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DESIGN OF AN ADAPTIVE
DYNAMIC VIBRATION ABSORBER
Christopher Ting-Kong
Department of Mechanical Engineering
The University of Adelaide
South Australia 5005
Thesis submitted for the degree of
Master of Engineering Science on the 21
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April, 1999.
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Contents
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DESIGN OF AN ADAPTIVE DYNAMIC VIBRATION ABSORBER
TABLE OF CONTENTS
Abstract viii
Statement of Originality ix
Acknowledgements x
CHAPTER 1. INTRODUCTION AND LITERATURE REVIEW 1
1.1 Introduction
1.2 Literature Review 3
1.2.1 Existing technology and prior research 3
1.2.2 Summary of contribution to current knowledge addressed by this thesis 7
1.2.3 Strategies taken here to achieve the objectives 8
1.2.4 Analysis of Dynamic Vibration Absorbers 9
1.2.5 Analysis of vibration in a base structure – simply supported beam 12
1.2.6 Governing Equations 13
CHAPTER 2. DYNAMIC VIBRATION ABSORBER USING ENCLOSED AIR 15
2.1 Introduction 15
2.2 First Prototype 16
2.3 Second prototype 18
2.4 Experimental Results 22
2.4.1 Frequency range of second prototype 22
2.4.2 Identified problems with the second absorber 23
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2.4.3 Comparison of experimental with theoretical values 25
2.4.4 Identified problems with prototype using rubber
diaphragm 26
2.5 Incorporating the use of an Aluminium diaphragm 28
2.6 Impedance of the absorber 31
2.7 Performance of the absorber 33
2.8 Summary 35
CHAPTER 3. DUAL-MASS CANTILEVERED DYNAMIC VIBRATION
ABSORBER 36
3.1 Introduction 36
3.2 Initial theoretical analysis of cantilevered absorber using discrete
system analysis 38
3.3 Theoretical analysis of the cantilevered absorber using continuous
system theory 41
3.4 Finite element analysis of the absorber 50
3.5 Experimental Setup 51
3.5.1 Introduction 51
3.5.2 Resonance frequency experimental measurement
of absorber (alone) 52
3.5.3 Experimental results 53
3.5.4 Experimental setup with the absorber on the beam 56
3.6 Control System 59
3.6.1 Controller Setup 59
3.6.2 Tuning algorithm 62
3.6.3 The linear transducer 65
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3.7 Experimental results for the case of the absorber mounted on the beam 67
3.7.1 Performance of the absorber on a sinusoidally excited
simply supported beam 67
3.7.2 Variation in natural frequency of the absorber due to
change in effective rod length 69
3.7.3 Speed of adaptation 70
3.8 Summary 72
CHAPTER 4. SUMMARY AND CONCLUSIONS 73
4.1 Summary of Dynamic Absorber using enclosed air 73
4.2 Summary of Dual Cantilevered Mass Absorber 74
4.3 Future work 75
4.3.1 Future work on the air-spring absorber 75
4.3.2 Future work on the dual cantilevered mass absorber 76
4.4 Conclusions 77
Appendices 78
References 94
Notation
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LIST OF FIGURES
Figure 1.1 Representation of an Adaptive Vibration Absorber
Figure 1.2 Resonance curves for a Dynamic Vibration Absorber
Figure 1.3 Changing the natural frequency of a beam
Figure 2.1 Initial concept of the absorber
Figure 2.2 Variation in stiffness when changing the height of the enclosed volume
Figure 2.3 Design of the second prototype
Figure 2.4 Transfer function of the second prototype
Figure 2.5 Identified problem with the absorber mass
Figure 2.6 Comparison of experimental and theoretical stiffness values
Figure 2.7 Variation in natural frequency with aluminium diaphragm
Figure 2.8 Variation between experimental and theoretical stiffness values
for Aluminium diaphragm
Figure 2.9 Harmonic response curve showing bandwidth and half power points
Figure 2.10 Experimental setup for aluminium absorber
Figure 2.11 Frequency response of aluminium diaphragm dynamic vibration absorber
Figure 3.1 The first 2 modes of the cantilevered absorber
Figure 3.3 Dimensions used for discrete system analysis
Figure 3.4 Dimensions used for continuous system analysis
Figure 3.5 Shear and moment sign conventions
Figure 3.6 Boundary conditions for lateral vibration in a beam
Figure 3.7 A meshed model of the Dynamic Absorber
Figure 3.8 Measuring resonance frequency of the absorber alone
Figure 3.9 Transfer function of the absorber