Development of a System Framework for Optimal Design of Tuned Mass Dampers

諧調質量阻尼器(tuned mass damper, TMD)是目前常用的一種控制振動的方法，然而TMD的變數是否最佳化決定了其效果，若變數設置不當，甚至可能引發反效果。傳統於變數最佳化大多假設系統阻尼為零，而有一系列的設計公式，但實際上系統阻尼並非為零，再加上建築物並非簡單的單自由度系統，TMD的擺放位置亦是考量因素之一，此時則須經由迭代或是變數搜尋才能得到最佳變數，因此本研究開發了一最佳化架構，將數學分析軟體MATLAB與有限元素套裝軟體ABAQUS做了適當的結合，以有限元素軟體做為主要分析引擎，可擴充分析模型的類型，再由數學分析軟體擷取數據做運算與設計變數之搜尋，達到TMD設計變數最佳化之目的。 本論文中，首先介紹了TMD的運動方程式推導，以及轉換函數，接著於第三章中介紹了最佳化題目的定義，以及TMD的設計變數有哪些，包含了質量比、頻率比、阻尼比、位置等等，並大略說明這些變數對整體系統反應的影響，並舉出TMD設計的目標函數，例如位移均方值等等。 在第四章首先介紹本研究所使用的軟體，再來詳細介紹了本研究所開發的最佳化設計架構，將整體架構分為三大部分，分別為資料處理模組、有限元素分析模組、最佳化分析模組，說明各模組負責的工作項目以及指令的使用方法。 而在第五章則利用本研究所開發的分析架構，對不同類的TMD設計題目進行最佳化分析，首先先對單自由度系統進行驗證確保本研究內容可行，接著變換目標函數、設計變數、外力輸入、主系統形式，同樣進行TMD設計，求取最佳變數解使得TMD可以發揮最好的效果。 綜合以上結果，本研究架構所得在TMD的設計上有不錯的成效。In recent years, tuned mass dampers have been widely used in structures to reduce the discomfort induced by vibration. However, the optimization of design variables for tuned mass dampers is very significant. There are some design formulas or closed form solutions for the structure without inherent damping, and simplified the structure as an one-degree-of freedom mass system. But in real structures, it is no possible for a structure without any damping and only one-degree-of freedom existed. Therefore, this thesis uses finite element package as the analysis engine to model and analyze the structure and then use the optimization tool to find the optimization variables in order to find a better solution to design tuned mass damper for any objective function. In this thesis, we derive the motion equation of the system with TMDs first, including different type of TMDs or system with different degree of freedom. While analyzing the response of system with TMD, transfer functions are always used. From transfer functions, we can understand the response of system in the frequency domain. Then we will introduce the design variables of TMD, for example, mass ratio, damping ratio, tuning frequency ratio and any variable needed like location of TMD. And introduce the objective function of TMD design problem. The root mean square of displacement or the peak value of response in frequency domain is often chosen. Then the system framework is developed in chapter 4. First of all, the optimal framework is verified by using a SDOF system without damping and validated the result of system with damping by iterative method and the proposed result in the reference paper. Secondly, make some discussion about series type tuned mass damper. Even if series type tuned mass damper is more effective than classic TMD, it will lose efficiency while the mistake in frequency ratio. So we adjust the form of objective function in order to improve the robustness of series type tuned mass damper. And then ,if we take force into account , we can get better result under the force we considered. Except SDOF system, MDOF systems like plate and beam are designed, too. At last, a ten-DOF system with a TMD or two TMDs is to make sure the feasibility of framework. According to the aforementioned, the framework constructed is performance well in TMD design problem