考慮多模態之黏性阻尼器最佳化分配及其於建築結構之應用

Optimal Allocation of Viscous Dampers Considering Multiple Modes and Application to Building Structures

盧易(Yi Lu)

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(2018年)

https://doi.org/10.6342/NTU201801691

摘要

黏性阻尼器(Viscous Damper)經常作為被動消能元件被應用於建築結構，但於目前的規範中，對於黏性阻尼器之配置方法較無具體的規定與建議。此研究之目的為尋找黏性阻尼器應用於結構物中之最佳化分配，期望使阻尼器能最有效的發揮其效能，降低結構物於地震下之反應。
本研究將現有之阻尼器分配法分為直接分配法及動力分析分配法。設計過程中直接藉由結構物本身特性進行分配，不須經過動力分析之分配法為直接分配法；而設計過程須經過動力分析之分配法為動力分析分配法。本研究利用層間位移頻率轉換函數及隨機振動之概念，修改並延伸了現有的幾種阻尼器分配法。
本文也利用了廣義阻尼系統模態之模態疊加法及有效模態質量之概念，提出了新的分配法－模態質量分配法。而經由廣義阻尼系統模態之模態疊加法推導出的廣義阻尼系統之反應譜法，也被本文使用作為最佳化結構物反應之方法，利用反應譜法可以相對於直接積分法減少許多最佳化的時間，並於之後探討反應譜法如何應用於此最佳化題目及其成效。
將各分配法應用於四種剪力構架，並以兩種案例分別以多筆真實地震及人工地震進行檢核，期望藉由兩種案例來比較分配法於單一地震事件與多事件下的差異，而性能指標則表示為與均勻配置反應之折減指標，期望最佳化分配法能比實務上最常見之均勻配置法有更良好之效益。
經由兩種案例之比較與討論，本文建議30層樓以下之建築物可以使用MMD或H-Lavan，而30至40層樓左右之建築建議使用MH、EDVD或E-EDVD。由於建築物或當地設計反應譜的不同可能導致最佳之分配法有所差異，因此仍建議使用多種建議的分配法分別來分配阻尼器並通過數值模型來檢核並選出較適合該建築物之分配法。

關鍵字

黏性阻尼器 ； 阻尼最佳化配置 ； 剪力構架 ； 非古典阻尼系統 ； 模態疊加法 ； 反應譜分析法

並列摘要

Viscous dampers are frequently used in buildings as passive energy dissipation devices. However, the issue of the efficient placement of viscous dampers has received less attention in existing codes. The purpose of this research is to find the optimal allocation of viscous dampers in the structure. We hope the viscous dampers work more efficiently with optimal allocation under seismic actions.
In this study, all existing distribution methods are divided into two groups, “Direct Distribution Methods” and “Dynamic Analysis Distribution Methods”. The methods that allocate viscous dampers based on structure properties without dynamic analysis are called “Direct Distribution Methods”. The methods with dynamic analysis are called “Dynamic Analysis Distribution Methods”. The inter-story drift transfer function and the theory of random vibration are used in this research to modify and extend the existing distribution methods.
A new distribution method called “Modal Mass Distribution” is proposed, which is based on non-classically damped system mode superposition methods and corresponding concept of effective modal mass. The response spectrum methods can be developed by corresponding mode superposition methods and is used in this study as the method to optimize the reaction of the structures. The response spectrum methods are more time efficient than the direct integration method with little error. The effectiveness and how the response spectrum methods applied to optimal problem will be discussed.
Different kinds of distribution methods are applied to four shear type buildings. The examination has two cases and each case is divided into two parts, real ground motion records examination and spectrum-compatible time histories examination, to compare the difference of distribution methods between single event and multiple events of earthquakes.
The reduction of seismic response from uniform distribution is chosen as the performance index. The performance index is chosen to demonstrate that the optimal distribution has better performance than the most common distribution, uniform distribution.
After the comparison of two cases, we suggest to use MMD and H-Lavan for the building under 30 floors and to use MH, EDVD or E-EDVD for the building within 30 to 40 floors. Because the difference of the structure and the design response spectrum, the best distribution method might be different. It is recommended to use multiple suggested distribution methods and run the analysis with numerical model to choose the best method for the structure.

並列關鍵字

viscous damper ； optimal placement of dampers ； shear type buildings ； non-classically damped system ； mode superposition method ； response spectrum analysis

參考文獻

Chopra, A. K. (2011). Dynamics of Structures: Theory and Applications to Earthquake Engineering (4th ed.). Fourth edition, Pearson.

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Hudson, D. E. (1962). Some problems in the application of spectrum techniques to strong-motion earthquake analysis. Bulletin of the Seismological Society of America. 52(2): 417-430.

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