多重調諧質塊阻尼系統之最佳控制理論及應用

Abstract

本文提出多重調諧質塊阻尼系統(MTMD)之廣義最佳設計法，適用於多自由度結構裝置多重TMD系統之設計，不僅擾動頻譜已知時可一併納入最佳化設計中，亦能將降低加速度反應作為最佳化控制目標。本研究經過廣泛之數值實例分析，驗證TMD廣義最佳設計法之正確性及優越性。此外，本文亦建立橋梁在車行載重下之動態反應分析模式，藉以評估高速鐵路營運時可能產生的車-橋共振效應，並探討裝置TMD降低車-橋共振效應之可行性。結果顯示，高鐵在營運車速(300 km/hr)下不致車-橋共振效應，若以次共振車速行駛造成車-橋共振反應時，裝置TMD確能有效降低其動態反應。

In this study, a generalized optimal design theory for multiple TMD (MTMD) structural control systems adaptive to multi-degree-of-freedom structures is developed. By the proposed theory, any specific external excitation can be taken into account in the optimal design if its spectrum is prescribed, and minimization of the acceleration response can be the design objective. Accuracy and superiority of the proposed theory has been verified through extensive numerical analyses. Furthermore, an analytical model for dynamic analysis of bridges subjected to moving vehicles is also developed for assessment of the possible train-bridge resonant effect during operation of the high-speed railway system. Feasibility of implementing TMD system for reducing the train-bridge resonant effect is also discussed. Simulation results indicate that no resonant effect will appear under the desired operating speed (300 km/hr), and the TMD can effectively reduce the resonant effect should resonance occurred by running the train in a sub-resonant speed intentionally.