應用反應譜分析法之阻尼器最佳化配置

Optimal Placement of Dampers in Building Structures Using Response Spectrum Analysis

黃婉婷(Wan-Ting Huang)

指導教授 ： 呂良正

國立臺灣大學/工學院/土木工程學研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.01120

摘要

最近十多年來，美、日及我國受北嶺地震、2011年東北地方太平洋近海地震及集集地震的影響，於耐震補強及新建築設計皆大量採用阻尼器為消能裝置。而阻尼器最佳化配置也為一熱門議題。本研究即討論如何將非古典阻尼結構動力系統解耦並推導其對應之反應譜法公式，將其應用於簡易法當中。
在過去，阻尼器最佳化配置其初始配置通常都假設為均勻配置，與勁度或是質量矩陣成正比，在此條件下，結構系統可以被解耦，為古典阻尼結構動力系統，並可以使用反應譜法來求得結構峰值反應；然而，初始配置在經過最佳化的步驟後，因為阻尼器的重排，在古典模態分析法中，無法將阻尼矩陣解耦，稱為為非古典阻尼結構動力系統，此系統在傳統僅能以直接積分法來求得結構系統的反應值。本研究即針對此種結構動力系統，首先採用相位同步法解耦系統，其原理為將由黏性阻尼器造成在每個振態的相位差，經過一個補償的動作，而使振態中的每個分量達到同相或是反相的運動，推得相位同步後之模態方程式；並且以此為基礎推導反應譜法。本研究尚使用另一種可將非古典阻尼結構動力系統解耦的方法，此法為對系統進行複模態分析後，透過拉氏轉換的應用，可得解耦之模態方程式；在此兩種方法中，相位同步法對實數特徵值會有配對的動作產生，而拉氏轉換法則不將實數特徵值配對，針對特徵值配對之問題在本研究將討論其對結構系統反應之影響。因而拉氏轉換法推導反應譜法時，在實數特徵值對應的過阻尼模態新產生一過阻尼模態反應譜。
最後，分別將此兩種反應譜之方法應用於簡易法當中，取代原本在簡易法中為了求得結構反應值之歷時分析法，此法在自由度較大的系統當中，需要花費較長之分析時間。若以反應譜法取代他，則可以減少大部分的分析時間，而得到效益差不多之結果，於工程界中則可更加廣泛的被採用。

關鍵字

簡易法 ； 非古典阻尼 ； 解耦 ； 過阻尼 ； 複數模態分析 ； 阻尼器最佳化配置 ； 反應譜分析法 ； 相位同步 ； 拉氏轉換

並列摘要

Dampers have been popularly used to retrofit existing building structures and for seismic design of new buildings since Northridge earthquake, The 2011 off the Pacific coast of Tohoku earthquake, and Chi-Chi earthquake. Optimal placement of dampers becomes a hot topic for researchers in structural mechanics and earthquake engineering.
For the past few years, the added dampers are assumed to be placed uniformly at each story of two selected bays. Thus, the damping matrix will be proportional to stiffness matrix or mass matrix. The system is called classical damped system. And it can be decoupled by modal analysis. So that, it could use response spectrum analysis to find the maximum response of the system. When we find the optimal allocation of supplemental dampers, the system will become non-classical damped system. One of the purpose in this research is to extend classical modal analysis to decouple non-classical damped system. First, we decouple the system by phase synchronization. The purpose of phase synchronization is to compensate for the time drifts caused by viscous damping. If suitable phase shifts are introduced into each damped mode of vibration so that all components are either in phase or out of pahse. On the basis of the method, the response spectrum could be derived. The other method that decoupled the non-calssical damped systesm is Laplace transform. In this method, the complex modal analysis is used. And then, use Laplace transform to the complex modal equation. After some processes the decouple system would be found. In phase synchronization, it paired the real eigenvalues by real quadratic conjugation. And in Laplace transform, it didn’t pair the real eigenvalues. So when deriving the response spectrum method for Laplace transformation method, it would be an over-damped mode response spectrum there. The problem of pair eigenvalue in group is to be disscuss in this research.
Finally, the above two response spectrum methods were used in simple method. When using response spectrum method to replace time history analysis, it can reduce most of the analysis time. And the result could be almost the same when it uses the time history analysis in simple method. So that, this method could be used extensively in earthquake engineering.

並列關鍵字

Simple method ； decouple ； over-damped ； complex modal analysis ； optimal placement of dampers ； response spectrum analysis ； phase synchronization method ； Laplace transform

參考文獻

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