass point / support spring portion 6A of the main vibration system A is determined. The rigidity ratio α, which is the ratio of the rigidity (shear rigidity kb (i) and bending rigidity kbθ (i)) of the additional system support spring part 9 in the damper / support spring part 6B of each group, is expressed by the following formula (1) or (2 ). Note that the rigidity of the main system support spring part 5 and the additional system support spring part 9 includes bending rigidity in addition to shear rigidity. However, in the following description, the shear rigidity and bending rigidity are summarized as appropriate. The rigidity of the main system support spring part 5 is represented by “Ks (i)”, and the rigidity of the additional system support spring part 9 is represented by “kb (i)”.

式（１）は、主振動系Ａの相対変位応答を、主振動系Ａと同じ自由度を有する付加振動系Ｂの同調効果により最小にするよう、定点理論から得られるものであり、剛性比αが、ステップ１において設定されたβの値に応じて算出される。一方、式（２）は、主振動系Ａの絶対加速度応答を、主振動系Ａと同じ自由度を有する付加振動系Ｂの同調効果により最小にするよう、定点理論から得られるものであり、剛性比αが、前記βの値に応じて算出される。 Equation (1) is obtained from the fixed point theory so that the relative displacement response of the main vibration system A is minimized by the tuning effect of the additional vibration system B having the same degree of freedom as that of the main vibration system A. α is calculated according to the value of β set in step 1. On the other hand, equation (2) is obtained from the fixed point theory so as to minimize the absolute acceleration response of the main vibration system A by the tuning effect of the additional vibration system B having the same degree of freedom as the main vibration system A. The stiffness ratio α is calculated according to the value of β.

そして、式（１）及び（２）からそれぞれ、下式（３）及び（４）により、各組のダンパ・支持バネ部６Ｂにおける付加系支持バネ部９の剛性ｋb(i)を算出する。

Then, from the equations (1) and (2), the rigidity kb (i) of the additional system support spring portion 9 in the damper / support spring portion 6B of each set is calculated by the following equations (3) and (4).

次いで、主振動系Ａの相対変位応答倍率及び絶対加速度応答倍率曲線の最大値が最小になるように、下式（９）により、付加振動系Ｂの最適減衰定数ｈdを算出する。式（９）は、主振動系Ａの相対変位や絶対加速度応答を、主振動系Ａと同じ自由度を有する付加振動系Ｂの同調効果により最小にするよう、定点理論から得られるものである。そして、算出した最適減衰定数ｈd、主振動系Ａのみの解析モデルの固有値解析結果から得られる１次固有円振動数ωs1、及び各組のダンパ・支持バネ部６Ｂにおける回転マス１３の回転慣性質量ｍd(i)を用い、下式（１０）に基づいて、各組のダンパ・支持バネ部６Ｂにおける粘性体１９による減衰係数ｃd(i)を算出する。

Next, the optimum damping constant hd of the additional vibration system B is calculated by the following equation (9) so that the maximum values of the relative displacement response magnification and the absolute acceleration response magnification curve of the main vibration system A are minimized. Expression (9) is obtained from the fixed point theory so as to minimize the relative displacement and absolute acceleration response of the main vibration system A by the tuning effect of the additional vibration system B having the same degree of freedom as the main vibration system A. . Then, the calculated optimum damping constant hd, the primary natural circular frequency ωs1 obtained from the eigenvalue analysis result of the analysis model of only the main vibration system A, and the rotational inertia mass of the rotary mass 13 in the damper / support spring portion 6B of each pair. Using md (i), the damping coefficient cd (i) by the viscous body 19 in each set of damper / support spring portion 6B is calculated based on the following equation (10).

以上のようにして設定又は算出された付加振動系Ｂの各組のダンパ・支持バネ部６Ｂの諸元、すなわち、回転マス１３の回転慣性質量ｍd(i)、付加系支持バネ部９のせん断剛性ｋb(i)及び曲げ剛性ｋbθ(i)、並びに粘性体１９の減衰係数ｃd(i)は、図３に示すように、剛性比α及び質量比βを用い、主振動系Ａの対応する組の質点・支持バネ部６Ａに応じてそれぞれ設定される。 Specifications of the damper / support spring 6B of each set of the additional vibration system B set or calculated as described above, that is, the rotational inertia mass md (i) of the rotary mass 13 and the shear of the additional system support spring 9 The stiffness kb (i) and the bending stiffness kbθ (i) and the damping coefficient cd (i) of the viscous body 19 correspond to the main vibration system A using the stiffness ratio α and the mass ratio β as shown in FIG. It is set according to the mass point / support spring portion 6A of the set.

方法２
この方法２ではまず、ステップ１（第１工程）として、付加振動系Ｂの各組のダンパ・支持バネ部６Ｂにおける付加系支持バネ部９の剛性ｋb(i)を、主振動系Ａの対応する組の質点・支持バネ部６Ａにおける主系支持バネ部５の剛性Ｋs(i)のα倍に設定する。なお、α倍は、例えば５％や１０％（α＝０．０５、０．１０）などが採用される。 Method 2
In this method 2, first, as step 1 (first process), the rigidity kb (i) of the additional system support spring portion 9 in each damper / support spring portion 6B of the additional vibration system B is determined as the correspondence of the main vibration system A. It is set to α times the rigidity Ks (i) of the main system support spring part 5 in the mass point / support spring part 6A of the set. For example, 5% or 10% (α = 0.05, 0.10) or the like is employed as the α-fold.

次いで、ステップ２（第２工程）として、主振動系Ａの各組の質点・支持バネ部６Ａにおける質点４の質量Ｍs(i)に対する各組のダンパ・支持バネ部６Ｂにおける回転マス１３の回転慣性質量ｍd(i)の比である質量比βを、下式（５）又は（６）に基づいて算出する。

Next, as step 2 (second step), rotation of the rotary mass 13 in each set of damper / support spring 6B with respect to mass Ms (i) of mass 4 in each set of mass / support spring 6A in the main vibration system A The mass ratio β, which is the ratio of the inertial mass md (i), is calculated based on the following formula (5) or (6).

式（５）は、主振動系Ａの相対変位応答を、主振動系Ａと同じ自由度を有する付加振動系Ｂの同調効果により最小にするよう、定点理論から得られるものであり、質量比βが、ステップ１において設定されたαの値に応じて算出される。一方、式（６）は、主振動系Ａの絶対加速度応答を、主振動系Ａと同じ自由度を有する付加振動系Ｂの同調効果により最小にするよう、定点理論から得られるものであり、質量比βが、前記αの値に応じて算出される。 Equation (5) is obtained from the fixed point theory so that the relative displacement response of the main vibration system A is minimized by the tuning effect of the additional vibration system B having the same degree of freedom as that of the main vibration system A. β is calculated according to the value of α set in step 1. On the other hand, equation (6) is obtained from the fixed point theory so as to minimize the absolute acceleration response of the main vibration system A by the tuning effect of the additional vibration system B having the same degree of freedom as the main vibration system A. The mass ratio β is calculated according to the value of α.

そして、式（５）及び（６）からそれぞれ、下式（７）及び（８）により、各組のダンパ・支持バネ部６Ｂにおける回転マス１３の回転慣性質量ｍd(i)を算出する。

Then, the rotary inertia mass md (i) of the rotary mass 13 in each set of damper / support spring portion 6B is calculated from the formulas (5) and (6), respectively, according to the following formulas (7) and (8).

次いで、前述した方法１と同様、主振動系Ａの相対変位応答倍率及び絶対加速度応答倍率曲線の最大値が最小になるように、前記式（９）により、付加振動系Ｂの最適減衰定数ｈdを算出し、それを用い、前記式（１０）に基づいて、各組のダンパ・支持バネ部６Ｂにおける粘性体１９による減衰係数ｃd(i)を算出する。そして、以上のようにして設定又は算出された付加振動系Ｂの各組のダンパ・支持バネ部６Ｂの諸元は、前述した方法１と同様、図３に示すように、主振動系Ａの対応する組の質点・支持バネ部６Ａに応じてそれぞれ設定される。 Next, as in the method 1 described above, the optimum damping constant hd of the additional vibration system B is obtained by the above equation (9) so that the maximum values of the relative displacement response magnification and the absolute acceleration response magnification curve of the main vibration system A are minimized. Is used to calculate the damping coefficient cd (i) due to the viscous body 19 in the damper / support spring portion 6B of each set based on the equation (10). The specifications of the damper / support spring portion 6B of each set of the additional vibration system B set or calculated as described above are the same as those of the method 1 described above, as shown in FIG. It is set in accordance with the corresponding mass point / supporting spring portion 6A.

次に、上述した方法１及び２をそれぞれ適用し、付加振動系Ｂにおける各組のダンパ・支持バネ部６Ｂの具体的な諸元の設定例、及びそれらの振動解析結果について、図１及び図４を参照しながら説明する。本例では、図４のモデル図で示すように、３階建てビルなどから成る３層構造物２２に制振装置２１を適用し、また、その構造物２２である主振動系Ａの諸元は、以下のとおりとする。
各層の質量：Ｍs1＝１２０(ton)、Ｍs2＝１００(ton)、Ｍs3＝１１０(ton)
各層の剛性：Ｋs1＝２００００(kN/m)、Ｋs2＝１９０００(kN/m)、Ｋs3＝１８０００(kN/m) Next, methods 1 and 2 described above are applied, and specific examples of setting specifications of each set of damper / support spring portions 6B in the additional vibration system B and their vibration analysis results are shown in FIGS. This will be described with reference to FIG. In this example, as shown in the model diagram of FIG. 4, the vibration damping device 21 is applied to a three-layer structure 22 composed of a three-story building, and the specifications of the main vibration system A that is the structure 22 are applied. Is as follows.
Mass of each layer: Ms1 = 120 (ton), Ms2 = 100 (ton), Ms3 = 110 (ton)
Rigidity of each layer: Ks1 = 20000 (kN / m), Ks2 = 19000 (kN / m), Ks3 = 18000 (kN / m)

上記の構造物２２のみの固有値解析結果は、下表１のとおりである。

The eigenvalue analysis results of only the structure 22 are as shown in Table 1 below.

また、構造物２２の各層（１Ｆ〜３Ｆ）における各次数モードの固有ベクトルは、下表２のとおりである。

Further, eigenvectors of the respective order modes in the respective layers (1F to 3F) of the structure 22 are as shown in Table 2 below.

まず、方法２を適用し、主振動系Ａの相対変位応答が、主振動系Ａと同じ自由度を有する付加振動系Ｂの同調効果により最小になるように制御する場合について説明する。ステップ１において、図４に示す付加振動系Ｂの各組のダンパ・支持バネ部６Ｂにおける付加系支持バネ部９の剛性ｋb1〜ｋb3を、主振動系Ａの対応する組の質点・支持バネ部６Ａにおける主系支持バネ部５の剛性Ｋs(i)の０．０５倍（α＝０．０５）に設定する。これにより、各組のダンパ・支持バネ部６Ｂにおける付加系支持バネ部９の剛性ｋb1〜ｋb3は、以下のとおりである。
ｋb1＝αＫs1＝１０００(kN/m)
ｋb2＝αＫs2＝９５０(kN/m)
ｋb3＝αＫs3＝９００(kN/m) First, a case will be described in which method 2 is applied and control is performed so that the relative displacement response of main vibration system A is minimized by the tuning effect of additional vibration system B having the same degree of freedom as main vibration system A. In step 1, the rigidity kb1 to kb3 of the additional system support spring 9 in the damper / support spring 6B of each group of the additional vibration system B shown in FIG. The rigidity is set to 0.05 times (α = 0.05) the rigidity Ks (i) of the main system support spring 5 in 6A. As a result, the rigidity kb1 to kb3 of the additional system support spring portion 9 in the damper / support spring portion 6B of each set is as follows.
kb1 = αKs1 = 1000 (kN / m)
kb2 = αKs2 = 950 (kN / m)
kb3 = αKs3 = 900 (kN / m)

次いで、ステップ２において、主振動系Ａの相対変位応答を、主振動系Ａと同じ自由度を有する付加振動系Ｂの同調効果により最小にするよう、前記式（５）に基づき、質量比βが以下のように算出される。
β＝ｍd(i)／Ｍs(i)
＝α／（α＋１）²
＝０．０５／（０．０５＋１）²
＝０．０４５３５１５ Next, in step 2, based on the above equation (5), the mass ratio β is set so that the relative displacement response of the main vibration system A is minimized by the tuning effect of the additional vibration system B having the same degree of freedom as the main vibration system A. Is calculated as follows.
β = md (i) / Ms (i)
= Α / (α + 1) ²
= 0.05 / (0.05 + 1) ²
= 0.0453515

そして、上記の質量比β及び前記式（７）により、付加振動系Ｂの各組のダンパ・支持バネ部６Ｂにおける回転マス１３の回転慣性質量ｍd1〜ｍd3が、以下のように算出される。
ｍd1＝βＭs1＝５．４４２(ton)
ｍd2＝βＭs2＝４．５３５(ton)
ｍd3＝βＭs3＝４．９８９(ton) Then, the rotational inertia masses md1 to md3 of the rotary mass 13 in the damper / support spring portion 6B of each set of the additional vibration system B are calculated by the mass ratio β and the equation (7) as follows.
md1 = βMs1 = 5.442 (ton)
md2 = βMs2 = 4.535 (ton)
md3 = βMs3 = 4.989 (ton)

次いで、前記式（９）に基づき、付加振動系Ｂの最適減衰定数ｈdが以下のように算出される。
ｈd＝√｛（３α）／８（α＋１）｝＝０．１３３３６３０７ Next, based on the equation (9), the optimum damping constant hd of the additional vibration system B is calculated as follows.
hd = √ {(3α) / 8 (α + 1)} = 0.133336307

そして、上記の最適減衰定数ｈdにより、前記式（１０）に基づいて、付加振動系Ｂの各組のダンパ・支持バネ部６Ｂにおける粘性体１９による減衰係数ｃd1〜ｃd3が、以下のように算出される。なお、主振動系Ａのみの１次固有円振動ωs1は、前記表１から、５．９７７２１(rad/s)である。
ｃd1＝２ｈdωs1ｍd1＝８．６９４(kNs/m)
ｃd2＝２ｈdωs1ｍd2＝７．２４５(kNs/m)
ｃd3＝２ｈdωs1ｍd3＝７．９６９(kNs/m) Based on the above equation (10), the damping coefficients cd1 to cd3 due to the viscous body 19 in the damper / support spring portion 6B of each set of the additional vibration system B are calculated by the above-described optimum damping constant hd as follows. Is done. Note that the primary natural circular vibration ωs1 of only the main vibration system A is 5.97721 (rad / s) from Table 1.
cd1 = 2hωs1md1 = 8.694 (kNs / m)
cd2 = 2hωs1md2 = 7.245 (kNs / m)
cd3 = 2hωs1md3 = 7.969 (kNs / m)

以上のように算出された各組のダンパ・支持バネ部６Ｂを備えた付加振動系Ｂである制振装置２１、及び構造物２２の固有値解析結果は、下表３のとおりである。また、これらの制振装置２１及び構造物２２の各層（１Ｆ〜３Ｆ）における各次数モードの固有ベクトルは、下表４のとおりである。

Table 3 below shows the eigenvalue analysis results of the vibration damping device 21 and the structure 22 that are the additional vibration system B including the damper / support spring portion 6B of each set calculated as described above. Further, eigenvectors of the respective order modes in the layers (1F to 3F) of the vibration damping device 21 and the structure 22 are as shown in Table 4 below.

図５は、構造物２２における各層（１Ｆ〜３Ｆ）において、地面からの相対変位応答倍率を示しており、（ａ）は構造物２２のみの場合、（ｂ）は制振装置２１を適用した場合を示している。図５の（ａ）と（ｂ）を対比して明らかなように、制振装置２１を適用した場合には、１Ｆ〜３Ｆの全ての層において、１次〜３次モードのいずれの相対変位応答倍率も低下し、特に、１次モードの振動による相対変位応答倍率が大幅に低減できることがわかる。なお、構造物２２（主振動系）自体の構造減衰は、１次モードに対し１％の剛性比例型減衰として解析している。 FIG. 5 shows the relative displacement response magnification from the ground in each layer (1F to 3F) in the structure 22, where (a) is the structure 22 only, and (b) is the vibration damping device 21 applied. Shows the case. As is clear by comparing (a) and (b) of FIG. 5, when the damping device 21 is applied, any relative displacement in the primary to tertiary modes is applied to all layers 1F to 3F. It can be seen that the response magnification also decreases, and in particular, the relative displacement response magnification due to vibration in the primary mode can be significantly reduced. The structural damping of the structure 22 (main vibration system) itself is analyzed as a stiffness proportional damping of 1% with respect to the primary mode.

次に、方法１を適用し、主振動系Ａの絶対加速度応答が、主振動系Ａと同じ自由度を有する付加振動系Ｂの同調効果により最小になるように制御する場合について説明する。ステップ１において、図４に示す付加振動系Ｂの各組のダンパ・支持バネ部６Ｂにおける回転マス１３の回転慣性質量ｍd(i)を、主振動系Ａの対応する組の質点・支持バネ部６Ａにおける質点４の質量Ｍs(i)の０．０５倍（β＝０．０５）に設定する。これにより、各組のダンパ・支持バネ部６Ｂにおける回転マス１３の回転慣性質量ｍd(i)は、以下のとおりである。
ｍd1＝βＭs1＝６．０(ton)
ｍd2＝βＭs2＝５．０(ton)
ｍd3＝βＭs3＝５．５(ton) Next, a case where the method 1 is applied and control is performed so that the absolute acceleration response of the main vibration system A is minimized by the tuning effect of the additional vibration system B having the same degree of freedom as the main vibration system A will be described. In step 1, the rotary inertia mass md (i) of the rotary mass 13 in each set of damper / support spring portion 6B of the additional vibration system B shown in FIG. The mass is set to 0.05 times the mass Ms (i) of the mass point 4 at 6A (β = 0.05). Thereby, the rotational inertia mass md (i) of the rotary mass 13 in each set of damper / support spring portion 6B is as follows.
md1 = βMs1 = 6.0 (ton)
md2 = βMs2 = 5.0 (ton)
md3 = βMs3 = 5.5 (ton)

次いで、ステップ２により、主振動系Ａの絶対加速度応答を、主振動系Ａと同じ自由度を有する付加振動系Ｂの同調効果により最小にするよう、前記式（２）に基づき、剛性比αが以下のように算出される。
α＝ｋb(i)／Ｋs(i)
＝｛１−√（１−２β）｝／√（１−２β）
＝０．０５４０９３ Next, in step 2, the rigidity ratio α is based on the above equation (2) so that the absolute acceleration response of the main vibration system A is minimized by the tuning effect of the additional vibration system B having the same degree of freedom as the main vibration system A. Is calculated as follows.
α = kb (i) / Ks (i)
= {1-√ (1-2β)} / √ (1-2β)
= 0.054093

そして、上記の剛性比α及び前記式（４）により、付加振動系Ｂの各組のダンパ・支持バネ部６Ｂにおける付加系支持バネ部９の剛性ｋb1〜ｋb3が、以下のように算出される。
ｋb1＝αＫs1＝１０８１．９(kN/m)
ｋb2＝αＫs2＝１０２７．８(kN/m)
ｋb3＝αＫs3＝９７３．７(kN/m) Then, the rigidity kb1 to kb3 of the additional system support spring part 9 in the damper / support spring part 6B of each set of the additional vibration system B is calculated by the rigidity ratio α and the above equation (4) as follows. .
kb1 = αKs1 = 1081.9 (kN / m)
kb2 = αKs2 = 1027.8 (kN / m)
kb3 = αKs3 = 973.7 (kN / m)

次いで、前記式（９）に基づき、付加振動系Ｂの最適減衰定数ｈdが以下のように算出される。
ｈd＝√｛（３α）／８（α＋１）｝＝０．１３８７２１９ Next, based on the equation (9), the optimum damping constant hd of the additional vibration system B is calculated as follows.
hd = √ {(3α) / 8 (α + 1)} = 0.387219

そして、上記の最適減衰定数ｈdにより、前記式（１０）に基づいて、付加振動系Ｂの各組のダンパ・支持バネ部６Ｂにおける粘性体１９による減衰係数ｃd1〜ｃd3が、以下のように算出される。なお、主振動系Ａのみの１次固有円振動ωs1は、前記表１から、５．９７７２１(rad/s)である。
ｃd1＝２ｈdωs1ｍd1＝９．９５０(kNs/m)
ｃd2＝２ｈdωs1ｍd2＝８．２９２(kNs/m)
ｃd3＝２ｈdωs1ｍd3＝９．１２１(kNs/m) Based on the above equation (10), the damping coefficients cd1 to cd3 due to the viscous body 19 in the damper / support spring portion 6B of each set of the additional vibration system B are calculated by the above-described optimum damping constant hd as follows. Is done. Note that the primary natural circular vibration ωs1 of only the main vibration system A is 5.97721 (rad / s) from Table 1.
cd1 = 2hωs1md1 = 9.950 (kNs / m)
cd2 = 2hωs1md2 = 8.292 (kNs / m)
cd3 = 2hωs1md3 = 9.121 (kNs / m)

以上のように算出された各組のダンパ・支持バネ部６Ｂを備えた付加振動系Ｂである制振装置２１、及び構造物２２の固有値解析結果は、下表５のとおりである。また、これらの制振装置２１及び構造物２２の各層（１Ｆ〜３Ｆ）における各次数モードの固有ベクトルは、下表６のとおりである。

Table 5 below shows the eigenvalue analysis results of the vibration damping device 21 and the structure 22 that are the additional vibration system B including the damper / support spring portion 6B of each set calculated as described above. Further, eigenvectors of the respective order modes in the layers (1F to 3F) of the vibration damping device 21 and the structure 22 are as shown in Table 6 below.

図６は、構造物２２における各層（１Ｆ〜３Ｆ）において、絶対加速度応答倍率を示しており、（ａ）は構造物２２のみの場合、（ｂ）は制振装置２１を適用した場合を示している。図６の（ａ）と（ｂ）を対比して明らかなように、制振装置２１を適用した場合には、１Ｆ〜３Ｆの全ての層において、１次〜３次モードのいずれの絶対加速度応答倍率も低下し、特に、１次モードの振動による絶対加速度応答倍率が大幅に低減できることがわかる。なお、構造物２２（主振動系）自体の構造減衰は、１次モードに対し１％の剛性比例型減衰として解析している。 FIG. 6 shows absolute acceleration response magnification in each layer (1F to 3F) in the structure 22, (a) shows the case of the structure 22 only, and (b) shows the case where the vibration damping device 21 is applied. ing. As is clear by comparing (a) and (b) of FIG. 6, when the damping device 21 is applied, any absolute acceleration in the primary to tertiary modes is applied to all layers 1F to 3F. It can be seen that the response magnification also decreases, and in particular, the absolute acceleration response magnification due to vibration in the primary mode can be greatly reduced. The structural damping of the structure 22 (main vibration system) itself is analyzed as a stiffness proportional damping of 1% with respect to the primary mode.

以上詳述したように、本実施形態によれば、構造物２である主振動系Ａの各組の質点・支持バネ部６Ａに対し、制振装置１である付加振動系Ｂの対応する組のダンパ・支持バネ部６Ｂにおける回転マス１３の回転慣性質量ｍd(i)、付加系支持バネ部９の剛性ｋb(i)、及び粘性体１９の減衰係数ｃd(i)が、定点理論に基づいて、最適に設定される。このように、主振動系Ａの複数組の質点・支持バネ部６Ａにそれぞれ対応し、かつ諸元が適切に設定された、主振動系Ａと同じ自由度を有する付加振動系Ｂの複数組のダンパ・支持バネ部６Ｂにより、全ての質点・支持バネ部６Ａを適切に制御しながら、主振動系Ａである構造物２を制振する。その結果、本実施形態では、構造物２の振動の全次数モードを、主振動系Ａと同じ自由度を有する付加振動系Ｂの同調効果により制御し、それにより、構造物２の振動を適切に抑制することができる。 As described in detail above, according to the present embodiment, the corresponding set of the additional vibration system B that is the vibration damping device 1 with respect to the mass point / support spring portion 6A of each set of the main vibration system A that is the structure 2. Based on the fixed point theory, the rotational inertia mass md (i) of the rotary mass 13 in the damper / support spring portion 6B, the rigidity kb (i) of the additional system support spring portion 9, and the damping coefficient cd (i) of the viscous body 19 are Is optimally set. In this way, a plurality of sets of additional vibration systems B having the same degree of freedom as the main vibration system A and corresponding to the plurality of sets of mass points / support spring portions 6A of the main vibration system A and having appropriate specifications. The structure 2 as the main vibration system A is damped while appropriately controlling all the mass points / support springs 6A by the damper / support springs 6B. As a result, in this embodiment, all order modes of the vibration of the structure 2 are controlled by the tuning effect of the additional vibration system B having the same degree of freedom as that of the main vibration system A, thereby appropriately controlling the vibration of the structure 2. Can be suppressed.

図７は、本発明の第２実施形態を示しており、制振装置３１を高層構造物３２の上半部に適用したものである。なお、以下の説明では、前述した第１実施形態と同一の構成部分については、同一の符号を付し、その詳細な説明を省略するものとする。 FIG. 7 shows a second embodiment of the present invention, in which the vibration damping device 31 is applied to the upper half of the high-rise structure 32. In the following description, the same components as those in the first embodiment described above are denoted by the same reference numerals, and detailed description thereof is omitted.

図７（ａ）に示すように、この高層構造物３２は、基礎３上に立設され、３２階建てビルなどから成る３２層の構造物である。また、この構造物３２は、ほぼ上半部（２０層）の上層部３４が、ほぼ下半部（１２層）の下層部３５に対して、セットバックされた状態に構成されている。一方、制振装置３１は、構造物３２における下層部３５の天井部３５ａ上に立設され、上層部３４とほぼ同じ高さを有するフレーム７と、上層部３４の各層とフレーム７の間を連結するように設けられた２０個のマスダンパ８とを備えている。 As shown in FIG. 7 (a), the high-rise structure 32 is a 32-layer structure that is erected on the foundation 3 and includes a 32-story building or the like. In addition, the structure 32 is configured such that the upper layer portion 34 of substantially the upper half (20 layers) is set back with respect to the lower layer portion 35 of the substantially lower half (12 layers). On the other hand, the vibration damping device 31 is erected on the ceiling portion 35 a of the lower layer portion 35 in the structure 32 and has a frame 7 having substantially the same height as the upper layer portion 34, and between each layer of the upper layer portion 34 and the frame 7. 20 mass dampers 8 are provided so as to be connected.

これらの構造物３２及び制振装置３１をモデル化した図７（ｂ）に示すように、構造物３２の上層部３４は、前記第１実施形態と同様、主振動系Ａを構成しており、上層部３４の層数と同じ数の２０個（図７（ｂ）では４個のみ図示）の質点４と、各質点４をそれぞれ支持する主系支持バネ部５により、２０組の質点・支持バネ部６Ａで構成されている。一方、制振装置３１は、前記第１実施形態と同様、付加振動系Ｂを構成しており、２０個のマスダンパ８と、各マスダンパ８をそれぞれ支持するフレーム７における付加系支持バネ部９により、２０組のダンパ・支持バネ部６Ｂで構成されている。そして、本実施形態における付加振動系Ｂの各組のダンパ・支持バネ部６Ｂは、主振動系Ａの各組の質点・支持バネ部６Ａにそれぞれ対応するように設けられ、諸元についても、前述した第１実施形態と同様にして、対応する組の質点・支持バネ部６Ａに応じて設定される。 As shown in FIG. 7B in which the structure 32 and the vibration damping device 31 are modeled, the upper layer portion 34 of the structure 32 constitutes the main vibration system A as in the first embodiment. 20 mass points 4 of the same number as the number of layers of the upper layer portion 34 (only four are shown in FIG. 7B) and the main system support spring portion 5 supporting each mass point 4 respectively, It is comprised by the support spring part 6A. On the other hand, the vibration damping device 31 constitutes the additional vibration system B as in the first embodiment, and includes the 20 mass dampers 8 and the additional system support spring portion 9 in the frame 7 that supports each mass damper 8. , 20 sets of damper / support spring portions 6B. The damper / support spring portion 6B of each set of the additional vibration system B in the present embodiment is provided so as to correspond to the mass point / support spring portion 6A of each set of the main vibration system A. In the same manner as in the first embodiment described above, it is set according to the mass point / support spring portion 6A of the corresponding set.

本実施形態によれば、構造物３２における上層部３４に対し、その振動の全次数モードを、主振動系Ａと同じ自由度を有する付加振動系Ｂの同調効果により制御し、制振効果を向上させることができ、特に、ホイッピング現象などを効果的に防止することができる。 According to this embodiment, with respect to the upper layer part 34 in the structure 32, the total order mode of the vibration is controlled by the tuning effect of the additional vibration system B having the same degree of freedom as the main vibration system A, and the vibration damping effect is controlled. In particular, the whipping phenomenon can be effectively prevented.

図８は、本発明の第３実施形態を示しており、制振装置４１のマスダンパ８を高層構造物４２の複数層ごとに設置したものである。同図（ａ）に示すように、この高層構造物４２は、基礎３上に立設され、例えば２５階建てビルなどからなる２５層の構造物であり、５層ごとに、鉄骨ブレース材の設置により形成されるスーパーラーメンフレーム４３を構成している。一方、制振装置４１は、基礎３上に立設され、構造物４２とほぼ同じ高さを有するフレーム７と、スーパーラーメンフレーム４３に対応する層とフレーム７の間を連結するように設けられた５つのマスダンパ８とを備えている。 FIG. 8 shows a third embodiment of the present invention, in which the mass damper 8 of the vibration damping device 41 is installed for each of the plurality of layers of the high-rise structure 42. As shown in FIG. 5A, the high-rise structure 42 is a 25-layer structure that is erected on the foundation 3 and is composed of, for example, a 25-story building. A super ramen frame 43 formed by installation is formed. On the other hand, the vibration damping device 41 is provided on the foundation 3 so as to connect the frame 7 with the frame 7 having the almost same height as the structure 42 and the layer corresponding to the super-ramen frame 43. And five mass dampers 8.

これらの構造物４２及び制振装置４１をモデル化した図８（ｂ）に示すように、構造物４２は、前記第１実施形態と同様、主振動系Ａを構成しており、スーパーラーメンフレーム４３が配置された層数と同じ数の５個の質点４と、各質点４をそれぞれ支持する主系支持バネ部５により、５組の質点・支持バネ部６Ａで構成されている。一方、制振装置４１は、前記第１実施形態と同様、付加振動系Ｂを構成しており、５個のマスダンパ８と、各マスダンパ８をそれぞれ支持するフレーム７における付加系支持バネ部９により、５組のダンパ・支持バネ部６Ｂで構成されている。そして、本実施形態における付加振動系Ｂの各組のダンパ・支持バネ部６Ｂは、主振動系Ａの各組の質点・支持バネ部６Ａにそれぞれ対応するように設けられ、諸元についても、前述した第１実施形態と同様にして、対応する組の質点・支持バネ部６Ａに応じて設定される。 As shown in FIG. 8B in which the structure 42 and the vibration damping device 41 are modeled, the structure 42 constitutes the main vibration system A as in the first embodiment, and is a super-ramen frame. The five mass points 4 having the same number as the number of layers 43 and the main support spring portions 5 that support the respective mass points 4 are constituted by five sets of mass points / support spring portions 6A. On the other hand, the vibration damping device 41 constitutes the additional vibration system B as in the first embodiment, and includes the five mass dampers 8 and the additional system support spring portion 9 in the frame 7 that supports each mass damper 8. It is composed of five sets of damper / support spring portions 6B. The damper / support spring portion 6B of each set of the additional vibration system B in the present embodiment is provided so as to correspond to the mass point / support spring portion 6A of each set of the main vibration system A. In the same manner as in the first embodiment described above, it is set according to the mass point / support spring portion 6A of the corresponding set.

本実施形態によれば、前述した第１実施形態と同様、構造物４２のスーパーラーメンフレーム（主振動系Ａ）の振動の全次数モードを、主振動系Ａと同じ自由度を有する付加振動系Ｂの同調効果により制御し、それにより、構造物４２の振動を適切に抑制することができる。また、複数層ごとにマスダンパ８を設置するので、各層にマスダンパ８を設置する第１実施形態に比べて、マスダンパ８の設置数を削減でき、その分、制振装置４１の設置コストなどを低減することができる。 According to the present embodiment, as in the first embodiment described above, the additional vibration system having the same degree of freedom as the main vibration system A is used for the all-order mode of vibration of the super-ramen frame (main vibration system A) of the structure 42. It is controlled by the tuning effect of B, whereby the vibration of the structure 42 can be appropriately suppressed. In addition, since the mass dampers 8 are installed for each of the plurality of layers, the number of mass dampers 8 can be reduced as compared with the first embodiment in which the mass dampers 8 are installed in each layer, and the installation cost of the vibration damping device 41 is reduced accordingly. can do.

図９は、本発明の第４実施形態を示しており、制振装置５１を橋梁である構造物５２に適用したものである。同図（ａ）に示すように、この構造物５２は、互いに所定距離を隔てた両岸間においてほぼ水平に延び、両岸の基礎５３、５３を連結するように設けられた鉄骨構造の橋梁である。一方、制振装置５１は、両岸間においてほぼ水平に延び、両端部が両岸の基礎５３、５３に固定され、前記フレーム７と同様に構成されたフレーム５４と、構造物５２とフレーム５４の間を連結するように設けられた複数のマスダンパ８とを備えている。 FIG. 9 shows a fourth embodiment of the present invention, in which the vibration damping device 51 is applied to a structure 52 that is a bridge. As shown in FIG. 2A, this structure 52 is a bridge having a steel structure provided so as to extend horizontally between both banks at a predetermined distance from each other and to connect foundations 53 and 53 on both banks. It is. On the other hand, the vibration damping device 51 extends substantially horizontally between the two banks, and both ends are fixed to the foundations 53, 53 on both banks, and is configured in the same manner as the frame 7, and the structure 52 and the frame 54. And a plurality of mass dampers 8 provided to connect the two.

これらの構造物５２及び制振装置５１をモデル化した図９（ｂ）に示すように、構造物５２は、前記第１実施形態と同様、主振動系Ａを構成しており、複数（本実施形態では８つであり、図９（ｂ）では４つのみ図示）の質点４と、各質点４をそれぞれ支持する主系支持バネ部５により、８組（図９（ｂ）では４組のみ図示）の質点・支持バネ部６Ａで構成されている。一方、制振装置５１は、前記第１実施形態と同様、付加振動系Ｂを構成しており、８個のマスダンパ８と、各マスダンパ８をそれぞれ支持するフレーム５４における付加系支持バネ部９により、８組（図９（ｂ）では４組のみ図示）のダンパ・支持バネ部６Ｂで構成されている。そして、本実施形態における付加振動系Ｂの各組のダンパ・支持バネ部６Ｂは、主振動系Ａの各組の質点・支持バネ部６Ａにそれぞれ対応するように設けられ、諸元についても、前述した第１実施形態と同様にして、対応する組の質点・支持バネ部６Ａに応じて設定される。 As shown in FIG. 9B in which the structure 52 and the vibration damping device 51 are modeled, the structure 52 constitutes the main vibration system A as in the first embodiment, and a plurality of (this In the embodiment, the number is 8 (only 4 are shown in FIG. 9B), and the main system support spring portion 5 that supports each mass point 4 is 8 sets (4 sets in FIG. 9B). Only the mass point / support spring portion 6A. On the other hand, the vibration damping device 51 constitutes the additional vibration system B, as in the first embodiment, and includes the eight mass dampers 8 and the additional system support spring portion 9 in the frame 54 that supports each mass damper 8. 8 sets (only 4 sets are shown in FIG. 9B) of dampers / support springs 6B. The damper / support spring portion 6B of each set of the additional vibration system B in the present embodiment is provided so as to correspond to the mass point / support spring portion 6A of each set of the main vibration system A. In the same manner as in the first embodiment described above, it is set according to the mass point / support spring portion 6A of the corresponding set.

本実施形態によれば、前述した第１実施形態と同様、構造物５２の振動の全次数モードを、主振動系Ａと同じ自由度を有する付加振動系Ｂの同調効果により制御し、それにより、構造物５２の振動を適切に抑制することができる。 According to the present embodiment, as in the first embodiment described above, the full-order mode of vibration of the structure 52 is controlled by the tuning effect of the additional vibration system B having the same degree of freedom as the main vibration system A, thereby The vibration of the structure 52 can be appropriately suppressed.

なお、本発明は、説明した各実施形態に限定されることなく、種々の態様で実施することができる。例えば、各実施形態の制振装置１、２１、３１、４１及び５１では、本発明の慣性質量要素及び減衰要素として、回転マス１３及び粘性体１９を備えたマスダンパ８を採用したが、本発明はこれに限定されるものではなく、慣性効果及び減衰効果がを得られるとともに、慣性質量及び減衰係数を調整可能なものであれば、種々のダンパを採用することが可能である。 In addition, this invention can be implemented in various aspects, without being limited to each described embodiment. For example, in the vibration damping devices 1, 21, 31, 41 and 51 of the embodiments, the mass damper 8 including the rotating mass 13 and the viscous body 19 is employed as the inertial mass element and the damping element of the present invention. However, the present invention is not limited to this, and various dampers can be employed as long as the inertial effect and the damping effect can be obtained and the inertial mass and the damping coefficient can be adjusted.

また、パルス型の入力による応答性状の向上や、制振装置の設計諸元変動に伴うロバスト性に関する制振効果の向上のために、本発明により算出される付加振動系Ｂの固有振動数を大きい方向、つまり、付加振動系Ｂの剛性を、質量比や剛性比に応じて、硬めに設定してもよい。 In addition, the natural frequency of the additional vibration system B calculated by the present invention is improved in order to improve the response characteristics by the pulse type input and to improve the vibration damping effect related to the robustness due to the fluctuation of the design specifications of the vibration damping device. The rigidity in the larger direction, that is, the rigidity of the additional vibration system B may be set to be hard according to the mass ratio or the rigidity ratio.

さらに、実施形態で示した制振装置１などの細部の構成などは、あくまで例示であり、本発明の趣旨の範囲内で適宜、変更することができる。 Further, the detailed configuration of the vibration damping device 1 and the like shown in the embodiment is merely an example, and can be appropriately changed within the scope of the gist of the present invention.

１制振装置
２構造物
４質点
５主系支持バネ部
６Ａ質点・支持バネ部
６Ｂダンパ・支持バネ部
７フレーム
８マスダンパ（ダンパ）
９付加系支持バネ部
１３回転マス（慣性質量要素）
１９粘性体（減衰要素）
２１制振装置
２２構造物
３１第２実施形態の制振装置
３２第２実施形態の構造物
４１第３実施形態の制振装置
４２第３実施形態の構造物
４３スーパーラーメンフレーム
５１第４実施形態の制振装置
５２第４実施形態の構造物
５４フレーム
Ａ主振動系
Ｂ付加振動系
Ｍs(i) 質点の質量
Ｋs(i) 主系支持バネ部の剛性、主系支持バネ部のせん断剛性
Ｋsθ(i) 主系支持バネ部の曲げ剛性
ｍd(i) 回転マス（慣性質量要素）の慣性質量
ｋb(i) 付加系支持バネ部の剛性、付加系支持バネ部のせん断剛性
ｋbθ(i) 付加系支持バネ部の曲げ剛性
ｈd 最適減衰定数
ｃd(i) 粘性体（減衰要素）の減衰係数 DESCRIPTION OF SYMBOLS 1 Damping device 2 Structure 4 Mass point 5 Main system support spring part 6A Mass point and support spring part 6B Damper and support spring part 7 Frame 8 Mass damper (damper)
9 Additional system support spring 13 Rotating mass (Inertial mass element)
19 Viscous material (damping element)
21 Damping device 22 Structure 31 Damping device 32 of the second embodiment Structure 41 of the second embodiment 41 Damping device of the third embodiment 42 Structure of the third embodiment 43 Super ramen frame 51 Fourth embodiment Vibration damping device 52 Structure 54 of the fourth embodiment Frame A Main vibration system B Additional vibration system Ms (i) Mass of mass Ks (i) Rigidity of main system support spring part, shear rigidity of main system support spring part Ksθ (i) Bending rigidity of main system support spring part md (i) Inertial mass of rotating mass (inertial mass element) kb (i) Additional system support spring part rigidity, additional system support spring part shear rigidity kbθ (i) addition Flexural rigidity of system support spring part hd Optimal damping constant cd (i) Damping coefficient of viscous body (damping element)

Claims

A structure damping device for suppressing vibration of a structure that is installed so as to extend in a predetermined direction and can be modeled by a vibration model having a plurality of mass points,
A frame that extends continuously along the length of the structure and is installed separately from the structure;
A plurality of dampers each having an inertial mass element and a damping element, each corresponding to the plurality of mass points and provided to connect between the structure and the frame;
With
The structure constitutes a main vibration system by a plurality of sets of mass points and support springs, each of which includes the respective mass points and a main system support spring that is a support spring for supporting the mass points.
The vibration damping device is a set of each of the dampers and a support spring part that supports the damper, and the additional system support spring part of the frame, and the same number as the plurality of sets of mass points and support spring parts. An additional vibration system for suppressing the vibration of the main vibration system is constituted by a plurality of corresponding damper / support spring portions,
In the damper / support spring part of each set of the additional vibration system,
One of the inertial mass of the inertial mass element and the rigidity of the additional system support spring part is the mass of the corresponding mass point / support spring part of the main vibration system and the rigidity of the main system support spring part. The other of the inertial mass of the inertial mass element and the rigidity of the additional system support spring portion is set to a full multiple mode of the main vibration system according to the set multiple. A damping device for a structure, which is set so as to be tuned to the natural frequency of the structure.

The inertia mass md (i) of the inertia mass element in the damper / support spring portion of each set of the additional vibration system is the mass point Ms (i) of the mass point in the corresponding set mass point / support spring portion of the main vibration system. Is set to β times
Rigidity of the additional system support spring part in the damper / support spring part corresponding to the additional vibration system with respect to the mass Ks (i) of the main system support spring part in the mass point / support spring part of the main vibration system The stiffness ratio α, which is the ratio of kb (i), is set by the formula (1) or the formula (2). Based on these, the stiffness kb (i) is set based on the formula (3) or (4). The structure damping device according to claim 1, wherein

The rigidity kb (i) of the additional system support spring part in each set of dampers and support spring parts of the additional vibration system is equal to the mass point / support spring part of the corresponding system of the main vibration system. When set to α times the rigidity Ks (i),
The inertia mass md (i) of the inertia mass element in the damper / support spring portion of the corresponding set of the additional vibration system with respect to the mass Ms (i) of the mass point in the mass / support spring portion of each set of the main vibration system The mass ratio β, which is the ratio, is set by the formula (5) or the formula (6), and based on these, the inertial mass md (i) is set based on the formula (7) or the formula (8). The structure damping device according to claim 1, wherein:

Using the value of α, the optimum damping constant hd is set from the equation (9), and using this, the damping coefficient cd (i) of the damping element in each damper / support spring portion of the additional vibration system is The structure damping device according to claim 2, wherein the structure damping device is set based on the formula (10).

A structure setting method for a structure damping device for suppressing vibration of a structure that is installed so as to extend in a predetermined direction and can be modeled by a vibration model having a plurality of mass points,
The vibration damping device extends continuously along the length direction of the structure, has a frame installed separately from the structure, and each includes an inertial mass element and a damping element. A plurality of dampers corresponding to each other and provided to connect between the structure and the frame,
The structure constitutes a main vibration system by a plurality of sets of mass points and support springs, each of which includes the respective mass points and a main system support spring that is a support spring for supporting the mass points.
The vibration damping device is a set of each of the dampers and a support spring part that supports the damper, and the additional system support spring part of the frame, and the same number as the plurality of sets of mass points and support spring parts. An additional vibration system for suppressing the vibration of the main vibration system is constituted by a plurality of corresponding damper / support spring portions,
In the damper / support spring part of each set of the additional vibration system,
One of the inertial mass of the inertial mass element and the rigidity of the additional system support spring part is the same as the mass of the mass point in the corresponding set of mass points and support spring parts of the main vibration system, and the rigidity of the main system support spring part. A first step of setting a predetermined multiple for the corresponding one of
The other of the inertial element of the inertial mass element and the rigidity of the additional system support spring portion is set so as to be tuned to the natural frequency of all the order modes of the main vibration system in accordance with the set multiple. A second step;
A specification setting method for a vibration damping device for a structure, comprising:

In the first step, the inertia mass md (i) of the inertia mass element in each set of damper / support spring portion of the additional vibration system is expressed as the mass point in the corresponding set mass point / support spring portion of the main vibration system. Set to β times the mass Ms (i) of
In the second step, the addition in the damper / support spring portion of the corresponding set of the additional vibration system to the stiffness Ks (i) of the main support spring portion in the mass point / support spring portion of each set of the main vibration system The stiffness ratio α, which is the ratio of the stiffness kb (i) of the system support spring portion, is set by the formula (1) or (2), and based on these, the stiffness kb (i) is set by the formula (3) or (4 6. The specification setting method for the vibration damping device for a structure according to claim 5, wherein the specification is set based on

In the first step, the rigidity kb (i) of the additional system support spring part in each set of damper / support spring part of the additional vibration system is set to the mass point / support spring part of the corresponding group of the main vibration system. Set to α times the rigidity Ks (i) of the main support spring,
In the second step, the inertia of the inertial mass element in the corresponding damper / support spring of the additional vibration system with respect to the mass Ms (i) of the mass in each mass / support spring of the main vibration system The mass ratio β, which is the ratio of the mass md (i), is set by the equation (5) or (6), and based on these, the inertial mass md (i) is based on the equation (7) or (8). The specification setting method of the vibration damping device for a structure according to claim 5, wherein the setting is performed.

Using the value of α, the optimum damping constant hd is set from the equation (9), and using this, the damping coefficient cd (i) of the damping element in the damper / support spring portion of each set of the additional vibration system is The specification setting method of the vibration damping device for a structure according to claim 6 or 7, wherein the setting is performed based on the equation (10).