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：	林暐智 Lin, Wei-Jr
論文名稱：	軸向移動系統動態特性之研究 A Study on Dynamic Characteristics of Axially Moving System
指導教授：	崔兆棠 Choi, Siu-Ting
學位類別：	博士 Doctor
系所名稱：	工學院 - 航空太空工程學系 Department of Aeronautics & Astronautics
論文出版年：	2007
畢業學年度：	95
語文別：	英文
論文頁數：	120
中文關鍵詞：	週期性來回伸縮運動、傅羅凱理論、穩定性、有限元素法、軸向移動樑、自旋
外文關鍵詞：	spin, back-and-forth periodical motion, stability, Floquet theory, axially moving beam, finite element method
相關次數：	點閱：102 下載：3
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

在本論文中將研究具有移動支撐或固定支撐之軸向移動且自旋樑的動態特性，並探討等速率伸長及週期性來回伸縮之兩種軸向移動型態對軸向移動樑之動態特性的影響。首先，以考慮旋轉慣性的雷利樑(Rayleigh beam)理論來描述軸向移動樑之變形，利用漢彌頓原理(Hamilton's principle)及具時變元素和非時變元素之有限元素法推導出系統之運動方程式。利用阮奇-庫達(Runge-Kutta)數值積分方法，解出系統之振動響應，並分別使用特徵值之實部與虛部或傅羅凱理論(Floquet theory)來判別具軸向等速率伸長或週期性來回伸縮運動型態之移動樑的穩定性，並由響應分析結果確認穩定性分析之正確性。
由結果可知，等速率伸長之移動樑存在不穩定性，其不穩定之發生與移動樑之長度及移動速率有關。週期性來回伸縮之移動樑也存在不穩定性，其不穩定之發生與軸向振動頻率及振幅有關，且其不穩定區域發生在自然頻率之線性組合之鄰近區域。樑的自旋運動可抑制等速率伸長移動樑之振幅，並使週期性來回伸縮之移動樑之不穩定區域由轉速為零時之V型態轉變成W型態，隨著轉速增加，其不穩定區域也隨之擴大。附加於移動樑上之彈性支撐會提高系統之自然頻率、抑制暫態響應的振幅及使不穩定區域偏移到較高軸向振動頻率的區域。

In this dissertation, the dynamic characteristics of an axially moving system is investigated. An axially moving and spinning Rayleigh beam with and without an intermediate elastic support is discussed. Two kinds of axial motion including constant-speed extension deployment and back-and-forth periodical motion are considered. The axially moving beam is modeled by using Rayleigh beam theory in which the rotary inertia is taken into account. Finite element models for the above system are developed by using Hamilton's principle and the finite element method with variable-domain and fixed-domain elements for determination of natural frequencies, transient responses and stability. Direct time numerical integration, based on a Runge-Kutta algorithm, is used to perform the dynamic analysis. For stability analysis, eigenvalues of motion equation of the beam with constant-speed axial extension deployment are obtained to determine its stability, while Floquet theory is employed to investigate the stability of the beam with back-and-forth periodical axial motion. Time histories are obtained to confirm the results from Floquet theory.
The present results show that instability exists for the beam with constant-speed axial extension deployment and the protruded length at which instability occurs depends on the extension rate. Instability also exists for the beam with back-and-forth periodical axial motion and the occurrence of instability depends on the axial-oscillation amplitude and frequencies and its unstable regions are near the combination of the corresponding natural frequencies. The spinning motion of the beam has the effect of suppression on the vibration amplitude of the beam with constant-speed axial extension deployment. Instability regions of the beam with back-and-forth periodical axial motion are changed from V-shaped for non-spinning case to W-shaped and broadened as the spin speed increases. An added intermediate elastic support to the axially moving beam raises the natural frequencies, suppresses the transient responses and shifts the unstable regions to higher axial-oscillation frequencies.

ABSTRACT  i
LIST OF TABLES  vi
LIST OF FIGURES  vii
NOMENCLATURE  xii

CHAPTER I	 INTRODUCTION  1
1.1 Motivation and Objective  1
1.2 Literature Review  2
1.3 Dissertation Outline  10
II VIBRATION AND STABILITY OF AN AXIALLY MOVING
RAYLEIGH BEAM  11
2.1 Theory and Formulation  11
2.1.1 Finite Element Discretization  12
2.1.2 System Equations of Motion  16
2.2 Stability Analysis  17
2.2.1 Stability Analysis by Eigenvalues  17
2.2.2 Stability Analysis by Floquet Theory  19
2.3 Numerical Results and Discussion  19
2.3.1 Comparison with Available Results  19
2.3.2 Effect of Axial-oscillation Frequency on the Quasi-frequency	  20
2.3.3 Dynamics and Stability of Beams with Constant-speed Axial Extension Deployment  22
2.3.4 Dynamics and Stability of Beams with Back-and-forth Periodical Axial Motion  22
2.4 Conclusions  23
III VIBRATION AND STABILITY OF AN AXIALLY MOVING AND
SPINNING RAYLEIGH BEAM  25
3.1 Theory and Formulation  25
3.1.1 Finite Element Discretization  26
3.1.2 System Equations of Motion  33
3.2 Numerical Results and Discussion  34
3.2.1 Vibration and Stability of Beams with Constant-speed Axial Extension Deployment  34
3.2.2 Vibration and Stability of Beams with Periodical Axial Motion  35
3.3 Conclusions  36
IV VIBRATION AND STABILITY OF AN AXIALLY MOVING
RAYLEIGHT BEAM WITH AN ELASTIC SUPPORT  38
4.1 Theory and Formulation  38
4.1.1 Finite Element Discretization  39
4.1.2 System Equations of Motion  41
4.2 Numerical Results and Discussion  41
4.2.1 Initial Conditions  41
4.2.2 Dynamic Behavior of Beams with Constant-speed Axial Extension Deployment with a Stationary Elastic Support  42
4.2.3 Dynamic Behavior of Beams with Constant-speed Axial Extension Deployment with a Moving Elastic Support  43
4.2.4 Vibration and Stability of Beams with Periodical Axial Motion with a Stationary Elastic Support  44
4.3 Conclusions  47
V CONCLUSIONS  48
REFERENCES  51
APPENDIX A  57
APPENDIX B  62
TABLES  73
FIGURES  75
PUBLICATION LIST  118
VITA  120
                                    

Adams, G. G., 1982, An Elastic Strip Moving Across a Rigid Step, International Journal of Solids and Structures, 18(9), 763-774.
Adams, G. G., and Manor, H., 1981, Steady Motion of an Elastic Beam across a Rigid Step, Journal of Applied Mechanics, 48(3), 606-612.
Al-Bedoor, B. O., and Khulief, Y. A., 1996a, Vibrational Motion of an Elastic Beam with Prismatic and Revolute Joints, Journal of Sound and Vibration, 190(2), 195-206.
Al-Bedoor, B. O., and Khulief, Y. A., 1996b, An Approximated Analytical Solution of Beam Vibrations during Axial Motion, Journal of Sound and Vibration, 192(1), 159-171.
Al-jawi, A. A. N., Pierre, C., and Ulsoy, A. G., 1995a, Vibration Localization in Dual-Span Axially Moving Beam, Part I: Formulation and Results, Journal of Sound and Vibration, 179(2), 243-266.
Al-jawi, A. A. N., Pierre, C., and Ulsoy, A. G., 1995b, Vibration Localization in Dual-Span Axially Moving Beam, Part II: Perturbation Analysis, Journal of Sound and Vibration, 179(2), 267-287.
Alspaugh, D. W., 1967, Torsional Vibration of a Moving Band, Journal of the Franklin Institute, 283(4), 328-338.
Barakat, R., 1967, Transverse Vibrations of a Moving Rod, Journal of the Acoustical Society of America, 43(3), 533-539.
Buffington, K. W., and Kane, T. R., 1985, Dynamics of a Beam Moving Over Supports, International Journal of Solids and Structures, 21(7), 617-643.
Cepon, G., and Boltezar, M., 2007, Computing the Dynamic Response of an Axially Moving Continuum, Journal of Sound and Vibration, 300, 316-329.
Chen, L. Q., and Yang, X. D., 2005, Stability in Parametric Resonance of an Axially Moving Viscoelastic Beams with Time-dependent Speed, Journal of Sound and Vibration, 284, 879-891.
Chen, L. Q., and Zhao, W. J., 2005, A Conserved Quantity and the Stability of Axially Moving Nonlinear Beams, Journal of Sound and Vibration, 286, 663-668.
Chen, L. Q., Yang, X. D., and Cheng, C. J., 2004, Dynamic Stability of an Axially Accelerating Viscoelastic Beam, European Journal of Mechanics A/Solids, 23, 659-666.
Chonan, S., 1986, Steady State Response of an Axially Moving Strip Subjected to a Stationary Lateral Load, Journal of Sound and Vibration, 107(1), 155-165.
Chubachi, T., 1958, Lateral Vibration of Axially Moving Wire or Belt Form Materials, Bulletin of the Japan Society of Mechanical Engineers, 1(1), 24-29.
Elmaraghy, R. and Tabarrok, B., 1975, On the Dynamic Stability of an Axially Oscillating Beam, Journal of the Franklin Institute, 300(1), 25-39.
Fryba, L., 1972, Vibration of Solids and Structure under Moving Loads, Noordhoff International Pub., Groningen, Netherlands.
Fung, R. F., Lu, P. Y., and Tseng, C. C., 1998, Non-linearly Dynamic Modeling of an Axially Moving Beam with a Tip Mass, Journal of Sound and Vibration, 218(4), 559-571.
Gosselin, F., Paidoussis, M. P., and Misra, A. K., 2007, Stability of a Deploying/extruding Beam in Dense Fluid, Journal of Sound and Vibration, 299, 123-142.
Jankovic, M. S., 1983, Comments on Dynamics of a Spacecraft during Extension of Flexible Appendages, Journal of Guidance, 7(1), 128.
Kong, L. and Parker, R. G., 2004, Approximate Eigensolutions of Axially Moving Beams with Small Flexural Stiffness, Journal of Sound and Vibration, 276, 459-469.
Kozin, F., and Milstead, R. M., 1979, The Stability of a Moving Elastic Strip Subjected to Random Parametric Excitation, Journal of Applied Mechanics, 46(2), 404-410.
Lee, H. P., 1994, Vibrations of a Pretwisted Spinning and Axially Moving Beam, Computers & Structures, 52(3), 595-601.
Lee, H. P., 1995, Flexural Vibration of an Orthotropic Rotating Shaft Moving over Supports, Journal of Sound and Vibration, 179(2), 347-357.
Lee, U., Kim, J., and Oh, H., 2004, Spectral Analysis for the Transverse Vibration of an Axially Moving Timoshenko Beam, Journal of Sound and Vibration, 271, 685-703.
Liu, K., and Deng, L., 2006, Identification of Pseudo-natural Frequencies of an Axially Moving Cantilever Beam Using a Subspace-based Algorithm, Mechanical Systems and Signal Processing, 20, 94-113.
Manor, H., and Adams, G. G., 1983, An Elastic Beam Moving with Constant Speed across a Drop-out, International Journal of Mechanical Sciences, 25(2), 137-147.
Mote, C. D., Jr., 1965, A Study of Bandsaw Vibrations, Journal of the Franklin Institute, 279(6), 430-444.
Mote, C. D., Jr., 1968, Divergence Buckling of an Edge-Loaded Axially Moving Band, International Journal of Mechanical Sciences, 10(4), 281-295.
Mote, C. D., Jr., 1972, Dynamic Stability of Axially Moving Materials, The Shock and Vibration Digest, 14(4), 2-11.
Mote, C. D., Jr., and Naguleswaran, S., 1966, Theoretical and Experimental Band Saw Vibrations, Journal of Engineering for Industry, 88(2), 151-156.
Nayfeh, A. H., and Mook, D., 1979, Nonlinear Oscillations, Wiley, New York, USA.
Nelson, H. D., and McVaugh, J. M., 1976, The Dynamics of Rotor-Bearing Systems Using Finite Elements, Journal of Engineering for Industry, 98, 593-600.
Nelson, H. M., 1979, Transverse Vibration of a Moving Strip, Journal of Sound and Vibration, 65(3), 381-389.
Oz, H. R., and Pakdemirli, M., 1999, Vibrations of an Axially Moving Beam with Time-dependent Velocity, Journal of Sound and Vibration, 227(2), 239-257.
Oz, H. R., Pakdemirli, M., and Boyaci, H., 2001, Non-linear Vibrations and Stability of Axially Moving Beam with Time-dependent Velocity, International Journal of Non-Linear Mechanics, 36, 107-115.
Ozkaya, E., and Oz, H. R., 2002, Determination of Natural Frequencies and Stability Regions of Axially Moving Beams Using Artificial Neural Networks Method, Journal of Sound and Vibration, 252(4), 782-789.
Ozkaya, E., and Pakdemirli, M., 2000, Vibrations of an Axially Accelerating Beam with Small Flexural Stiffness, Journal of Sound and Vibration, 234(3), 521-535.
Pakdemirli, M., and Batan, H., 1993, Dynamic Stability of a Constantly Accelerating Strip, Journal of Sound and Vibration, 168, 371-378.
Patula, E. J., 1976, Attenuation of Concentrated Loads in a Thin Moving Elastic Strip, Journal of Applied Mechanics, 43(3), 475-479.
Pellicano, F., and Vestroni, F., 2000, Nonlinear Dynamics and Bifurcations of an Axially Moving Beam, Journal of Vibration and Acoustics, 122, 21-30.
Pellicano, F., and Vestroni, F., 2002, Complex Dynamics of High-speed Axially Moving Systems, Journal of Sound and Vibration, 258(1), 31-44.
Pellicano, F., and Zirilli, F., 1998, Boundary Layers and Nonlinear Vibrations of an Axially Moving Beam, International Journal of Non-Linear Mechanics, 33(4), 691-711.
Simpson, A., 1973, Transverse Modes and Frequencies of Beams Translation between Fixed End Supports, Journal of Mechanical Engineering Science, 15(3), 159-164.
Soler, A. I., 1968, Vibration and Stability of a Moving Band, Journal of the Franklin Institute, 286(4), 295-307.
Stylianou, M., and Tabarrok, B., 1994a, Finite Element Analysis of an Axially Moving Beam, Part I: Time Integration, Journal of Sound and Vibration, 178(4), 433-453.
Stylianou, M., and Tabarrok, B., 1994b, Finite Element Analysis of an Axially Moving Beam, Part II: Stability Analysis, Journal of Sound and Vibration, 178(4), 455-481.
Sze, K. Y., Chen, S. H., and Huang, J. L., 2005, The Incremental Harmonic Balance Method for Nonlinear Vibration of Axially Moving Beams, Journal of Sound and Vibration, 281, 611-626.
Tabarrok, B., Leech, C. M., and Kim, Y. I., 1974, On the Dynamics of an Axially Moving Beam, Journal of the Franklin Institute, 297(3), 201-220.
Theodore, R. J., Arakeri, J. H., and Ghosal, A., 1996, The Modelling of Axially Translation Flexible Beams, Journal of Sound and Vibration, 191(3), 363-376.
Tsuchiya, K., 1983, Dynamics of a Spacecraft during Extension of Flexible Appendages, Journal of Guidance, 6(2), 100-103.
Wang, P. K. C., and Wei, J. D., 1987, Vibrations in a Moving Flexible Robot Arm, Journal of Sound and Vibration, 116(1), 149-160.
Wickert, J. A., 1992, Non-linear Vibration of a Traveling Tensioned Beam, International Journal of Non-Linear Mechanics, 27, 503-517.
Wickert, J. A., and Mote, C. D., Jr., 1988, Current Research on Vibration and Stability of Axially-moving Materials, The Shock and Vibration Digest, 20(4), 3-13.
Wickert, J. A., and Mote, C. D., Jr., 1990, Classical Vibration Analysis of Axially Moving Continua, Journal of Applied Mechanics, 57, 738-744.
Wickert, J. A., and Mote, C. D., Jr.,1991, Response and Discretization Methods for Axially Moving Materials, Applied Mechanics Reviews, 44, 279-284.
Wu, W. Z., and Mote, C. D., Jr., 1986, Parametric Excitation of an Axially Moving Band by Periodic Edge Loading, Journal of Sound and Vibration, 110(1), 27-39.
Yuh, J., and Young, T., 1991, Dynamics Modeling of an Axially Moving Beam in Rotation: Simulation and Experiment, Journal of Dynamic Systems, Measurement, and Control, 113, 34-40.
Zajaczkowski, J., and Lipinski, J., 1979, Instability of the Motion of a Beam of Periodically Varying Length, Journal of Sound and Vibration, 63, 9-18.
Zajaczkowski, J., and Yamada, G., 1980, Further Results on Instability of the Motion of a Beam of Periodically Varying Length, Journal of Sound and Vibration, 68, 173-180.

校內：2009-07-12公開
校外：2009-07-12公開

簡易檢索 / 詳目顯示

相關論文