指導教授：呂良正臺灣大學：土木工程學研究所廖春滿Liao, Chun-ManChun-ManLiao2014-11-252018-07-092014-11-252018-07-092014http://ntur.lib.ntu.edu.tw//handle/246246/260710近年來，主、被動式消能裝置已被廣泛應用在建築耐震設計，以消散地震造成的能量，降低結構物的受震反應，因此許多研究皆致力於結構控制系統的應用。現行的規範如FEMA 273/274提供了阻尼器設計參數利於工程界使用，但阻尼器配置與數量的相關準則皆尚未成熟。本研究的目的在尋找線性黏性阻尼器在結構物中的最佳化配置，使阻尼器有效地發揮功能，控制結構物的受震反應。進行最佳化配置的過程中，必須以動力分析得到結構物的反應，例如：直接積分法，但是此法在自由度龐大的結構物下會相當耗時，故本研究提出以反應譜分析法取代線性歷時分析。然而加裝阻尼器的結構系統往往為非古典阻尼動力系統，無法以一般的古典阻尼反應譜法(CQC)做分析，因此文中提出兩種針對非古典阻尼系統的反應譜分析法(CCQC, GCQC)，首先介紹這兩種方法的解耦方程式，再由解耦方程式推導其反應譜公式，最後利用這兩種反應譜分析法進行阻尼器的最佳化配置。 阻尼器最佳化配置的方法包含簡化循序搜尋演算法(Simplified Sequential Search Algorithm, SSSA)以及呂等人(2010)提出的簡易法(Simple Approach)等，簡易法和簡化循序搜尋演算法最大的差別在於阻尼器的初始配置，簡易法提出阻尼器數量應為結構物自由度的兩倍，並均勻配置在結構物上，兩者方法的性能指標皆為最大層間位移。應用反應譜分析法於簡易法中，由於非古典阻尼結構最大層間位移之計算誤差偏大，導致阻尼器最佳化過程中之判斷不準確。文中由簡易法出發，針對不同的性能指標（如：最大頂層位移、結構系統應變能……等）進行阻尼器最佳化配置。阻尼器於迭代過程中依據敏感度因子在樓層間進行移動，其中樓層之敏感度因子使用有限差分法計算。 結果發現使用結構系統總應變能做為性能指標較為可靠，因其性能指標於迭代過程中具有較佳的收斂性。雖然迭代步內都需要進行多次結構動力分析以計算敏感度因子，但利用反應譜分析法便能在更短的計算時間完成阻尼器最佳化配置，其結果也令人滿意。最後，以設計反應譜之人工合成地震應用本文所提出的最佳化阻尼配置方法探討最佳配置的結果。進行最佳化配置後的結果顯示，利用反應譜分析法進行最佳化配置後的最大層間變位和應用其人工合成地震以直接積分法的方式得到之最佳化配置的結果差不多，由此證明本研究使用反應譜分析法並以結構系統應變做為阻尼器最佳化配置問題的性能指標是可行的。 然而本文所提出的例子只適用於剪力屋架結構，故期盼未來能針對平面剪力屋架以及三維不對稱結構進行研究。In order to reduce the vibration of structures, buildings are designed to resist earthquakes by active or passive energy dissipation devices. The current codes such as FEMA 273/274 suggested the equivalent damping ratio, but the development of efficient procedures which leads to optimal placement of dampers has received less attention. Therefore, the current research on optimum design of dampers was conducted in order to detect the optimal damper placement in the structures which are effective in reducing the seismic responses. Passive energy dissipating devices, such as linear viscous dampers are easy to be instal in the structures. However, the structure with the supplemental dampers usually belongs to the non-classically damped system. Generally, these systems can be analyzed by direct integration methods like Newmark method, so that the responses of the structures can be obtained. But if the degree-of-freedom of the structures is considerable, the direct integration method is thus time consuming. This study presents current researches on mode superposition methods for the non-classically damped systems. Base on the concept in decoupling the non-classically damped system, the response spectrum methods are developed to implement on the Simple Approach proposed by Leu (2010) and it affects computational efficiency of optimizing placement of dampers. The illustrative examples show that the search algorithm can not be base on the inter-story drifts when response spectrum analysis methods are implemented on the Simple Approach. Hence, the pseudo strain energy and the roof displacements of the structure are adapte for the optimization strategy. The effectiveness of different optimization strategies are then verified by numerical examples. Numerical results show that all damper designs are truly effective in reducing the dynamic response of the structure. To observe from the application of the articial earthquake synthesized from the design response spectrum, it is efficient by applying response spectrum analysis methods in the relocation process when the pseudo strain energy of the structure is used in the optimization strategy. Although the computational efficiency of optimizing placement of dampers is improved greatly by using response spectrum analysis methods, the results in the higher story shear frames obtained from conducting the optimization where the sensitivity of pseudo strain energy is used may be not so good that the maximum inter-story drifts would over the limit, thus the optimal strategy lose its effectiveness. To make a suggestion, it can be improved by using other optimization strategies and the search algorithms. Besides, the planar shear building structure frames should be taken into consideration for conducting the further research.ABSTRACT I 摘要 III CONTENTS V LIST OF TABLE X LIST OF FIGURES XI Chapter 1 Introduction 1 1.1 Research purposes and motivations 1 1.2 Literature review 2 1.2.1 General damped system 2 1.2.2 Dynamic analysis 3 1.2.3 Statement of optimization problems of placing dampers 5 1.2.4 Optimization problems of structures with viscous dampers 7 1.3 Thesis organization 8 Chapter 2 Mode Superposition Method of Non-Classically Damped System 10 2.1 Introduction 10 2.2 Traditional modal analysis method 11 2.3 Generalized eigenvalue problem 13 2.3.1 The features of eigenvalue problem 13 2.3.2 The characteristics of eigenvalues 15 2.3.3 Orthogonality 16 2.4 Mode superposition method I of non-classically damped system 17 2.4.1 Characteristics of eigenvalues 17 2.4.2 Modal decomposition (overdamped modes are in pairs) 18 2.4.3 Mode superposition method I (MSM-I) 20 2.5 Mode superposition method II of non-classically damped system 25 2.5.1 Characteristics of eigenvalues 26 2.5.2 Modal decomposition (overdamped modes are independent) 26 2.5.3 Mode superposition method II (MSM-II) 27 2.6 The equivalent of two mode superposition methods 29 2.7 Reduction to classically damped system 32 2.7.1 Mode shapes of undamped and damped systems 32 2.7.2 Reduction to undamped system 33 2.7.3 The compatibility of mode superposition methods of non-classically and classically damped system 35 2.8 Numerical examples and discussions 36 2.8.1 Example 2.1 37 2.8.2 Example 2.2 39 2.9 Summary 43 Chapter 3 Response Spectrum Method of Non-classically Damped System 49 3.1 Introduction 49 3.2 Response spectrum methods for MSM-I 49 3.3 Response spectrum methods for MSM-II 55 3.4 Correlation coefficient 59 3.5 Response spectrum 60 3.5.1 Overdamped mode response spectrum of CCQC and CSRSS 61 3.5.2 Overdamped mode response spectrum of GCQC and GSRSS 62 3.6 Numerical examples and discussions 62 3.6.1 Example 3.1 63 3.6.2 Example 3.2 64 3.7 Summary 65 Chapter 4 Damper Placement Optimization 76 4.1 Introduction 76 4.2 Simplified Sequential Search Algorithm (SSSA) 77 4.3 Simple Approach 78 4.3.1 Initial damper distribution 78 4.3.2 Objective function 79 4.3.3 Relocation strategy 79 4.4 Optimization strategies 80 4.4.1 Dynamic analysis 80 4.4.2 Search algorithm 81 4.4.2.1 Sensitivities 81 4.4.2.2 Pseudo strain energy 83 4.4.3 Relocation strategy 84 4.4.4 Termination criteria 85 4.4.5 Applications of artificial earthquake 86 4.4.5.1 Computer program 87 4.4.5.2 Introduction to SIMQKE 87 4.4.5.3 Data used in programming in Fortran 87 4.4.5.4 Simulation of earthquake 90 4.5 Numerical examples and discussions 90 4.5.1 Accuracy of response spectrum analysis methods 91 4.5.1.1 Numerical results - Peak inter-story drifts 91 4.5.1.2 Discussion 92 4.5.2 Convergences of different optimization strategies 92 4.5.2.1 Numerical results – Search algorithm using inter-story drift 93 4.5.2.2 Numerical results - Search algorithm using sensitivity of pseudo strain energy 93 4.5.2.3 Numerical results - Search algorithm using sensitivity of the maximum roof displacement 94 4.5.2.4 Discussion 95 4.5.3 Evaluation of optimal solutions of different optimization strategies 95 4.5.3.1 Numerical results - Search algorithm using sensitivity of pseudo strain energy 96 4.5.3.2 Numerical results - Search algorithm using sensitivity of the maximum roof displacement 98 4.5.3.3 Discussion 99 4.5.4 Evaluation of modal damping ratio 100 4.5.4.1 Numerical results – Effect of supplemental dampers 100 4.5.4.2 Numerical results - Modal damping ratios of the first mode 101 4.5.4.3 Discussion 102 4.6 Summary 103 Chapter 5 Applications and Validations 145 5.1 Introduction 145 5.2 Implementation of optimization strategy 146 5.2.1 Effectiveness of optimization strategy 146 5.2.2 Consistency of response spectrum analysis 148 5.2.3 Comparison in optimization strategies 149 5.3 Application of artificial earthquakes 150 5.4 Summary 151 Chapter 6 Conclusions 182 6.1 Summary 182 6.2 Future work 183 References 18414826725 bytesapplication/pdf論文公開時間：2016/08/12論文使用權限：同意有償授權(權利金給回饋學校)非古典阻尼系統模態疊加法反應譜分析法阻尼器最佳化配置人工合成地震設計反應譜thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/260710/1/ntu-103-R01521207-1.pdf