調諧質量阻尼器最佳化設計與效能之探討

Abstract

調諧質量阻尼器(Tuned Mass Damper, TMD)是目前常見的一種控制震動之方法，對於超高樓層的結構物，常用於抗風用途上。然而，對於TMD 的最佳化設計方法與形式在文獻上與本研究團隊中有許多研究與探討，但討論TMD 效能方面大多著重於折減效果，而忽略強健性的部分，本研究以綜合性指標同時檢討TMD 有效性與強健性之效能，凸顯本研究團隊所提出之懲罰函數考量之重要性，並比較出各形式、方法、目標函數下之TMD 效能優劣。此外，本研究也檢核多筆地震歷時下最佳化TMD 的減振效果。 本研究團隊在過去使用的演算法，因屬於局域、梯度搜尋的方式進行最佳化計算，然而會因為初始條件的不同，而使之落入局域解的可能，必須使用多組的初始條件進行計算，以避免此情況的發生。本研究提出使用兩種最佳化演算法使計算過程能夠快速且更準確的求得最佳設計變數。此外，對於主系統阻尼比大於零之情況，在過去，必須以迭代的方式計算最佳設計變數，而無法以公式直接進行計算，因此本研究也針對此問題，以回歸的方式得出主系統阻尼比大於零時之最佳化設計公式，方便後續學術或實務上使用。 在學術研究上，常常以剪力構架或是將原多自由度模型簡化為單自由度模型進行模擬，一來可以減少計算量，二來能夠使問題更為單純。然而與真實構架相比，確實有差異，因此本研究針對此問題進行TMD 減震誤差的比較與討論。

In recent years, tuned mass dampers have been adopted in high-rise building to reduce the vibration under wind forces. However, there are many researches discussing the reducing effect of different methods and forms of TMDs without considering the robustness. This study used a “composite index” to take both the effectiveness and robustness into consideration, and pointed out the improvements after using the penalty function and compared the TMDs in different forms, methods, and objective functions.Furthermore, the actual earthquake records were used to examine the result statistically in this study. Because the optimization method used in previous study is a gradient-based algorithm, optimal parameters could be the local minimum depending on the given initial conditions. This study used two algorithms to solve this problem thus making it more efficient to get the global minimum. Nevertheless, when the damping ratio of the main system is greater than zero, it is necessary to use the iteration method to obtain the optimal parameters. The equations we proposed to design the optimal TMD was calculated by using the regression method. In the researches, it is quite common to design the TMDs by using the shear type buildings or simplifying MDOF to SDOF rather than the real structure. Although it’s much easier and faster to solve the problem, they are still different from real structures, and this study also precedes to discuss the differences between them.