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研究生：	蕭力銘 Shiau, Li-Ming
論文名稱：	鐘擺式黏彈頻譜儀於鬆弛模數之量測 Pendulum-type viscoelastic spectroscopy for relaxation modulus measurements
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：	2014
畢業學年度：	102
語文別：	英文
論文頁數：	140
中文關鍵詞：	鐘擺式黏彈頻譜儀、鬆弛模數、潛變量、正切消散模數、頻率
外文關鍵詞：	Pendulum-type viscoelastic spectroscopy, relaxation modulus, creep compliance, loss tangent, frequency
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鐘擺式黏彈頻譜儀，是以磁力加載系統給予試體純彎或純扭，並用雷射位移測量系統得到其位移，進而得到固體材料的線性黏彈性質。而磁力加載方式是使用‘赫姆赫茲線圈’驅動‘磁鐵’進行加載，雷射位移測量系統則是以固態雷射與矽製成的四象限位置感測器組成。目前鐘擺式黏彈頻譜儀使用了PID回饋控制系統，PID為了進行位移控制實驗，改變輸入赫姆赫茲線圈的電流，使其可維持變形量，以量測試體的鬆弛函數。此外、使用LabView整合程式，進行鐘擺式黏彈頻譜儀的實驗，包括潛變、鬆弛與動態加載。對高分子聚合物與橡膠的線黏彈性進行了實驗量測，如聚甲基丙烯酸甲酯(PMMA)與矽橡膠(Silicone Rubber)。實驗所測得的‘潛變量’與‘鬆弛函數’以及‘正切消散模數’與‘動態模數，以用來研究線黏彈性理論。

The pendulum-type viscoelastic spectroscopy (PVS) is designed to measure linear viscoelastic properties of solid materials with a magnetic loading system and laser-based displacement measurement system. The magnetic loading system consists of a permanent magnet and Helmholtz coils. The displacement measurement system contains a solid state laser and silicon-based fourquadrant position sensor. Current refinement enables PVS to measure relaxation function under constant deformation with a PID feedback control system. The PID maintains the deformation of the sample while changing the electric current being sent into the Helmholtz coil. A limitation of current relaxation experiment is the deformation must be small. A LabView code is developed to systematically operate the PVS experiment, including creep, relaxation and dynamic loading. In this work, linear viscoelastic properties of polymer and rubbery materials, such as PMMA and silicone rubber, are experimentally measured. The measured creep compliances and relaxation functions, as well as loss tangent and complex modulus, are examined by the theory of linear viscoelasticity.

CHINESE ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1 Goals and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
3 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Theoretical foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1 Viscoelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Dynamic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1 Stress determination . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Strain determination . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Modulus determination in the sub-resonant regime . . . . . . . . . . . 8
2.4 Modulus determination in the resonant regime . . . . . . . . . . . . . 8
2.5 Determination of loss tangent . . . . . . . . . . . . . . . . . . . . . . 9
2.6 Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Constitutive relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.1 Stress and strain in viscoelastic materials . . . . . . . . . . . . . . . . 12
3.2 Creep compliance vs. relaxation function . . . . . . . . . . . . . . . . 12
3.3 Standard linear solid and related models . . . . . . . . . . . . . . . . . 13
4 Proportional-integral-derivative (PID) control theory . . . . . . . . . . . . . . 17
Experimental considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1 General aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 Description of the PVS apparatus . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.1 Generation torque and pure bending moment . . . . . . . . . . . . . . 23
2.2 Laser-based displacement measurement system . . . . . . . . . . . . . 23
3 Silicon-based position sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1 Dual axis position sensor (DL100-7PCBA3) . . . . . . . . . . . . . . . 25
3.2 Medium-frequency position sensor . . . . . . . . . . . . . . . . . . . . 26
3.3 High-frequency position sensor . . . . . . . . . . . . . . . . . . . . . 27
4 Solid-state laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5 Motorized Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6 Data acquisition system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.1 NI-PXI system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.2 NI-PCI system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
6.3 LabView . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6.4 Virtual Instrument (VI) . . . . . . . . . . . . . . . . . . . . . . . . . . 33
7 Standard operation procedures . . . . . . . . . . . . . . . . . . . . . . . . . . 33
8 Description of specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
8.1 Silicone rubber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
8.2 PMMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
1 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
1.1 Relaxation VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
1.2 Automatic Centering VI . . . . . . . . . . . . . . . . . . . . . . . . . 52
2 Measured material properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.1 Silicone Rubber relaxation measured . . . . . . . . . . . . . . . . . . 58
2.2 Silicone Rubber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.3 PMMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
APPENDICES
Appendix A: Studies of temperature effects with PVS . . . . . . . . . . . . . . . 83
Appendix B: PVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Appendix C: Aluminum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Appendix D: PVS data for biomaterials . . . . . . . . . . . . . . . . . . . . . . . 93
Appendix E: PVS data for wood . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Appendix F: The Fluid Buckets design schematic . . . . . . . . . . . . . . . . . . 103
Appendix G: Instruments and materials information . . . . . . . . . . . . . . . . 105
Appendix H: Presentation slide . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
                                    

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校內：2019-08-29公開
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