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研究生: 洪佑岡
Hung, Yu-Kang
論文名稱: 利用反共振機制抑制樑振動行為之分析
Vibration reduction of beams using antiresonance mechanism
指導教授: 陳蓉珊
Chen, Jung-Shan
學位類別: 碩士
Master
系所名稱: 工學院 - 工程科學系
Department of Engineering Science
論文出版年: 2014
畢業學年度: 101
語文別: 英文
論文頁數: 76
中文關鍵詞: 反共振效應減震暫態反應
外文關鍵詞: Antiresonance Effect, Vibration Reduction, Explicit Response
相關次數: 點閱:106下載:10
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  • 本論文的研究目的在討論利用反共振機制抑制樑振動之行為分析,由先前的研究發現裝置合適諧振器之樑可以有效降低於特定頻率下外力所造成之振幅。由二維質量彈黃振動系統之運動方程式可以用來近似並模擬裝有諧振器之樑之振動行為,並推出當激發反共振效應時樑之位移方程式。
    本論文主要以實驗去論證裝置諧振器之樑之振動行為,透過振動器激發出樑之反共振頻率並擷取訊號進行分析,進而討論反共振效應對於處於共振狀態下之樑之效應。利用有限元素法模擬樑之振動行為,模擬外力的衝擊並激發反共振效應時暫態與穩態的反應結果,另與實驗做驗證。另兩個重點討論在於裝置不同質量比重之諧振器對於樑共振頻率之影響,以及裝置不同個數之諧振器對於樑共振時振幅之影響。均透過理論、模擬以及實驗去驗證其正確性。

    A method for reducing the vibration of a beam using the antiresonance effect is presented. It is found that a beam with appropriate resonators consisting of a combination of spring and mass may reduce external excitation at certain frequencies effectively. A simple two degree of freedom system contain of an absorber mass that is connected by springs to a drive mass is discussed and demonstrated to display the vibration behaviour of a beam with resonators.
    The finite element method is used to simulate the vibration behaviour of the present beam. A transient response is a mode that immediately displays the behaviour of a beam subject to external excitation. To demonstrate the validity of FE results, experiments were performed. Another focus of this study is to investigate the relation between the mass ratio and the location of the resonance frequency and the relation between the numbers of unit cells and the effect of vibration reduction. The unit numbers eight, twelve and eighteen were chosen as cases for comparison.

    中文摘要 I Abstract II Acknowledgement III List of Figures VII List of Tables XI Nomenclature XIII CHAPTER 1 INTRODUCTION 1 1.1 Motivation 1 1.2 Literature Review 1 1.3 Chapter Outline 2 CHAPTER 2 THEORY 4 2.1 Forced Vibration of Two-degree-of Freedom System 4 2.1.1 Effect of mass ratio on vibration behavior 7 2.2 Forced Vibration of a Beam with Resonators 9 2.2.1 Equation of motion for Timoshenko beam 10 CHAPTER 3 FINITE ELEMENT SIMULATION 12 3.1 Introduction of ABAQUS 12 3.1.1 Preprocessing 14 3.1.2 Construct the model 14 3.1.3 Establish the steps of analysis and boundary loads 14 3.1.4 Meshing 15 3.1.5 Simulation 15 3.1.6 Postprocessing 15 3.2 Basic Formulations of Finite Element Simulations 15 3.2.1 Modal analysis 15 3.2.2 Steady-state analysis 16 3.2.3 Explicit dynamic analysis 19 CHAPTER 4 NUMERICAL RESULTS 21 4.1Free Vibration Analysis of a Supported Beam without Resonators 21 4.2 Steady-state Response of a Supported Beam with Resonators 22 4.3 Transient Response of a Beam with Resonators 27 4.3.1 Simply-supported beam 29 4.3.2 Clamped-clamped beam 32 CHAPTER 5 VIBRATION EXPERIMENT 35 5.1 Purpose of the Experiment 35 5.2 Introduction of the Experimental Equipment 35 5.2.1 Fixture, shockproof table 38 5.2.2 Uniaxial accelerometers 40 5.3 Introduction to Labview 42 5.3.1 Front panel 43 5.3.2 Block diagram 44 5.3.3 Introduction to DAQ – Data acquisition 45 5.4 Experimental Procedure 46 5.4.1 Free vibration of the beam without resonators 47 5.4.2 Forced vibration of the beam with resonators 51 5.5 Effect of Spacing on Beam Response 57 5.5.1 Simply-support beam 57 5.5.2 Clamped-clamped beam 61 5.6 Effect of Mass Ratio on Beam Response 65 5.6.1 Simple support beam 65 5.6.2 Clamped-clamped beam 69 CHAPTER 6 CONCLUSIONS 74 Reference 75

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