臺灣博碩士論文加值系統

現今對於調諧質塊阻尼器的研究與應用已相當廣泛，但經由解析相位去了解調諧質塊阻尼器之減振效果，仍著墨較少且不完全。因此本文先針對調諧質量阻尼器之能量流理論(power flow theory)進一步闡述，探討調諧質量阻尼器與結構之間的相位關係，其顯示調諧質量阻尼器於90度相位差落後時為吸收結構能量，但於90度相位差超前時，則反將能量傳回結構。此外，並探討調諧質量阻尼器與外力之間的相位，對減振效果的影響，提出調諧質量阻尼器之能量阻抗的概念，其顯示與外力為180度相位差時有最佳之阻抗效果，較全面性的討論相位對調諧質量阻尼器減振效果的影響。而後，本文提出半主動式相位控制調諧質量阻尼器，其模型為傳統調諧質量阻尼器外加一半主動控制之摩擦裝置，藉由半主動控制之摩擦力，於調諧質塊擺動之特定時間，施加摩擦力，可調整質量塊與結構之間之相位，使其能盡量維持與結構為一落後90度之相位差，因而如能量流理論所述般達到最佳減振效果。為驗證相位控制調諧質量阻尼器之可行性，分別以單自由度結構或多自由度結構，於諧和外力、風力或基底振動下，進行一系列之數值模擬。數值模擬結果顯示，結構加裝相位控制調諧質量阻尼器後，於風力或基底振動下，與傳統調諧質量阻尼器相比皆可有較大的減振頻率帶寬，且不論多自由度結構或其經單自由度化之結構，結構反應皆可有更佳之控制效果。由相位控制調諧質量阻尼器設計參數之敏感度分析顯示，相位控制調諧質量阻尼器對於其設計之頻率比及阻尼比皆不敏感，因此可同時於風力下及基底振動下之應用，解決傳統調諧質量阻尼器適應式之問題。唯所需之摩擦力限制較多，如施加之摩擦力太小，則失去相位控制效果，如施加之摩擦力太大，則摩擦力將對於結構加速度將有一負面影響，因此設計時需仔細考量。最後以實際案例進行風力及地震力之數值分析，驗證相位控制調諧質量阻尼器確實可發揮減振效果，滿足其舒適度之要求，更可降低離頻效應之影響。

Although the energy absorbing ability of the TMD has been discussed by power flow theory, the phase-mechanism of the TMD is not comprehensively discussed. In this study, the phase of the TMD relative to the structure is presented in power flow theory and discussed in detail, and the phase of the TMD relative to the external force is further discussed and described by the power reactance which shows the TMD has the ability to balance the external energy input to the system. Based on the power flow theory, the semi-active phase control tuned mass damper (PC-TMD) is developed and investigated. The phase control algorithm is proposed for the PC-TMD to judge the specific moment to apply friction force by semi-active friction device. By applying the friction force, the PC-TMD mass block moves along the desired trace and back to the 90-degree phase lag to the structure for achieving the maximum power flow. The numerical simulations demonstrate that the PC-TMD outperforms the conventional TMD in structural vibration reduction, especially for mitigating the detuning problem. The simulation results also indicate that the PC-TMD can be utilized for wind loads or base excitation application, and for single-degree-of-freedom (SDOF) structure or multiple-degree-of-freedom (MDOF) structure. In addition, the design parameters of the PC-TMD is the same for both wind loads and base excitation application so that the PC-TMD can be well performed for wind loads and base excitation simultaneously.

審定書 i
Abstract v
中文摘要 vii
Contents ix
Chapter 1 Introduction 1
1.1 Background and motivation 1
1.2 Literature review 5
1.3 Organization and objectives of the dissertation 10
Chapter 2 Essence of Phase for Tuned Mass Damper 13
2.1 Modeling of SDOF structure implemented with TMD 13
2.1.1 Equation of motion 13
2.1.2 State-Space representation 16
2.1.3 Transfer function and frequency responses function 17
2.2 Power flow theory 19
2.3 Power reactance 24
2.4 TMD stroke 26
2.5 Numerical Simulations 27
2.5.1 Frequency response function 29
2.5.2 Free vibration simulations 34
2.6 Discussion 45
Chapter 3 SDOF Structure Implemented with PC-TMD for Wind Loads Application 47
3.1 Equations of motion for a SDOF structure with a phase control tuned mass damper under wind loads 49
3.2 Real time phase observation and phase control strategies 51
3.3 Sign judgment criteria for friction force applications 58
3.4 The on-off friction force calculation 63
3.5 Phase Control Algorithm 65
3.6 Numerical Verification of a SDOF structure implemented with a PC-TMD 69
3.6.1 Sinusoidal loads 70
3.6.1.1 External load with a frequency of 1.0 times the natural frequency of the structure 71
3.6.1.2 External load with a frequency of 0.95 times the natural frequency of the structure 74
3.6.1.3 External load with a frequency of 1.05 times the natural frequency of the structure 79
3.6.2 Frequency Response Function 84
3.6.2.1 Optimal design parameters of TMD and PC-TMD 84
3.6.2.2 Off-tuned effect of TMD and PC-TMD 87
3.6.2.3 Comparison of maximum friction force of PC-TMD 92
3.6.3 Free Vibration 94
3.6.4 Design Wind Loads 98
3.6.4.1 Sensitivity analysis of the TMD frequency ratio under design wind force 103
3.6.4.2 Sensitivity analysis of the TMD damping ratio under design wind force 105
3.6.4.3 Sensitivity analysis of the maximum friction force of PC-TMD under design wind force 107
3.7 Conclusions of SDOF structure implemented with the PC-TMD for wind loads applications 110
Chapter 4 MDOF Structure Implemented with PC-TMD for Wind Loads Application 115
4.1 A 3-DOF structure implemented with two PC-TMDs 115
4.1.1 Modeling of a 3-DOF structure implemented with two PC-TMDs 115
4.1.2 Phase control algorithm for 3-DOF structure 122
4.1.3 The on-off friction force calculation 123
4.1.4 Numerical Simulations 127
4.1.4.1 Frequency Response Functions 130
4.1.4.2 Design Wind Loads Time History Analysis 134
4.1.5 Conclusions of A 3-DOF structure implemented with two PC-TMDs 143
4.2 A 42-story building implemented with a PC-TMD 145
4.2.1 Modeling of a 42-DOF structure implemented with a PC-TMD 145
4.2.2 Parameters of Primary Structure and TMDs 150
4.2.3 Phase control algorithm for MDOF structure 151
4.2.4 Real-time filter application for phase control algorithm 152
4.2.5 Numerical Simulation 156
4.2.6 Conclusions of A 42-DOF structure implemented with the PC-TMD 162
Chapter 5 SDOF Structure Implemented with PC-TMD for Base Excitation Application 165
5.1 Equations of motion for a SDOF structure with a phase control tuned mass damper under base excitation 165
5.2 Phase control algorithm for base excitation 168
5.3 The on-off friction force calculation 168
5.4 Numerical Verification of a SDOF structure implemented with a PC-TMD 170
5.4.1 Frequency Response Function 172
5.4.1.1 Without de-tuning effect for TMD and PC-TMD 172
5.4.1.2 Off-tuned effect of TMD and PC-TMD 175
5.4.2 Design Earthquakes 180
5.4.2.1 Sensitivity analysis of the TMD frequency ratio under the in-site earthquake 187
5.4.2.2 Sensitivity analysis of the TMD damping ratio under the in-site earthquake 189
5.4.2.3 Sensitivity analysis of the maximum friction force of PC-TMD under the in-site earthquake 191
5.4.2.4 Sensitivity analysis of the earthquakes 194
5.5 Conclusions of SDOF structure implemented with the PC-TMD for base excitation applications 197
Chapter 6 Conclusions and Future Works 201
6.1 Summaries and Conclusions 201
6.2 Recommendations for future works 205
Reference 207
Appendix A. Frequency Response Function of A 2DOF System 215
Appendix B. Instantaneous Phase Calculation by Hilbert Transform 217
Appendix C. Preliminary Design of Maximum Friction Force for the PC-TMD 219

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