臺灣博碩士論文加值系統

調諧質量阻尼器（Tuned Mass Damper, TMD）是目前常見的一種控制振動的方法，大多裝設於超高樓層建築、大跨度橋梁以及高科技廠房的機台上，以抗振並提高舒適性。然而TMD的參數設置是否得當決定了其效果，過去大多假設主系統不含阻尼，並發展出一系列TMD參數的設計公式，但實際上主系統阻尼並非為零，此時需經由迭代的方式才能求得最佳的設計變數，因此本研究團隊研究開發了一種最佳化架構，藉由兩種最佳化演算法的結合，使得最佳化過程能夠快速且準確的求得最佳設計變數。

一般對於TMD最佳化設計多著重於其折減效果，而忽略強健性方面的問題，事實上TMD的控制效果對頻率相當敏感，當頻率略偏離設計值時，效果會大幅的下降。因此本研究提出了強健式調諧質量阻尼器之最佳化設計方法，同時考慮裝設TMD後的折減效果與頻率有變異性的情況，並比較一般式TMD與強健式TMD的效能優劣。

在學術研究上，常常將原多自由度模型簡化為單自由度模型進行模擬分析，若分析結果與多自由度模型相差不多，則有減少計算量與將問題簡化等優點。此外，由於裝設TMD的結構物有時於地震發生時會有反應放大的情形，本研究亦檢核多筆地震歷時下TMD的減振效果，並比較一般式TMD與強健式TMD於地震下的表現。

In recent years, tuned mass dampers have been widely used to control the vibrations. TMDs are often adopted in high-rise buildings, long-span bridges, and machines of high-tech factory to reduce the vibration and the discomfort. However, the values of TMD parameters determine the effectiveness. There are several design formulas for the structure without inherent damping, but in reality the structure has inherent damping. Therefore, it is necessary to use the iteration method to obtain the optimal design variables, and this study integrates two algorithms to find the best solution and optimal design variables rapidly and efficiently.

Generally, the tuned mass damper design emphasizes the reducing effect rather than the robustness. However, TMD is sensitive to the frequency between the structure and the TMD. The reducing effect deteriorates if the frequency shift away from the optimal value. Therefore, this study proposes the optimal design method of robust tuned mass damper, considering the condition of the reducing effect and the variability of the frequency simultaneously, and then make a comparison between the effectiveness of the general design and the robust design.

In the researches, it is quite common to design TMDs by simplifying MDOF model to SDOF model rather than the real structure. If the analytical results are similar, it is much rapider and easier to solve the problem by using SDOF model. Furthermore, the performance of system with TMD sometimes becomes worse when the structure is affected by the earthquakes, so the actual earthquake records are used to examine the result statistically in this study, and finally make a comparison between the performance of the general design and the robust design under the earthquakes.

致謝 I
摘要 III
ABSTRACT V
目錄 VII
表目錄 IX
圖目錄 X
第一章 緒論 1
1.1 研究動機與目的 1
1.2 文獻回顧 2
1.3 研究內容 3
第二章 調諧質量阻尼器簡介 5
2.1 前言 5
2.2 單自由度主系統(SDOF System) 5
2.2.1 加裝單自由度調諧質量阻尼器 5
2.2.2 加裝串聯式調諧質量阻尼器 9
2.2.3 加裝並聯式調諧質量阻尼器 11
2.3 多自由度主系統(MDOF System) 13
2.4 小結 16
第三章 調諧質量阻尼器最佳化設計 17
3.1 最佳化問題敘述 17
3.2 調諧質量阻尼器最佳化設計之目標函數 18
3.2.1 一般式調諧質量阻尼器最佳化設計 18
3.2.2 強健式調諧質量阻尼器最佳化設計 22
3.2.3 強健式調諧質量阻尼器最佳化設計目標函數之簡化 28
3.3 調諧質量阻尼器最佳化設計之設計變數 31
3.4 調諧質量阻尼器最佳化設計之控制變數 32
3.5 小結 35

第四章 最佳化設計系統軟體 36
4.1 調諧質量阻尼器最佳化公式 36
4.2 分析軟體與演算法介紹 38
4.2.1 FMINCON 39
4.2.2 模擬退火法SIMULANNEALBND 40
4.3 演算法結果之檢核 41
4.3.1 FMINCON 41
4.3.2 模擬退火法 44
4.4 數值模擬與理論之驗證 45
4.5 小結 47
第五章 實例分析結果討論 49
5.1 單自由度主系統(SDOF System) 49
5.1.1 串聯式與並聯式調諧質量阻尼器 52
5.1.2 多頻式調諧質量阻尼器 54
5.1.3 強健式調諧質量阻尼器 56
5.2 多自由度主系統（MDOF System） 66
5.2.1 剪力構架 66
5.2.2 多自由度簡化為單自由度 68
5.3 地震歷時檢核 69
5.3.1 一般式調諧質量阻尼器 69
5.3.2 強健式調諧質量阻尼器 70
第六章 結論與未來展望 73
6.1 結論 73
6.2 未來展望 74
附錄 450筆地震歷時資料 75
參考文獻 87

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