成功大學博碩士論文系統

簡易檢索 / 詳目顯示

回結果列表

研究生：	吳泓寬 Wu, Hung-Kuan
論文名稱：	高分子泡沫及其複合材料之線黏彈性質 Linear viscoelastic properties of polymeric foam and its composites
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：	2012
畢業學年度：	100
語文別：	英文
論文頁數：	114
中文關鍵詞：	黏彈性、頻譜、高分子、泡沫材料、複合材料
外文關鍵詞：	Viscoelasticity, Spectroscopy, Polymer, Foam, Composite materials
相關次數：	點閱：109 下載：2
分享至:	分享至facebook 分享至twitter

查詢本校圖書館目錄查詢臺灣博碩士論文知識加值系統勘誤回報

本研究探討利用鐘擺式頻譜儀(PVS)測量不同孔隙大小之高分子泡沫材料及其複合材料的線彈性性質，鐘擺式頻譜儀是由亥姆霍茲(Helmholtz)線圈的磁場和試體端點上強磁的磁場交互作用，讓一個懸臂樑產生一個純彎矩或扭矩的受力行為，再由雷射位移量測儀量測受力時的位移。正切消散模數和動態下楊氏模數與剪力模數在此儀器上的量測頻率，上限為兩萬赫茲。根據克萊默，克羅尼格轉換(Kramer-Kronig relationship)，可由潛變試驗中得到在極低頻的正切消散模數。在非共振的頻率域，經由鎖相放大器可以得到施力和位移之間的相位差。在共振的頻率域，由於材料的黏彈性質，可由共振的頻率和共振峰的寬度分別求得材料模數和正切消散模數，量測到的聚氨酯泡沫材料，材料模數介於幾十到幾百kPa，正切消散模數介於0.1到0.5之間。矽凝膠和泡沫材料組成的複合材料，材料模數介於幾十到幾百kPa，正切消散模數介於0.1到0.6之間。利用Biot理論得到不同孔隙大小之泡沫材料在不同頻率下的阻尼。Cosserat理論是利用泡沫材料在動態下的spin inertia和尺寸效應來得到材料模數。論文中的方法是藉由共振頻得到的spin inertia帶入Cosserat cantilever rod under torsion vibration解析解中算出材料模數。

An experimental apparatus is developed to measure the linear viscoelastic properties of polymer foam with various pore sizes and its composites formed by combining foam with other polymer. The apparatus consists of two sets of Helmholtz coils to generate torque or bending moment on the cantilever-beam sample by magnetic interaction between the coils and a permanent magnet that is attached to the free end of the cantilever. The deformation of the sample is measured by a laser-based measurement system, consisting of a solid-status laser and silicon-based position sensor. Loss tangent and the magnitude of complex Young's modulus and shear modulus are measured in the frequency range up to 20 kHz. Loss tangent data in the low frequency limit are inferred from creep data by the Kramer-Kronig relationship. In the sub-resonant frequency, the Lissajous method or the lock-in amplifiers achieve direct measurement of phase lag. Around the resonant frequency, viscoelastic properties are determined by the resonant frequency and peak width for modulus and loss tangent, respectively. Polyurethane foam is found that in the tested frequency range the loss tangent of the foam materials is on the order of 0.1 to 0.5. Their modulus is on the order of decades to hundreds kPa. Silicone gel with polyurethane foam and its composites are found that in the tested frequency range the loss tangent of the foam materials is on the order of 0.1 to 0.6. Their modulus is on the order of decades to hundreds kPa. The Biot theory is adopted to model the damping of the porous material in the frequency domain. The Cosserat theory is adopted to interpret the dynamic behavior of the foam with its spin inertia, and the size effects on measured modulus data. A method of using resonate frequency to determine the spin inertia is proposed by using the exact solution of the Cosserat cantilever rod under torsion vibration.

CHINESE ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1 Motivation and goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
3 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1 Viscoelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Classical elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3 The Cosserat (micropolar) model . . . . . . . . . . . . . . . . . . . . . 6
4 Micromorphic (microstructure) theory . .. . . . . . . . . . . . . . . . 8
5 Torsional vibration of a Cosserat cantilever . .. . . . . .. . . . . 10
6 Gent theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
6.1 The uniform tension and compression . . . . . . . . . . . . . . . 14
Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1 In sub-resonant situation with different angular displacement and torque getting Young’s modulus, shear modulus . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.1 Light detector calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.2 Magnet calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.3 Making Helmholtz coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.4 Specimen preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.5 Determination of angular displacement and of torque  . . . . . . . . . . . 25
2 Find resonant frequency for get Young’s modulus, shear modulus, tanδ. .  25
2.1 Determination of angular displacement and of torque by LabVIEW . . . . 25
2.2 Measure of the tan by resonance curve at half maximum . . . . . . . . . . 26
2.3 Measure of the tan by Lorentzian curve fit .  . . . . . . . . . . 26
3 Plot Lissajous figure by signal from angular displacement and torque, its let us get storage modulus and loss modulus . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1 Sensor correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Measure of the tan by elliptical Lissajous . . . . . . . . . . . . . 28
4 Creep experiment; in order to observe foam’s creep behavior . . . .  . . . 28
4.1 Periodic function and constant torque . . . . . . . . . . . . . . 28
4.2 Measure of the tan by second stage (steady state) Slope . . . . . . . . . . 28
5 Assistant tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.1 The DS345 function generator . . . . . . . .. . . . . . . . . . . . . . 29
5.2 Switch polarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.3 SR830 lock-in amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.4 DSO7032A Oscilloscope: 350 MHz, 2 channels . . . . . . . . 30
5.5 National Instrument: PXI (PCI eXtensions for Instrumentation) . . . . . . 31
5.6 Access and deal with data were by LabVIEW.  . . . . . . . 31
5.7 Using K-graph software processed data in a figure . .  . 31
Results and discussion . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 35
1 Analysis of light detector calibration data . . . . . . . . . . . . . 35
2 Analysis of magnet calibration data . . . . . . . . . . . . . . . . . . 37
3 6061T6 Al alloy data . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . 37
4 PMMA data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5 White foam data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6 Orange foam data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.1 Why frequency-scan direction would change the resonant frequency? . 55
7 Yellow foam data . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . 65
8 Compare with different material composite with silicone gel. . . . . . . . . 72
9 Compare damping with different foams under Biot theory . . . . . . .  . . . 86
Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 87
LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
APPENDICES
Appendix
Appendix A: Phase angle . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . 90
Appendix B: Polar area moment of inertia . . . . . . . . . . . . . . . . 91
Appendix C: Estimation of glue compliance . . . . . . . . . . . . . . 92
Appendix D: Presentation slide . . . . . . . . . . . . . . . . . . . . . . . . . . 93
VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
                                    

[1] R. S. Lakes. A pathological situation in micropolar elasticity . J. Applied Mechanics, 52:234–235, 1985.
[2] A.N. Gent and K.C. Rusch. Permeability of open-cell foamed materials. Journal of Cellular Plastic, 2:46–51, 1966.
[3] R. S. Lakes. Experimental methods for study of cosserat elastic solids and other generalized elastic continua. In H.-B.M¨uhlhaus, editor, Continuum models for materials with microstructure, pages 1–22, New York, 1996. John Wiley & Sons.
[4] Cihan Teko˘glu. Size effects in cellular solids. MSC PhD thesis series, 2007.
[5] P. R. Onck. Cosserat modeling of cellular solids . Journal of Mecanique, 330:717–722, 2002.
[6] A. C. Eringen. Microcontinuum field theories . 2001.
[7] W. Ehlers. Porous Media Viscoelasticity with Application to Polymeric Foams . University of Stuttgart master thesis, 2005.
[8] E.J. Graesser and C.R.Wong. The relationship of traditional damping measures for materials with high damping capacity: A Review, in M3D: Mechanics and Mechanisms of Material Damping, V.K. Kinra and A. Wolfenden, eds . ASTM STP1169, 1992.
[9] R. D. Mindlin and H. F. Tiersten. Effect of couple stresses in linear elasticity . Arch. Rational Mech. Analy, 11:415–448, 1962.
[10] S. C. Cowin. An incorrect inequality in micropolar elasticity theory . J. Appl. Math. Phys., 21:494–497, 1970.
[11] R. S. Lake. Viscoelastic materials . 2009.

校內：2017-09-05公開
校外：不公開電子論文尚未授權公開，紙本請查館藏目錄

簡易檢索 / 詳目顯示

相關論文