臺灣博碩士論文加值系統

雙穩態振動吸收器是種能抑制主結構因受到外部激振而產生振動的非線性振動吸收器。當外部激振在特定的力量大小和頻率範圍時，振動吸收器內部的振盪器可能會產生「單穩態」、「混沌現象」與「雙穩態」振動行為。為了定量各個振動狀態的效能，非線性程度對本系統來說是一個非常重要的指標。非線性程度可以想像成瞬時頻率的平均變化量。對於一個受到弦波外力激振的線性系統來說，非線性程度為零。而對於一個非線性系統來說，不同的激振力大小、激振頻率和振動狀態會產生不同的非線性程度。在本研究中，非線性程度被區分為不同的等級，從而分析非線性程度與振動抑制效能之間的關係。雙穩態的杜芬振動吸收器為本研究的主要目標，並探討非線性程度、激振頻率與穩定平衡點之間的關係。

Bi-stable vibration absorber is a kind of nonlinear vibration absorber which can suppress the vibration of host structure under the external excitation. The attachment in the nonlinear absorber may present “mono-stable”, “chaos” or “snap-through” behaviors when the external excitation is under the specific force and frequency range. In order to quantify the performance of the system in each state, the degree of nonlinearity is an important index for evaluating this system. The degree of nonlinearity can be imagined as the average magnitude of the instantaneous frequency. For a linear system under harmonic excitations, the degree of nonlinearity is zero. For a bi-stable system, the response presents different degrees of nonlinearity with different vibration states, different input force magnitude and different excitation frequency range. In this research, the degree of nonlinearity is classified into different ranks, and then the relationships between the degree of nonlinearity and vibration absorbing performance can be analyzed. A negative linear-positive cubic duffing absorber was employed as the objective model in this study. The relationships among the degree of nonlinearity, the excitation frequency and the stable equilibrium points were discussed.

摘要 i
ABSTRACT ii
ACKNOWLEDGEMENTS iii
CONTENTS iv
LIST OF TABLE vi
LIST OF FIGURE vi
NOMENCLATURE xi
CHAPTER 1: INTRODUCTION 1
1.1 Motivation 1
1.2 Background and literature review 1
1.3 Problem statement and research contribution 7
1.4 Outline 8
CHAPTER 2: THEORY 9
2.1 Bi-stable system 9
2.1.1 The overview of bi-stable system 9
2.1.2 The vibration behavior of bi-stable system 10
2.1.3 Snap-through phenomenon 13
2.1.4 Duffing equation and bi-stable system 14
2.1.5 Bi-stable absorber 17
2.1.6 Average dissipation ratio 19
2.2 Degree of nonlinearity 20
2.2.1. Instantaneous frequency 20
2.2.2 Mean frequency 22
2.2.3 The definition of degree of nonlinearity 23
CHAPTER 3: NUMERICAL SIMULATION AND DISCUSSION 25
3.1 Response and degree of nonlinearity 25
3.1.1 The response and degree of nonlinearity of monostable state 26
3.1.2 The response and degree of nonlinearity of chaos 31
3.1.3 The response and degree of nonlinearity of snap-through 33
3.1.4 Summary 36
3.2 Degree of nonlinearity and performance 37
3.2.1 Degree of nonlinearity to parameters 38
3.2.2 Degree of nonlinearity to excitation force 44
3.2.3 Performance to degree of nonlinearity 52
3.2.4 Summary 59
CHAPTER 4: CONCLUSIONS 61
4.1 Conclusions 61
4.2 Future perspectives 62
REFERENCES 63

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