| 摘要: | 本研究針對考慮即時濾波之絕對加速度回饋相位控制主動調諧質量阻尼器(Phase Control absolute Acceleration feedback-Active Tuned Mass Damper, PCA-ATMD) 應用於單自由度(Single-Degree-of-Freedom, SDOF)構架與多自由度(Multiple-Degree-of-Freedom, MDOF)構架，結合Bouc-Wen Model進行非線性系統反應之數值模擬，並以構架加裝PCA-ATMD情況進行頻率反應函數、歷時反應分析，且探討各情況之減震效果與特性。相位控制主動調諧質量阻尼器(PC-ATMD)是於調諧質量阻尼器(TMD)與結構間施加控制力，能即時調整TMD之運動，使TMD與結構維持-90度相位差，此時TMD有最大Power Flow，因此減震效果最佳。本文將Bouc-Wen Model回復力與線性回復力相加，得到軟硬化回復力，並保持狀態空間系統矩陣為常係數穩定矩陣，由此軟硬化回復力計算結構進入非線性行為時，可有較佳之數值穩定性。由於本文利用Runge-Kutta Method進行數值模擬分析，需將離散時間之濾波器(Filter)轉移函數(Z-Transfrom)轉為連續時間之濾波器轉移函數，並以構架加裝PCA-ATMD結合濾波器系統，再利用Direct Output Feedback來求得最佳增益矩陣。隨後探討未控制、加裝被動TMD控制與加裝PCA-ATMD控制之頻率反應函數，結果顯示構架達降伏位移後當結構產生輕微非線性行為時，構架加裝PCA-ATMD之反應皆有下降，且優於被動TMD，並具有良好之減震效果；當結構產生較多非線性行為時，構架加裝PCA-ATMD動力系統整體反應皆仍有一定之減震成效，且PCA-ATMD為穩定並具有可控性。最後，數值模擬歷時反應分析以多筆近遠域地震作為地表加速度輸入，得到單自由度與多自由度構架加裝PCA-ATMD之反應。結果顯示，結構進入非線性段時結構系統仍為穩定狀態，其位移與結構基底剪力皆小於未控制或加裝被動TMD，結構之損傷度亦較低。然而，結構絕對加速度反應略為放大，整體而言PCA-ATMD仍有減震效果，但減震效果會逐漸受限。
關鍵字：調諧質量阻尼器、主動控制、相位控制、非線性結構、Bouc-Wen Model、Runge-Kutta Method;The purpose of this study is to verify the application of the Phase Control absolute Acceleration feedback-Active Tuned Mass Damper (PCA-ATMD) with real-time filter to the Single-Degree-of-Freedom (SDOF) and Multiple-Degree-of-Freedom (MDOF) structure, which combines the Bouc-Wen Model to simulate the response of the nonlinear behavior. These structures are implemented with the PCA-ATMD for numerical simulations, including frequency response functions and time history responses analysis. PCA-ATMD is to apply a control force between the TMD mass and the structure, so that the PCA-ATMD can achieve 90-degree phase lag of structure to induce maximum power flow resulting in outstanding vibration reduction capability. In the equation of motion, the Bouc-Wen Model′s restoring force is combined with the linear restoring force of the structure, resulting in a softening-hardening restoring force. This configurtion is to maintain the state-space system matrix as a constant coefficient stable matrix, which leads to improved numerical stability when calculating the structural response under nonlinear behavior. In order to use the Runge-Kutta Method in the numerical simulation analysis, the discrete-time filter transfer function is transformed into a continuous-time filter. Subsequently, the system of the structure with the PCA-ATMD is combined with the filter, and then the Direct Output Feedback is used to optimal design the PCA-ATMD to obtain the optimal gain matrix. This study investigates the frequency response functions of both uncontrolled and controlled structures, the results indicate that when the structure reaches yielding displacement and exhibits slight nonlinear behavior, the response of the structure is suppressed by implemented with the PCA-ATMD, which outperforms the passive Tuned Mass Damper (PTMD). When the structure shows significantly nonlinear behavior, the response of the structure implemented with the PCA-ATMD still exhibits certain seismic reduction effects, and the PCA-ATMD system remains stable and controllable. Finally, time history response analyses are conducted using multiple earthquake records as input ground accelerations, and than the responses of the SDOF and MDOF structure implemented with the PCA-ATMD separately can be obtained. When the structure enters into the nonlinear behavior, the structural responses of displacement and base shear are both less than the uncontrolled and PTMD controlled system. The damage of the structure is therefore reduced and also the active controlled system is still stable. However, the absolute acceleration response of the structure is slightly enlarged. Overall, the PCA-ATMD still exhibits seismic mitigation effects, but the performce is gradually constrained because of the nonlinear behavior of the structure.
Keywords： tuned mass damper, active control, phase control, nonlinear structural behavior, Bouc-Wen Model, Runge-Kutta Method |
