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研究生:伊柏
研究生(外文):Ivo Stachiv
論文名稱:一維多層性材料之機械振動系統研究及其在光學黏度計之應用
論文名稱(外文):A study of one-dimensional mechanical vibrating systems with piecewise constant properties and its applications as an optical viscosimeter
指導教授:王安邦王安邦引用關係A.I.Fedorchenko
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:應用力學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:英文
論文頁數:122
中文關鍵詞:自然頻率光學黏度計
外文關鍵詞:normal modesoptical viscosimetervibration
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本文主要探討一維震動機制系統(one-dimensional mechanical systems with piecewise constant properties)的分析與應用。而振動分析的第一步驟通常是利用數值解或分析解找到自然頻率(natural frequency)下之振盪頻譜。對一個有固定材料參數的振盪系統如同樑(beam)、繩(string)和懸臂樑(cantilever beam)是比較簡單處理的。然而,很多實際的應用包含了不連續的非固定的材料參數。
對一個複合系統(composed system)來說,數值解常常被用判定其模態。但藉由數值計算並無法正確得到各個參數(彈性係數、密度、斷面長度、斷面材料等)對複合系統的影響。為了求得各參數對該複合系統的影響,分析解是有必要的。
本文假設一維系統與N段固定參數(N-piecewise constant properties),並導入一「有效傳遞速度」(effective propagation velocity)求得其分析解。為了測試本理論在第二模態(N=2)的可靠度,利用散射光圖樣辦識的光學實驗方法得到,第一模態頻率的實驗數據與分析解所得的解相同。為了延伸此分析解,吾人設計一實驗如下:將一繩(fiber)之下半部分浸入液體中並振動該繩,並視液體為阻尼後量測該繩的振盪機制。無論是最大振幅(maximum vibrational amplitude)或是能量帶寬的變異(power bandwidth variation),分析解所得之值與實驗數據是吻合的,而由該設計實驗所推出分析解也列在本論文中。
This thesis deals with an analysis and application of the vibrating one-dimensional mechanical systems with piecewise constant properties. It is a well known fact that the fist step in a vibration analysis of any mechanical system is to find spectrum of their natural frequencies. It can be done either numerically or analytically. For simple vibrating systems like beam, string or cantilever with constant mechanical properties the analytical determination of the normal modes is known and is preferable one. However many real applications involve not a constant but a piecewise constant and, factually discontinuous properties. For composed systems the numerical determination of the normal modes is usually performed. We have found here that the normal modes for one–dimensional mechanical problems with piecewise constant properties can be obtained by solving an appropriate transcendental equation. This equation of course contains all information about given mechanical system (elastic moduli, density, cross-sectional area of material, thickness of each layer with constant mechanical properties, etc.). In this thesis transcendental equation is derived for case of one-dimensional systems with N - piecewise constant properties. The physical interpretation of normal modes for this kind of mechanical systems by introducing the “effective” propagation velocity has been put forward. An optical method utilizing a forward light scattering pattern has been carried out to test the validity of the theory for N = 2. Theoretical predictions of the first mode frequency and experimental data agree precisely. Moreover the extension of the analysis and experiments for a case of the partially submerged fiber in fluid with taking into account of a viscous damping has been performed. From obtained results a simple way for viscosity extraction from either the maximum vibrational amplitude or the power bandwidth variation has been suggested and tested experimentally. Besides an explicit formula for the achievable accuracy of the viscosity sensing is derived here as well.
Abstract.....................................................................................................................................................i
中文摘要................................................................................................................................................ii
Dedication...............................................................................................................................................iv
Contents...................................................................................................................................................v
List of figures..........................................................................................................................................ix
List of tables.........................................................................................................................................xvii
1 Introduction..................................................................................................................................1
1.1 Vibration, Normal modes, Resonance.......................................................................................2
1.1.1 Resonance and natural frequencies in nature and engineering·········································2
1.1.2 One-dimensional mechanical systems and methods of solution······································3
1.2 Viscometers and viscosity measurement techniques.................................................................6
2 Normal modes of the vibrating one dimensional mechanical systems with piecewise constant properties................................................................................................................................................18
2.1 Mathematical description of the mechanical system with N piecewise constant properties...19
2.2 Mathematical models for mechanical systems with one, two and three piecewise constant properties (Inverse Laplace transform technique)...............................................................................20
2.3 Mathematical models for mechanical systems with an arbitrary number of the piecewise constant properties..............................................................................................................................34
2.4 Effective model for the normal modes.....................................................................................35
3 Optical viscosimeter...................................................................................................................37
3.1 Experimental system setup and the sensor principle...............................................................38
3.1.1 System setup··················································································································38
v
3.1.2 Sensor principle·············································································································40
3.2 Mathematical model.................................................................................................................42
3.2.1 Dimensionless analysis··································································································42
3.2.2 Forced vibration of the fiber fully submerged in fluid···················································44
3.2.2.1 Forced vibration of the fully submerged fiber in fluid without damping 45
3.2.2.2 Forced vibration of the fully immersed fiber in fluid 48
3.2.3 Partially submerged fiber in fluid··················································································52
3.2.3.1 Normal modes – an effective model of the velocity propagation 52
3.2.3.2 Normal modes – analytical determination 53
3.2.3.3 Forced vibration of the partially submerged fiber (Numerical method) 57
4 Results and comparison..............................................................................................................70
4.1 Experimental studies................................................................................................................70
4.2 Numerical computation results for the fiber partially submerged in fluid...............................82
4.3 Comparison of the theoretical predictions, numerical computations data and experimental results .................................................................................................................................................93
4.4 Achievable accuracy of the viscosity measurement................................................................98
4.4.1 Viscosity extraction from experimental data·······························································103
5 Conclusions..............................................................................................................................107
Acknowledgement...............................................................................................................................110
References............................................................................................................................................112
Appendix..............................................................................................................................................116
A.1 Finite difference scheme........................................................................................................116
A.2 Properties of the glycerol/sucrose – water solutions (GWS/SWS)........................................122
[1] Strogatz, S. H., Abrams, D. M., McRobie, A., Eckhardt, B., Ott, E. Crowd synchrony on the Millennium Bridge. Nature 438, 43 - 44 (2005).
[2] Eckhard, B., Ott, E., Strogatz, S. H., Abrams, D. M., McRobie, A. Modeling walker synchronization on the Millennium Bridge. Phys. Rev. E 75, 021110 (2007).
[3] Zettl, A., Sturm–Liouville theory (Providence, R.I.: American Mathematical Society, 2005).
[4] Al-Gwaiz, M. A., Sturm–Liouville theory and its applications (London, Springler, 2008).
[5] Goldstein, H., Classical mechanics (Addison-Wesley Pub. Co., 1980).
[6] Morse, P. M., Vibration and sound (New York, Amer. Inst. of the physics for the acoustical soc of Amer. Co., 1981).
[7] Rayleigh, B., Strutt J.W., The theory of sound (New York, Dover Pub. Co., 1945).
[8] Timoshenko, S., Vibration problems in engineering (New York, D. van Nostrand Co., 1959).
[9] O’Neil P. V., Advanced engineering mathematics (Brooks/Cole Publ. Co., 1995).
[10] Tikhonov, A. N., Samarski A. A., Partial differential equations of mathematical physics (San Francisco, Holden-Day, Inc., 1964).
[11] Stakgold, I. Boundary value problems of mathematical physics, vol. I. & II. (New York, SIAM, 1968).
[12] Franklin, P., An introduction to Fourier methods and the Laplace transformation (New York, Dover Publ. Co., 1958).
[13] Morse, P. M., Feshbach H., Methods of theoretical physics (New York, McGraw – Hill, 1953).
[14] Street, R. L., The analysis and solution of partial differential equations (New York, Brooks/Cole Publ. company, 1973).
[15] Prudnikov, A. P., Brychkov, Y. A., Marichev, O. I., Integral and series (New York, Gordon and Beach Science Publ., 1986).
[16] Spiegel, M. R., Theory and problems of Laplace transform (New York, Schaum publ., 1965).
[17] Jaeger, J. C., Newstead, G. H. An introduction to the Laplace transformation with engineering applications (London, Metheum Pulb., 1969).
[18] Kuhfittig, K. F. P. An introduction to the Laplace transform (New York, Plenum Press., 1980).
[19] Lebedev, N. N., Skalskaya, I. P., Ufland, Y. S., Worked problems in applied mathematics (New York, Dover Publ. Inc, 1965).
[20] Fox, R. W., McDonald, A. T., Introduction to fluid mechanics (New York, John Wiley & Sons Inc, 1998).
[21] Landau, L. D., Lifshitz, E. M., Fluid mechanics (Oxford, England, Pergamon Press, 1987).
[22] Liptak, B. G., Venczel K., Instrument engineers` handbook, Process measurement (Chilton Book Co, 1982).
[23] Streeter, V. L., Fluid mechanics (New York, McGraw-Hill, 1998).
[24] Martin, S. J., Ricco, A. J., Hughes, R. C. Acoustics wave device for sensing in liquids. Transducer 87, 478 – 481(1987).
[25] Martin, B. A., Wenzel, S. W., White, R. M. Viscosity and density sensing with ultrasonic plate waves. Sensors and Actuators, A: physical 22, 704 – 708 (1990).
[26] Muramatsu, H, Suda, M., Ataka, T., Seki, A., Tamyia, E., Karube, I. Piezoelectric resonator as a chemical and biochemical sensing device. Sensors and Actuators, A: physical 21, 362 – 368 (1990).
[27] Wang, W. - C., A new optical Microsensor for mechanical detection using scattering of a micro-pipette, Master Thesis, University of Washington, Electrical Engineering Department (Seattle, 1992).
[28] Wang, W. - C., Afromowitz, M., Hannaford, B. Technique for mechanical measurement using optical scattering from a micro-pippete. IEEE Transaction Biomedical Engineering, A: physical 41, 298 – 304 (1994).
[29] Wang, W. - C., Yee, S., Reinhall, P. Optical viscosity sensor using forward light scattering. Sensor & Actuator Proc. for the fifth int''l meeting on chemical sensors, Rome, Italy (1994).
[30] L. I. Mandelshtam, Lectures on the theory of oscillations (Moscow, Nauka, 1972).
[31] Wang, W.-C., Yee, S., Reinhall, P. Optical viscosity sensor using forward light scattering, Sensors and Actuators, B: chemical 25, 735-755 (1995).
[32] Wang, W.-C., Reinhall, P., Yee, S. Fluid viscosity and mass flow measurement using forward light scattering, SPIE Proc. for the pacific fiber optics sensor workshop, Portland, Oregon, USA May (1995).
[33] Spiegel, M. R., Theory and problems of Laplace transform (Schaum publ., New York, (1965).
[34] Churchill, R. R., Operational mathematics (McGraw – Hill, New York, 1972).
[35] Carslaw, H. S., Jaeger, J. C., Operational methods in applied mathematics (Oxford University Press, 1963).
[36] Churchill, R. R., Brown, J. W., Complex variables and applications (New York, McGraw–Hill Book comp., 1984).
[37] Fedorchenko, A. I., Gorin, A. V. Film absorption on a plane surface imbedded in a granulated medium. J. of Applied Mechanics and Technical Physics, 3, 406 - 421 (1995).
[38] Wang, W. - C., A study of fluid viscosity and flow measurement using fiber-optic transducer, Doctoral Dissertation, University of Washington, Electrical Engineering Department (Seattle, 1996).
[39] Yamada, H., Mohri, N., Saito, N., Magara, T., Furutani, K. Modal analysis of wire electrode vibration in wire-EMD, Int. J. of Electrical machining, 2, 19-24 (1997).
[40] Melnikova, T. S., Pikalov, V. V.. Tomographic diagnostic of low temperature plasmas, Sov. J. Appl. Phys. 1(6), 61-70 (1987).
[41] Farlow, S. J., Partial differential equations for scientists and engineers (John Wiley & Sons, Inc., 1982).
[42] Cain, G., Meyer, G. H., Separation of variables for partial differential equations, An Eigenfunction approach (Chapman & Hall/CRC, 2006).
[43] Jeffreys, H., Jeffreys, B. S. Methods of mathematical physics. (Cambridge: The University press, 1972).
[44] Powers, D.L., Boundary value problems (Harcourt Academic press, 1983).
[45] Weast, R.C. (Editor), CRC Handbook of chemistry and physics, 57th edition (CRC Press, Cleveland, 1976).
[46] Tikhonov, A. N., Samarskii, A. A. Equations of mathematical physics (translated by Robson A. R. M.) (Pergamon press, 1963).
[47] Budak, B. M., Samarskii, A. A., Tikhonov, A. N. A collection of problems on mathematical physics. (translated by Robson A. R. M.) (Pergamon press, 1964).
[48] Logan, D. L. A first course in the finite element method. (Boston, PWS-KENT Publ. comp., 1992).
[49] Smith, G. D. Numerical solution of the partial differential equations, finite difference methods. (Oxford Press, 1978).
[50] Fedorchenko, A. I., Chernov, A. A. Simulation of the microstructure of a thin film metal layer quenched from a liquid state. Int. Journal of heat and mass transfer, 46, 921 – 929 (2003).
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