- 學位論文
應用相位控制於被動及半主動調諧質塊阻尼器之耐震設計
Application of Phase Control for Seismic Design of Passive and Semi-active Tuned Mass Dampers
摘要
本文旨在探討於線性被動式調諧質塊阻尼器 (Tuned Mass Damper, TMD) 之最佳化設計，以及相位控制之控制律 (control algorithm) 於半主動式TMD受基底振動下之減振效益的研究。首先，以單自由度系統加裝一線性被動式TMD，在白雜訊 (white noise) 基底加速度作用下，分別推導其結構位移及絕對加速度均方 (mean square) 最小化，使用迭代法及設計公式等兩種方式，提出線性被動式TMD之參數最佳化設計方法。接著，以相位控制為控制原理，提出一組控制律，欲使半主動式TMD之相對位移與結構位移保持 -90度的相位差。隨後以一週期為3秒之單自由度結構，分別受正弦波與隨機基底加速度作數值模擬，其結果顯示結構加裝TMD後，可有效降低結構整體反應，加裝半主動式TMD可較加裝被動式TMD有更大之減振頻率帶寬，且由頻率比敏感度及TMD阻尼比敏感度分析，半主動式TMD有較好的適應性，不需額外的阻尼；而經由三維圖搜尋半主動式TMD之最佳設計值頻率比與直接取TMD之頻率等於結構第一振態之頻率進行比較，其減振效果差異不大，有著很好的強健性。最後以兩個實際地震歷時進行數值模擬，分別為東西向El Centro地震及300%東西向花蓮331地震，其分析結果顯示，無論是被動式TMD或半主動式TMD，對於降低結構極值之效果皆屬不佳，但半主動式TMD仍對其設計參數不敏感，且相較於被動式TMD，有著更佳的整體減振效果；同樣以三維圖尋找半主動式TMD之最佳設計值頻率比與直接取TMD之頻率等於結構第一振態之頻率進行比較，其減振效果亦差異不大，可不需進行最佳化設計，即可有不錯的減振效果。由上述之模擬，可驗證以此控制律作用之半主動式TMD確實有效並有其優點。
並列摘要
The vibration suppression effect under base excition is proposed in this study that the optimal design for linear passive tuned mass damper (PTMD) and control algorithm of phase control for semi-active tuned mass damper (SATMD). Firstly, a linear tuned mass damper is installed on a single-degree-of-freedom (SDOF) system. The minimum mean square of structural displacement and absolute acceleration can be derived respectively under the white noise base acceleration. So the two methods of optimal parameters design for linear PTMD are proposed by using the iteration method and the design formula. Then making use of the phase control as the control principle, the control algorithm can be proposed. It makes the relative displacement of SATMD maintain 90 degree lag to the structural displacement. The SDOF structure with a period of 3 seconds is subjected to sinusoidal and random base acceleration, respectively. The results of numerical simulations show that after installing TMD, the structural response can be reduced effectively. To compare the effective frequency range of vibration suppression, SATMD is wider than PTMD. In addition, the sensitivity analyses of frequency ratio and TMD damping ratio, respectively, show that SATMD has better adaptability than PTMD and needs no additional damper. Searching through the three-dimensional figure of structural response with frequency ratio and TMD damping ratio can find that the mininmum structural response is little different to the structural response with frequency ratio equals to one. It means that the SATMD a good robustness. Finally, the numerical simulations of two earthquake excitations show some results. Whether the TMD is passive or semi-active, it is not good for reducing the peak value of structural response. However, SATMD is still not sensitive to the parameters and has more effective vibration suppression than PTMD on the whole. Searching through the three-dimensional figure can also find that the mininmum structural response is little different to the structural response with frequency ratio of SATMD equals to one. The SATMD may not need to use the optimal design, and it can have good vibration suppression effect. By the above numerical simulation, it can be verified that the SATMD by using the proposed control algorithm is indeed valid and has its advantages.
參考文獻
延伸閱讀
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