臺灣博碩士論文加值系統

The object of this thesis is to investigate the vibration reduction effectiveness of MTMD (Multiple Tuned Mass Dampers). First of all, the governing equations for the entire vibrating system (i.e., the single degree-of-freedom spring-mass-damper main system installed with a MTMD) and the expression for calculating the dynamic magnification factor of the spring-mass-damper main system are derived. Then, based on the last expression of dynamic magnification factor, the influence of MTMD parameters (e.g. mass ratio, frequency ratio, frequency spacing, etc.) on its vibration reduction effectiveness is studied. Next, by replacing the single degree-of-freedom spring-mass-damper main system with a multiple degree-of-freedom beam-typed (or plate-typed) structures, the influence of MTMD parameters on its vibration reduction effectiveness is further investigated. From the presented numerical results, it can be found that the MTMD parameters affect its vibration reduction effectiveness significantly.

Contents
Abstract…………………………………………………………………..I
Acknowledgement………………………………………………………II
Contents……………………………………………………………...…III
List of Figures……………………………………………………..…...VI
Nomenclature……………………………………………………….......X
Chapter 1 Introduction…………………………………………............1
1.1 Literature review……………………………………………..1
1.2 Research method……………………………………………...3
1.3 Thesis structure……………………………………………….3
Chapter 2 Equations of motion of the entire vibrating system and dynamic magnification factor of the spring-damper-mass main system………………………………………………..6
2.1 Derivation of governing equations for the entire vibrating
system………………………………………………………...6
2.2 Dynamic magnification factor of the spring-damper-mass
main system…………………………………………………10
Chapter 3 Vibration reduction effectiveness of MTMD…………….17
3.1 Comparison of TTMD and STMD………………………….17
3.2 Influence of natural frequency ratio and frequency range..…20
3.3 Influence of exciting frequency ratio…...…………………...22
3.4 Influence of damping ratio………………………………….23
3.5 Influence of total number of MTMD……………………..…25
3.6 Influence of mass ratio…………………………….………..27
3.7 Conclusions…………………………………………………28


Chapter 4 Free and forced vibration analyses of a structure installed
with a MTMD using finite element method……...............29
4.1 Element property matrices of MTMD………………………29
4.2 Free vibration analysis of the structure……………...………30
4.3 Forced vibration analysis of the structure installed with a
MTMD and subjected to an external harmonic load………..31
Chapter 5 Vibration reduction of a beam and a plate subjected to an
external dynamic load using a MTMD………………...…33
5.1 Vibration suppression of a beam subjected to a dynamic load using a MTMD………………………...……………………34
5.1.1 Natural frequencies and the corresponding mode shapes
of the pinned-pinned beam……………………….…36
5.1.2 Influence of position of MTMD……………………..38
5.1.3 Influence of frequency range………………………...39
5.1.4 Influence of damping ratio…………………………..41
5.1.5 Influence of total number of MTMD………………...43
5.1.6 Influence of mass ratio………………………………46
5.2 Vibration suppression of a plate subjected to a dynamic load using a MTMD……………………………..……………….48
5.2.1 Natural frequencies and the corresponding mode shapes
of the CCFF plate………………...…………………49
5.2.2 Influence of position of MTMD…………………..…50
5.2.3 Influence of frequency range…………………..…….52
5.2.4 Influence of damping ratio…………………………..53
5.2.5 Influence of total number of MTMD………….……..54
5.2.6 Influence of mass ratio………………………………56
5.3 Conclusions…………………………………………………57

Chapter 6 Conclusions and Recommendations………….…………..58
6.1 Conclusions…………………………………………………58
6.2 Recommendations for Future Work…………………………58
References………………..………………………………..……………60

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