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研究生： 柯朝智
Ko, Chao-Jhih
論文名稱： 以懸臂樑基底振動量測薄膜的黏彈力學性質
Measurement of viscoelastic properties of thin-film materials via cantilever beams under base excitation
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： 2011
畢業學年度： 99
語文別： 英文
論文頁數： 124
中文關鍵詞： 懸臂樑 、基底振動 、楊氏模數 、剪力模數 、線性黏彈性阻尼
外文關鍵詞： Cantilever Beam, Base Excitation, Young’s modulus, Shear modulus, Linear viscoelastic damping
相關次數： 點閱：107  下載：3 
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    • 本文將探討薄膜懸臂梁受基底振動時，所產生的力學行為。在實驗上，採取將薄膜懸臂梁簡稱試體，固定於壓電材料上，使壓電材料扮演試體基底的角色。然後給予壓電材料某一頻率範圍的電壓，壓電材料因受某一頻率範圍電壓的影響，將會產生週期性的基底振動。而試體同樣會受這週期性振動的影響，產生振動與變形。在觀察試體的變形位移與壓電材料的振動位移則由光纖位移器量測，透過光纖位移器的光纖束，射出光線與吸收反射，量測試體的與壓電材料兩者各自的位移量，觀察出試體的共振峰，藉此找出試體的共振頻率。測試多種不同尺寸的試體，找出數組共振頻率後，再透過古典梁理論公式，最後將可求得試體的楊氏模數。求得的楊氏模數如下:鋁膠帶75GP 、150um鋁箔60.7GPa、Alfa-Aesar鋁箔69.5GPa、銅膠帶110GPa、170um銅箔110GPa、Alfa-Aesar鈦箔104GPa、塑膠10.6GPa。並且比較不同試體長度與線性黏彈性阻尼損失之間的關係。另外還有嘗試不同的方法，例如尋找試體的扭轉模態與裂縫。在扭轉模態的部分是已經可以成功分辨試體的扭轉模態，再來是嘗試能否藉此找出剪力模數。但在裂縫分析，實驗還是有待改進，到目前還無法由頻譜決定裂縫長度及方向。

    Mechanical properties of thin-film-like materials are experimentally studied with the Thin-Film Beam Shaker (TFBS) device. The thickness of the materials is less than 200 m. Experimental data of the Young’s modulus, shear modulus and linear viscoelastic damping of various king of materials, such as metals and plastics, are obtained via the resonance of the vibrating cantilever beam under base excitation. The base excitation is generated by the bimorph piezoelectric plate, and the displacements of the bimorph and sample are monitored via the fiber-optic displacement measurement system. Mechanical properties are deduced from the resonant peaks. It was found that the Young’s modulus of the thin films can be accurately measured, but the linear viscoelastic damping measurements are strongly affected by the nteraction between the specimen and air, as well as he support damping. The aluminum tape of Young’s modulus is 75GPa. The 150um aluminum foil is 60.7GPa. The Alfa-Aesar aluminum foil is 69.5GPa. The copper tape is 110GPa. The 170um copper foil is 110GPa. The Alfa-Aesar titanium foil is 104GPa. The PET foil is 10.6GPa. The shear modulus may be determined if the width ofthe specimen is large enough so that the second resonant mode is the torsional mode, so that the TFBS apparatus can capture the resonance.

    CHINESE ABSTRACT . . . . . . . . . . . . . . . . . . . . ii ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . iii LIST OF TABLES . . . . . . . . . . . . . . . . . . . . vii LIST OF FIGURES . . . . . . . . . . . . . . . . . . . viii NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . xv 1 Introduction . . . . . . . . . . . . . . . . . . . . . 1 1.1 Goals and motivation . . . . . . . . . . . . . . . . 1 1.2 Literature review . . . . . . . . . . . . . . . . . . 2 1.3 Outline of this thesis . . . . . . . . . . . . . . . 3 2 Theory . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1 Beam vibration theory from mechanics of materials . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Torsional vibration of a beam . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 A two degrees of freedom discrete model . . . . . . . . . . . . . . . . . . . . 8 2.4 Three-dimensional beam bending theory under base excitation . . . . . . . . . 11 2.5 Loss mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5.1 Air loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.5.2 Support loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.5.3 Thermoelastic loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.5.4 Surface loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.5.5 Loss due to material microstructures . . . . . . . . . . . . . . . . . . . 13 2.6 Lorentzian curve fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.1 The TFBS apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.1.1 MTI-2100 Fotonic sensor . . . . . . . . . . . . . . . . . . . . . . . . 15 3.1.2 Piezoelectricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.1.3 The apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 Data acquisition system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.1 Lock-in amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.2 National Instrument: PXI (PCI eXtensions for Instrumentation) . . . . 27 3.2.3 LabView . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3 Microscopic work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.3.1 Optical microscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.3.2 Scanning electron microscope . . . . . . . . . . . . . . . . . . . . . . 40 3.4 Specimens introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.1 Aluminum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.1.1 Aluminum tape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.1.2 150 m aluminum foil . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.1.3 Alfa-Aesar aluminum foil . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2 Copper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.2.1 Copper tape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.2.2 170 m copper foil . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.3 Titanium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.3.1 Alfa-Aesar Titanium foil . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.4 Polyethylene terephthalate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.4.1 Polyethylene terephthalate foil . . . . . . . . . . . . . . . . . . . . . . 73 4.5 Determination of shear modulus from torsional mode . . . . . . . . . . . . . . 77 4.6 Defect detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 APPENDICES Appendix A: TFBS Experimental Step . . . . . . . . . . . . . . . . . . . . . . . 88 Appendix B: Optical Microscope Use Step . . . . . . . . . . . . . . . . . . . . . 92 Appendix C: Extended Chinese Abstract . . . . . . . . . . . . . . . . . . . . . . 99 VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

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