JP3724829B2 - Vibration control method for elastic structure - Google Patents

Description

【００２６】
ここで、３次モードの節である点２０と点３４の１次の固有モード成分をφ ₁₁，φ₂₁、２次の成分をφ₁₂，φ₂₂とすると、仮の正規モード行列は次のようになる。
【００２７】
【数２】

【００２８】
よって、式(1) は次式で表すことができる。
【００２９】
【数３】

【００３０】
これより質量集中の条件を満たすためには、次の拘束条件を満足しなければならない。
【００３１】
【数４】

【００３２】
そこで、上式を物理モデルの変換誤差と考え、次の誤差関数ε₁ を定義する。
【００３３】
【数５】

【００３４】
この誤差関数ε₁ を零にするような正規化固有モードΦの修正を行うために、Φに対する誤差関数の感度行列を次のようにおく。
【００３５】
【数６】

【００３６】
ここで、φ₁₁、φ₂₁、φ₁₂、φ₂₂について修正量をそれぞれδφ₁₁、δφ₂₁、δφ₁₂、δφ₂₂とすると、誤差関数ε₁ を零とする修正量は次式で求められる。
【００３７】
【数７】

【００３８】
上式に最小ノルム解を使った一般化逆行列を適用すると、修正量は次式で求めることができる。
【００３９】
【数８】

【００４０】
この修正量を用いて誤差関数を零に収束させれば、式(5) を満足する固有モードが得られる。
【００４１】
こうして得た固有モードを式(1),(2) に代入して、質量行列Ｍ、剛性行列Ｋを求めるわけだが、このような値をもつ２自由度系物理モデルは、自由端に仮想のばねを取り付けることによって実現が可能となる。
【００４２】
以下に得られた各物理定数を示す。
【００４３】
Ｍ₁₁＝2.0Kg ，Ｍ₁₂＝1.5Kg
Ｍ₂₁＝1.1Kg ，Ｍ₂₂＝0.8Kg
Ｋ₁₀＝-18532N/m ，Ｋ₁₁＝44904N/m，Ｋ₁₂＝40177N/m
Ｋ₂₀＝-3060N/m，Ｋ₂₁＝7233N/m ，Ｋ₂₂＝6752N/m
さて、以上により作成した集中定数系モデルに基づき状態方程式を導入する。図３に２つの２自由度系に低次元化された制御対象と２つのハイブリッド型のアクチュエータからなる力学モデルを示す。図において、Ｋ₁₀、Ｋ₂₀は低次元化の際に考慮した仮想のばねである。また、用いたハイブリッドアクチュエータの減衰係数は次のようになっている。
【００４４】
Ｃ₁ ＝2.2Ns/m ，Ｃ₂ ＝1.9Ns/m
この力学モデルの運動方程式を求め、状態変数ベクトルを次のように定義すると、
【００４５】
【数９】

【００４６】
状態方程式は次のようになる。
【００４７】
【数１０】

【００４８】
ただし、
【００４９】
【数１１】

【００５０】
Ｋ_c1，Ｋ_c2：各々のアクチュエータの制御力ｆ_c と制御量ｕの関係を示す力変換係数
次に、制御系の設計にはＬＱ制御理論を用いる。設計パラメータは、次に示す線形二次形式の評価関数Ｊに与える重み係数行列Ｑ、Ｒである。ただし、Ｑは状態ベクトルＸに、Ｒは制御量ｕに掛かる重み係数行列である。
【００５１】
【数１２】

【００５２】
ＬＱ制御理論に基づけば、この評価関数Ｊを最小にする制御量ｕは次のように定式化されており、リカッチ方程式を解くことによりフィードバックゲインＫを決定することができる。
【００５３】
【数１３】

【００５４】
ここに、Ｐは次のリカッチ方程式の解である。
【００５５】
【数１４】

【００５６】
図４は、重み係数行列Ｑの違いによる、各構造物の周波数応答を比較したシミュレーション結果を示す。ここで、細い実線は非制御時、中太実線は変位項に次のような重みを掛けた場合、
【００５７】
【数１５】

【００５８】
また、太い実線は速度項に次のような重みを掛けた場合を示す。
【００５９】
【数１６】

【００６０】
同図（ａ）は、各構造物の点20を加振したことによる、各構造物１の点35、（ｂ）は構造物２の点35で、各々観測された周波数応答である。見られるように、構造物１の１次と２次の共振ピークは、5.8Hz と37Hzに現れ、構造物２のそれは、3.2Hz と21Hzに現れている。これらの共振ピークは、変位に重みを掛けた場合には各構造物共に１次のピークは良く抑制されるが、２次はあまり抑制されない。一方、速度に重みを掛けることによって、各構造物共に１次、２次の共振ピークが良く抑制され、良好な振動制御結果が得られることが分る。
【００６１】
次に、各質点のインパルス応答をシミュレーションによって比較したものを図５に示す。ここに、細線は非制御時の応答、太い実線は上記の重みを掛けた場合の制御時の応答を示す。図５（ａ）に見られるように、変位に重みを掛けた場合には、明かに２次モードの振動が良く抑制されないままに持続している。一方、速度項に重みを掛けた場合のインパルス応答を図５（ｂ）に示す。制御を掛けることにより全ての質点において１次と２次モードの振動が速やかに収束していることが確認される。
【００６２】
また、非制御時にも振動が収束していることから、ここで提案するハイブリッド型のアクチュエータは、アクティブ制御が使用できない場合にも、減衰力によりある程度の信頼性を確保できることが確認できる。
【００６３】
次に、上述のシミュレーション結果を確認するために行った制御実験の結果を示す。
【００６４】
先ず図６に実験装置の構成を示す。実験装置は４つの変位センサ、パーソナルコンピュータ、A/D 変換器、D/A 変換器、二つの電磁アクチュエータ３，４、および駆動回路から構成されている。アクチュエータ３，４は、図７に示すコイルと永久磁石からなる非接触の電磁力タイプであり、コイルを巻いたアルミケースと永久磁石との間の渦電流損失によりパッシブ制御力も得ることのできるハイブリッド型のものである。
【００６５】
各板構造物１，２の絶対変位は、変位センサにより検出され、A/D 変換器を介してコンピュータに入力される。そしてコンピュータ内で、入力された変位信号の差分をとることで速度信号を求め、８個の状態量を得ている。また、シミュレーションにより得られたフィードバックゲインを実験でも直接使用して制御系を決定し、制御実験を行っている。
【００６６】
前述の通り、アクチュエータを３次モードの節に設置することで３次モードによる制御スピルオーバを、センサを４次モードの節に設置することで４次モードによる観測スピルオーバを防いでいる。ちなみに、アクチュエータは図２に示す20点と34点付近に、センサは25点と36点付近にそれぞれ設置している。
【００６７】
なお、ここで扱ったような、一様断面、同一高さの構造物では、振動モード形はほぼ類似しており、振動の節も同じ様な位置に現れるので、アクチュエータを同一高さにとる手法にはかなり一般性があると考えている。
【００６８】
図８には、図５（ｂ）のシミュレーションに対応する、速度に重みを掛けた場合のインパルス応答の実験結果を示す。細線が非制御時、太線が制御時の応答であり、これもシミュレーション結果と実験結果は極めてよく一致している。このことは、ここで扱うような分布定数系特性を有する弾性構造物の振動制御における、本モデル化方法の有効性が改めて確認されたことになる。
【００６９】
また、いずれも制御結果においても、全ての質点においてスピルオーバを起こすことなく、１次と２次の振動が速やかに収束していることが確認される。これより、３次と４次のスピルオーバの防止においても、本方法が有効であることが確認できる。また、非制御時の応答よりアクチュエータの信頼性が確認できる。
【００７０】
最後に、各構造物の上部２つのセンサ測定された周波数応答の実験結果を図９に示す。これは速度に重みを掛けた図４のシミュレーション結果に対応するものであるが、これらの実験結果もシミュレーション結果と良く一致しており、各共振ピークが制御によって十分に抑制されている。このことは、各振動モードがアクティブにダンピングを得たことを示すものであり、超々高層ビルのダンピング不足による風励振の問題は、このような振動制御方法で解消できることを示している。
【００７１】
このように、アクチュエータを含む制振系が最適化され、超々高層ビルなどで課題となる風による揺れ制御に、かかる弾性構造物のモデル化方法及び振動制御方法が有効であることが確認された。
【００７２】
尚、かかる方法は、高層ビルに限らず宇宙構造物、弾性車両、建築機械等、並立する構造物が存在する多くの対象に対して適用可能である。
【００７３】
【発明の効果】
本発明は次の如き優れた効果を発揮する。
【００７４】
（１）実際の弾性構造物を最適にモデル化することができる。
【００７５】
（２）最適なモデルに基づく最適な振動制御が可能になる。
【図面の簡単な説明】
【図１】図１０の並立する弾性構造物をモデル化した斜視図である。
【図２】各板構造物の１次から４次までの振動モード形と集中定数系モデルを示し、（ａ）は板構造物１の場合、（ｂ）は板構造物２の場合である。
【図３】２つのアクチュエータを有する並立構造物の力学モデルを示す。
【図４】周波数応答のシミュレーション結果を示し、（ａ）は板構造物１の場合、（ｂ）は板構造物２の場合である。
【図５】インパルス応答のシミュレーション結果を示し、（ａ）は変位に重みを掛けた場合、（ｂ）は速度に重みを掛けた場合である。
【図６】実験装置の構成図である。
【図７】アクチュエータを示す分解斜視図である。
【図８】速度に重みを掛けたときのインパルス応答の実験結果を示し、（ａ）は板構造物１の場合、（ｂ）は板構造物２の場合である。
【図９】周波数応答の実験結果を示し、（ａ）は板構造物１の場合、（ｂ）は板構造物２の場合である。
【図１０】並立する弾性構造物即ち超高層ビルを示す斜視図である。
【符号の説明】
１，２ 板構造物
ａ，ｂ 弾性構造物
ｃ アクチュエータ[0001]
[Industrial application fields]
The present invention relates to an elastic structure modeling method and a vibration control method, and more particularly to an elastic structure modeling method and a vibration control method that are effective in damping control of an elastic structure such as a high-rise building. .
[0002]
[Prior art]
With the development of science and technology, it has become possible to further increase the height of structures such as high-rise buildings and main towers of bridges, but there has been a problem of controlling fluctuations in the wind. Accordingly, attention has been paid to a vibration control method of an elastic structure of an active mass damper system that obtains a damping force by using an inertial force of mass, and many examples of application to a high-rise building have come to be seen in practice. However, if the high-rise building such as the recently announced 1000m-class skyscraper future concept is further advanced, the vibration caused by the wind will become a long cycle, and it will be difficult to obtain sufficient control power with the active mass damper system. It is expected that. Therefore, as an alternative vibration control method, a method called a building connection method has been proposed in which structures are arranged side by side, a plurality of actuators are arranged between the structures, and vibration is controlled simultaneously by the interaction of the structures. (Japanese Patent Application No.5-141917 etc.).
[0003]
More specifically, this vibration control method is a method of actively and simultaneously controlling the vibration of a structure by an actuator disposed between the two using an interaction between opposing elastic structures. When this method is compared with the active mass damper method, it has the following characteristics.
[0004]
(1) Since the damping force is received by the reaction force of each structure, static and dynamic damping force can be obtained. There is no problem of damping force against long-period shaking.
[0005]
(2) Since no auxiliary mass is required, the vibration damping device is reduced in weight, and its installation space is not required.
[0006]
(3) The connecting portion by the actuator can be used effectively for a passage connecting the two buildings.
[0007]
FIG. 10 shows two side-by-side elastic structures or skyscrapers to which this scheme is applied. Each building a and b alone is shaken by strong winds and the habitability is severely impaired. However, several control devices (actuators) c are arranged between the high-rise buildings a and b, and the buildings a and b shake each other. If we stop, this problem is solved. It is also possible to use the inside of the control device c as a passage. If this is used positively, a three-dimensional transportation system will be formed, and a convenient and comfortable skyscraper group will be constructed.
[0008]
[Problems to be solved by the invention]
By the way, in the past, two elastic structures close to a lumped parameter system, which is easy to design the control system, are arranged side by side, and the vibration control effect of the building connection system is investigated with the object of vibration control as a one-degree-of-freedom system. The system has been expanded to confirm its effectiveness through numerical analysis and experiments.
[0009]
However, the actual structure is a distributed parameter system, and there is no effective control system design method for controlling the vibration of the distributed parameter system.
[0010]
Accordingly, the present invention has been created to solve the above-mentioned problems, and the purpose of the present invention is to make an actual elastic structure into a low-dimensional model optimally in a lumped parameter system, and to enable optimal vibration control based on this model. Another object is to provide a modeling method and a vibration control method for an elastic structure.
[0011]
[Means for Solving the Problems]
In order to achieve the above object, the present invention provides a flexible constant distribution characteristic when controlling vibrations by connecting parallel elastic structures with an actuator and applying force via the actuator. The plate structures are arranged side by side, the vibration mode shape of each plate structure is analyzed, and the order of the vibration mode to be controlled is obtained and the higher order is ignored and ignored for the purpose of reducing the order. Determine the vibration node of the lowest order higher order mode, place the experimental actuators in the obtained nodes and sandwich them between the plate structures, thereby creating an experimental model that virtualizes the elastic structure, Each plate structure of the above experimental model is modeled as a lumped parameter system with the vibration node of the lowest order higher order mode as the mass point, and the experimental actuator is modeled to create a dynamic model. Then, based on the equation of state calculated from the dynamic model, obtain the control amount of the experimental actuator to control the vibration of the experimental model, and optimize the damping system of the elastic structure based on this To do .
[0013]
[Action]
According to the former, the elastic structure is hypothesized as a distributed constant system structure and is treated as a distributed constant system model.
[0014]
Further, according to the latter, the vibration damping system is optimized based on the distributed parameter system model.
[0015]
【Example】
Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings.
[0016]
FIG. 1 is a diagram in which the side-by-side elastic structure shown in FIG. 10 is modeled as a distributed constant plate structure. As shown in the figure, the model M (experimental model) includes two flexible plate structures 1 and 2 arranged side by side, and two actuators (experimental actuators) 3 and 4 sandwiched therebetween. The plate structures 1 and 2 have a rectangular shape, each having a height equal to L = 1000 mm, a width equal to W = 70 mm, and a thickness different from t ₁ = 8 mm and t ₂ = 12 mm. The plate structures 1 and 2 have typical distributed constant system characteristics. Since an actual skyscraper is an elastic structure close to a distributed constant system, an actual elastic structure can be optimally modeled by virtualizing it as plate structures 1 and 2 that are vibration models. . The details of the actuators 3 and 4 will be described later.
[0017]
By the way, when a plate structure having such a distributed constant system characteristic is used as a vibration control target, a problem is how to reduce the order from a distributed constant system to a lumped constant system. Therefore, in the following, the primary and secondary vibration modes of two parallel plate structures are determined as control objects, and the parallel plate structures are considered as two single structures, and each has a two-degree-of-freedom low-dimensional system. Create a physical model. In particular, in this case, the “method of creating a low-dimensional model utilizing uncontrollability and unobservability” proposed by the present inventors is used (reference: Kazuto Sado, active control of vibration, Acoustical Society of Japan 47, 9 (pp. 668-677, 1991).
[0018]
In general, LQ control theory is used for control system design. However, since there is no appropriate low-dimensional model creation method, generation of unstable vibration called spillover is a problem. Therefore, this proposed method takes advantage of the uncontrollable and unobservable nature of the mode-shaped nodes structurally, taking into account the prevention of spillover of higher-order modes ignored for lower dimensions This is a technique for creating a lumped parameter model with a specified point as a mass point. The experimental mode analysis and sensitivity analysis are used to correct the eigenmode matrix to obtain physical quantities such as mass and spring constant. In the following, the procedure for creating a low-dimensional model is briefly described.
[0019]
(1) Analyze the vibration mode shape of each plate structure by the experimental mode analysis method or FEM.
[0020]
(2) Specify the vibration node of the lowest order higher order mode that should be ignored for reduction of dimensions as the mass point of the lumped parameter model.
[0021]
(3) At that point, the mode component of the controlled object mode is read and a temporary mode matrix is created.
[0022]
(4) The mode matrix is modified by applying the sensitivity analysis method, and the physical quantity of the lumped parameter system is obtained using it.
[0023]
FIG. 2 shows the first to fourth vibration mode shapes of the plate structures 1 and 2 obtained by the experimental mode analysis method. Here, up to the second-order mode is the vibration suppression target mode, and the two-degree-of-freedom system model as shown in the figure is set with the two nodes of the third-order mode as the mass points. If an actuator is attached to the actuator, the third-order mode is not excited and control spillover of the third-order mode is prevented. In addition, if a sensor is attached to the fourth-order mode node, the fourth-order mode observation spillover will not occur.
[0024]
Here, a physical model having two masses and a spring shown in FIG. 2 is assumed, and a two-degree-of-freedom physical model is created from first-order and second-order modal parameters. Here, the eigenmode that is normalized so that the mode mass becomes a unit matrix is called a normalized eigenmode Φ, and when the frequency matrix having the natural frequency as a diagonal element is denoted by Ω, the mass matrix M and the stiffness matrix K Is as follows.
[0025]
[Expression 1]

[0026]
Here, assuming that the primary eigenmode components of points 20 and 34 which are nodes of the third-order mode are φ ₁₁ and φ ₂₁ , and the second-order components are φ ₁₂ and φ ₂₂ , the temporary normal mode matrix is It becomes like this.
[0027]
[Expression 2]

[0028]
Therefore, Formula (1) can be expressed by the following formula.
[0029]
[Equation 3]

[0030]
In order to satisfy the mass concentration condition, the following constraint condition must be satisfied.
[0031]
[Expression 4]

[0032]
Therefore, considering the above equation as a conversion error of the physical model, the following error function ε ₁ is defined.
[0033]
[Equation 5]

[0034]
In order to correct the normalized eigenmode Φ so that the error function ε ₁ becomes zero, the sensitivity matrix of the error function with respect to Φ is set as follows.
[0035]
[Formula 6]

[0036]
Here, assuming that the correction amounts for φ ₁₁ , φ ₂₁ , φ ₁₂ , and φ ₂₂ are δφ ₁₁ , δφ ₂₁ , δφ ₁₂ , and δφ ₂₂ , the correction amounts that make the error function ε ₁ zero are obtained by the following equations.
[0037]
[Expression 7]

[0038]
Applying the generalized inverse matrix using the minimum norm solution to the above equation, the correction amount can be obtained by the following equation.
[0039]
[Equation 8]

[0040]
If the error function is converged to zero using this correction amount, an eigenmode satisfying Equation (5) is obtained.
[0041]
Substituting the eigenmodes obtained in this way into equations (1) and (2) to find the mass matrix M and stiffness matrix K. The two-degree-of-freedom physical model with these values Realization is possible by attaching a spring.
[0042]
Each physical constant obtained is shown below.
[0043]
M ₁₁ = 2.0Kg, M ₁₂ = 1.5Kg
M ₂₁ = 1.1Kg, M ₂₂ = 0.8Kg
_{K 10 = -18532N / m, K} 11 = 44904N / m, K 12 = 40177N / m
_{K 20 = -3060N / m, K} 21 = 7233N / m, K 22 = 6752N / m
Now, the equation of state is introduced based on the lumped parameter system model created as described above. FIG. 3 shows a dynamic model composed of a controlled object reduced to two two-degree-of-freedom systems and two hybrid actuators. In the figure, K ₁₀ and K ₂₀ are virtual springs that are taken into consideration when the dimensions are reduced. The damping coefficient of the hybrid actuator used is as follows.
[0044]
C ₁ = 2.2Ns / m, C ₂ = 1.9Ns / m
Obtaining the equation of motion of this dynamic model and defining the state variable vector as
[0045]
[Equation 9]

[0046]
The equation of state is as follows.
[0047]
[Expression 10]

[0048]
However,
[0049]
[Expression 11]

[0050]
K _c1 , K _c2 : Force conversion coefficients indicating the relationship between the control force f _c of each actuator and the control amount u Next, LQ control theory is used for designing the control system. The design parameters are weight coefficient matrices Q and R given to the evaluation function J in the linear quadratic form shown below. Here, Q is a state vector X, and R is a weighting coefficient matrix applied to the control amount u.
[0051]
[Expression 12]

[0052]
Based on the LQ control theory, the control amount u that minimizes the evaluation function J is formulated as follows, and the feedback gain K can be determined by solving the Riccati equation.
[0053]
[Formula 13]

[0054]
Here, P is a solution of the following Riccati equation.
[0055]
[Expression 14]

[0056]
FIG. 4 shows a simulation result in which the frequency response of each structure is compared due to the difference in the weighting coefficient matrix Q. Here, when the thin solid line is not controlled, the thick solid line is multiplied by the following weight on the displacement term:
[0057]
[Expression 15]

[0058]
A thick solid line indicates a case where the following weight is applied to the speed term.
[0059]
[Expression 16]

[0060]
FIG. 6A shows the frequency response observed at the point 35 of each structure 1 and FIG. 5B shows the frequency response observed at the point 35 of the structure 2 due to the vibration of the point 20 of each structure. As can be seen, the primary and secondary resonance peaks of structure 1 appear at 5.8 Hz and 37 Hz, and that of structure 2 appears at 3.2 Hz and 21 Hz. As for these resonance peaks, when the weight is applied to the displacement, the primary peak is well suppressed in each structure, but the secondary is not much suppressed. On the other hand, it can be seen that by applying a weight to the speed, the primary and secondary resonance peaks of each structure are well suppressed and a good vibration control result can be obtained.
[0061]
Next, FIG. 5 shows a comparison of impulse responses of the respective mass points by simulation. Here, the thin line shows the response at the time of non-control, and the thick solid line shows the response at the time of control when the above weight is applied. As seen in FIG. 5 (a), when the displacement is weighted, the vibration in the secondary mode is clearly not suppressed well. On the other hand, FIG. 5B shows the impulse response when the speed term is weighted. By applying the control, it is confirmed that the vibrations of the primary and secondary modes are quickly converged at all mass points.
[0062]
In addition, since the vibration converges even during non-control, it can be confirmed that the hybrid actuator proposed here can secure a certain degree of reliability by the damping force even when active control cannot be used.
[0063]
Next, the result of the control experiment performed in order to confirm the above-mentioned simulation result is shown.
[0064]
First, FIG. 6 shows the configuration of the experimental apparatus. The experimental device consists of four displacement sensors, a personal computer, an A / D converter, a D / A converter, two electromagnetic actuators 3 and 4, and a drive circuit. The actuators 3 and 4 are non-contact electromagnetic force types composed of a coil and a permanent magnet shown in FIG. 7, and a hybrid capable of obtaining a passive control force by eddy current loss between the aluminum case wound with the coil and the permanent magnet. Of the type.
[0065]
The absolute displacement of each plate structure 1 and 2 is detected by a displacement sensor and input to a computer via an A / D converter. In the computer, the speed signal is obtained by taking the difference between the input displacement signals, and eight state quantities are obtained. In addition, the feedback gain obtained by the simulation is directly used in the experiment to determine the control system and conduct the control experiment.
[0066]
As described above, the control spillover by the third-order mode is prevented by installing the actuator in the third-order mode section, and the observation spillover by the fourth-order mode is prevented by installing the sensor in the fourth-order mode section. Incidentally, the actuators are installed near the 20 and 34 points shown in FIG. 2, and the sensors are installed near the 25 and 36 points, respectively.
[0067]
In the structure with the same cross section and the same height as described here, the vibration mode shape is almost similar, and the vibration nodes appear at the same position. I think the method is quite general.
[0068]
FIG. 8 shows the experimental results of the impulse response when the speed is weighted, corresponding to the simulation of FIG. The thin line is the non-control response and the thick line is the control response. The simulation results and the experimental results also agree very well. This confirms the effectiveness of the present modeling method in vibration control of an elastic structure having distributed constant system characteristics as dealt with here.
[0069]
Also, in both control results, it is confirmed that the primary and secondary vibrations converge quickly without causing spillover at all mass points. From this, it can be confirmed that the present method is also effective in preventing third-order and fourth-order spillover. In addition, the reliability of the actuator can be confirmed from the response during non-control.
[0070]
Finally, the experimental results of the measured frequency response of the top two sensors of each structure are shown in FIG. This corresponds to the simulation result of FIG. 4 in which the speed is weighted, but these experimental results also agree well with the simulation results, and each resonance peak is sufficiently suppressed by the control. This indicates that each vibration mode has actively obtained damping, and that the problem of wind excitation due to insufficient damping of a super high-rise building can be solved by such a vibration control method.
[0071]
In this way, the damping system including the actuator has been optimized, and it has been confirmed that the modeling method and the vibration control method of such an elastic structure are effective for the vibration control due to wind, which is a problem in ultra-high-rise buildings and the like. .
[0072]
In addition, this method is applicable not only to a high-rise building but to many objects in which a parallel structure exists such as a space structure, an elastic vehicle, and a construction machine.
[0073]
【The invention's effect】
The present invention exhibits the following excellent effects.
[0074]
(1) An actual elastic structure can be modeled optimally.
[0075]
(2) Optimal vibration control based on the optimal model becomes possible.
[Brief description of the drawings]
1 is a perspective view modeling the side-by-side elastic structures of FIG. 10;
FIGS. 2A and 2B show vibration mode shapes from the first to fourth orders and a lumped parameter system model of each plate structure, where FIG. 2A shows the case of the plate structure 1 and FIG. 2B shows the case of the plate structure 2; .
FIG. 3 shows a dynamic model of a side-by-side structure with two actuators.
4A and 4B show simulation results of frequency response, where FIG. 4A shows the case of the plate structure 1 and FIG. 4B shows the case of the plate structure 2;
FIGS. 5A and 5B show simulation results of impulse responses, in which FIG. 5A shows a case where weight is applied to displacement, and FIG. 5B shows a case where weight is applied to velocity.
FIG. 6 is a configuration diagram of an experimental apparatus.
FIG. 7 is an exploded perspective view showing an actuator.
FIGS. 8A and 8B show experimental results of impulse responses when weight is applied to the speed, where FIG. 8A shows the case of the plate structure 1 and FIG. 8B shows the case of the plate structure 2;
9A and 9B show experimental results of frequency response, where FIG. 9A shows the case of the plate structure 1, and FIG. 9B shows the case of the plate structure 2. FIG.
FIG. 10 is a perspective view showing a side-by-side elastic structure or skyscraper.
[Explanation of symbols]
1, 2 Plate structure a, b Elastic structure c Actuator

Claims (1)

When controlling vibrations by connecting parallel elastic structures to each other with an actuator and applying a force through the actuator,
Flexible plate structures with distributed constant system characteristics are arranged side by side, the vibration mode shapes of each plate structure are analyzed, and the order of the vibration mode to be controlled is obtained for further reduction in order to reduce the dimension. Ignore the next and determine the lowest order higher order mode vibration node, and place the experimental actuators in the determined nodes and sandwich them between the plate structures, so that the elastic structure Create a virtual experimental model,
Each plate structure of the experimental model is modeled as a lumped parameter system with the vibration node of the lowest order higher order mode as a mass point, and the experimental actuator is modeled to create a dynamic model,
Based on the equation of state calculated from the dynamic model, obtain the control amount of the experimental actuator for controlling the vibration of the experimental model, and optimize the damping system of the elastic structure based on this A vibration control method for an elastic structure characterized by the above.

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