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研究生：	張天澍 Chang, Tien-Shu
論文名稱：	薄膜振動力學頻譜儀之發展 Development of thin film shaker mechanical spectroscopy
指導教授：	王雲哲 Wang, Yun-Che
學位類別：	碩士 Master
系所名稱：	工學院 - 土木工程學系 Department of Civil Engineering
論文出版年：	2013
畢業學年度：	101
語文別：	英文
論文頁數：	122
中文關鍵詞：	薄膜、力學性質、壓電材料、基底振動、裂紋辨識
外文關鍵詞：	Thin film, mechanical properties, piezoelectric materials, base excitation, crack identification
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本研究改良薄膜基底振動懸臂梁實驗，用來量測薄膜材料之力學性質，包含楊氏
模數、剪力模數，以及正切消散模數。經由實驗獲得之第一共振頻，使用古典梁理論能夠獲得薄膜楊氏模數，結果為：PET 7.4 GPa,鋁64.8 GPa,鈦106.1 GPa。然而，要獲得具有等向性及均質性材料的兩個彈性常數，還需要由實驗獲得之扭轉模態共振頻，本研究發現古典梁理論不適用於薄膜的扭轉模態。因此，本研究提出另外一個方法，我們對材料常數做最佳化，目標函數是將有限元素法模型獲得之共振頻減掉實驗獲得之共振頻後的平方。經由將有限元模型對實驗結果最佳化的方法，我們可以同時決定楊氏模數以及剪力模數，以此方法算出不鏽鋼之楊氏模數為194 GPa，剪力模數為70 GPa。我們也嘗試使用頻譜圖在接近共振頻尖端的形狀，來求出材料黏彈性質，求出PET的正切消散模數為0.069。此外，最佳化方法也能用在辨識薄膜材料中的缺陷，特別是裂縫。單條橫直裂縫之長度或距離固定端之位置可分別辨識出來。最後，為了能夠更妥善地模擬力電耦合的薄膜基底振動懸臂梁系統，我們使用壓電材料的模型來模擬雙層壓電材料致動器的行為。

This research is to refine the Thin Film Shaker (TFS) device to measure mechanical properties of materials, such as Young’s modulus, shear modulus and loss tangent. The classical Euler-Bernoulli beam model works well to extract the Young’s modulus of the thin film from the first resonant frequency, and the measured Young’s modulus are 64.8 GPa for aluminum, 106.1 GPa for titanium, 7.4 GPa for PET, separately. However, in order to obtain both elastic constants of isotropic, homogeneous materials, the resonant frequency associated to the torsional mode is identified experimentally. And, by solving the inverse problems with the COMSOL finite element software through optimization procedures, multiple elastic constants can be determined through one frequency-scan experiment with multiple identified resonant frequencies. For stainless steel, Young’s modulus 194 GPa and shear modulus 70 GPa are measured simultaneously. Attempts to extract linear viscoelastic properties of materials through fitting the shape of a resonant peak are conducted. The measured loss tangent is 0.069 for PET. Furthermore, by using the similar technique for the inverse problem, defects, such as cracks, in the thin film can be identified through TFS frequency sweep experiments. In addition, to better model the electric-mechanical system of the TFS apparatus, the finite element method is adopted to model the behavior of the bimorph piezo actuator.

CHINESE ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1 Goals and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Theoretical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1 Theory of three-dimensional cantilever beam . . . . . . . . . . . . . . . . . . 4
2 One-dimensional cantilever beam . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Duffing oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4 Consideration of extremely thin plates . . . . . . . . . . . . . . . . . . . . . . 15
5 Theory of piezoelectric actuator . . . . . . . . . . . . . . . . . . . . . . . . . 17
6 Solving inverse problems by optimization . . . . . . . . . . . . . . . . . . . . 19
6.1 Golden section search . . . . . . . . . . . . . . . . . . . . . . . . . . 19
6.2 Nelder-Mead simplex method . . . . . . . . . . . . . . . . . . . . . . 19
6.3 Genetic algorithm (GA) . . . . . . . . . . . . . . . . . . . . . . . . . 20
7 Lorentzian function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1 Working principles of thin film shaker . . . . . . . . . . . . . . . . . . . . . . 24
2 Bimorph piezoelectric transducers . . . . . . . . . . . . . . . . . . . . . . . . 26
2.1 Lead zirconate titanate (PZT) material . . . . . . . . . . . . . . . . . . 26
2.2 Types of bimorph piezoelectric transducers . . . . . . . . . . . . . . . 26
2.3 Bimorph piezoelectric used in thin film shaker experiment . . . . . . . 26
3 Calibration of fiber optics displacement sensors . . . . . . . . . . . . . . . . . 27
4 Standard operation procedures . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Numerical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
1 General description of COMSOL . . . . . . . . . . . . . . . . . . . . . . . . . 36
2 LiveLinkTM for MATLABR . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3 Details of numerical parameters . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.1 Global definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
1 Determination of E and G simultaneously . . . . . . . . . . . . . . . . . . . . 45
2 Determination of linear viscoelastic moduli . . . . . . . . . . . . . . . . . . . 52
3 Parasitic losses due to air damping . . . . . . . . . . . . . . . . . . . . . . . . 61
4 Identification of cracks in thin film . . . . . . . . . . . . . . . . . . . . . . . . 66
4.1 Comparison of FEM and experimental results . . . . . . . . . . . . . . 66
4.2 Polycrystalline titanium thin film crack identification . . . . . . . . . . 69
5 Detection of mechanical fatigue . . . . . . . . . . . . . . . . . . . . . . . . . 71
6 Simulation of piezoelectric actuator . . . . . . . . . . . . . . . . . . . . . . . 75
6.1 Direct piezoelectric effect . . . . . . . . . . . . . . . . . . . . . . . . 75
6.2 Converse piezoelectric effect . . . . . . . . . . . . . . . . . . . . . . . 77
7 Nonlinear effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
APPENDICES
Appendix A: Presentation slides . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Appendix B: MATLAB Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Appendix C: Crack theory according to material mechanics . . . . . . . . . . . . 113
Appendix D: Triangular cantilever beam . . . . . . . . . . . . . . . . . . . . . . 118
VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

                                    

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校內：2018-08-27公開
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