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Spectral Element Analysis for the Dynamic Characteristics of an Axially Moving Timoshenko Beam

축방향으로 이동하는 티모센코보의 동특성에 관한 스펙트럴요소 해석

  • 김주홍 (인하대학교 산업과학기술연구소) ;
  • 오형미 (인하대학교 대학원) ;
  • 이우식 (인하대학교 기계공학부)
  • Published : 2003.10.01

Abstract

The use of frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) in structural dynamics is known to provide very accurate solutions, while reducing the number of degrees-of-freedom to resolve the computational and cost problems. Thus, in the present paper, the spectral element model is formulated for the axially moving Timoshenko beam under a uniform axial tension. The high accuracy of the present spectral element is then verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions. The effects of the moving speed and axial tension on the vibration characteristics, the dispersion relation, and the stability of a moving Timoshenko beam are investigated, analytically and numerically.

Keywords

Moving Beam;Timoshenko Beam;Vibration;Spectral Element;Stability;Divergence;Flutter

References

  1. Bisplinghoff, R. L. and Ashley, H., 1962, Principles of Aerolasticity, New York: Dover Publications
  2. Lin, C. C., 1997, 'Stability and Vibration Characteristics of Axially Moving Plates,' International Journal of Solide & Structures, Vol. 34, No. 24, pp. 3179-3190 https://doi.org/10.1016/S0020-7683(96)00181-3
  3. Le-Ngoc, L. and McCallion, H., 1999, 'Dynamic Stiffness of an Axially Moving String,' Journal of Sound and Vibration, Vol. 220, No. 4, pp. 749-756 https://doi.org/10.1006/jsvi.1998.1945
  4. Blevins, R. D., 1979, Formulas for Natural Frequency and Mode Shape, New York: Van Nostrand Reinhold Company
  5. Petyt, M., 1990, Introduction to Finite Element Vibration Analysis, New York: Cambridge University Press
  6. Doyle, J. F., 1997, Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms. New York: Springer-Verlag
  7. Lee, U., Kim, J. and Leung, A. Y. T., 2000, 'The Spectral Element Method in Structural Dynamics,' The Shock and Vibration Digest, Vol. 32, No. 6, pp. 451-465 https://doi.org/10.1177/058310240003200601
  8. Kwon, Y. I. and Ih, J. G., 2000, 'Vibration Power Flow in the Moving Belt Passing through a Tensioner,' Journal of Sound and Vibration, Vol. 229, No. 2, pp. 329-353 https://doi.org/10.1006/jsvi.1999.2484
  9. Simpson, A., 1973, 'Transverse Modes and Frequencies of Beams Translating between Fixed end Supports,' Journal of Mechanical Engineering Science, Vol. 15, pp. 159-164 https://doi.org/10.1243/JMES_JOUR_1973_015_031_02
  10. Chonan, S., 1986, 'Steady State Response of an Axially Moving Strip Subjected to a Stationary Lateral Load,' Journal of Sound and Vibration, Vol. 107, No. 1, pp. 155-165 https://doi.org/10.1016/0022-460X(86)90290-7
  11. Lee, S. Y. and Mote, Jr., C. D., 1999, 'Wave Characteristics and Vibration Control of Translating Beams by Optimal Boundary Damping,' Journal of Vibration and Acoustics, Vol. 121, pp. 18-25 https://doi.org/10.1115/1.2893942
  12. Chakraborty, G. and Mallik, A. K. 2000, 'Wave Propagation in and Vibration of a Traveling Beam with and without Non-linear Effects, Part I: Free Vibration, Part II: Forced Vibration,' Journal of Sound and Vibration, Vol. 236, No. 2, pp. 277-305 https://doi.org/10.1006/jsvi.2000.2971
  13. Li, Y. and Rahn, C. D., 2000, 'Adaptive Vibration Isolation for Axially Moving Beams,' IEEE/ASME Transactions on Mechatronics, Vol. 5, No. 4, pp. 419-428 https://doi.org/10.1109/3516.891053
  14. Lee, S. Y. and Mote, Jr., C. D., 1997, 'A Generalized Treatment of the Energetics of Translating Continua, Part II: Beams and Fluid Conveying Pipes,' Journal of Sound and Vibration, Vol. 204, No. 5, pp. 735-753 https://doi.org/10.1006/jsvi.1996.0946
  15. Wang, Y. K. and Mote, Jr., C. D., 1996, 'Active and Passive Vibration Control of an Axially Moving Beam by Smart Hybrid Bearings,' Journal of Sound and Vibration, Vol. 195, No. 4, pp. 575-584 https://doi.org/10.1006/jsvi.1996.0446
  16. Oz, H. R., 2001, 'On the Vibrations of Axially Traveling Beam on Fixed Supports with Variable Velocity,' Journal of Sound and Vibration, Vol. 239, No. 3, pp. 556-564 https://doi.org/10.1006/jsvi.2000.3077
  17. Ozkaya, E. and Pakdemirli, M., 2000, 'Vibrations of an Axially Accelerating Beam with Small Flexural Stiffness,' Journal of Sound and Vibration, Vol. 234, No. 3, pp. 521-535 https://doi.org/10.1006/jsvi.2000.2890
  18. Tabarrok, B., Leech, C. M. and Kim, Y. I., 1974, 'On the Dynamics of an Axially Moving Beam,' Journal of the Franklin Institute, Vol. 297, No. 8, pp. 201-220 https://doi.org/10.1016/0016-0032(74)90104-5
  19. Sreeram, T. R. and Sivaneri, N. T., 1998, 'FE-Analysis of Moving Beam Using Lagrangian Multiplier Method,' International Journal of Solids and Structures, Vol. 35, Nos. 28-29, pp. 3675-3694 https://doi.org/10.1016/S0020-7683(97)00230-8
  20. Wickert, J. A. and Mote, C. D., Jr., 1990, 'Classical Vibration Analysis of Axially Moving Continua,' Journal of Applied Mechanics, Vol. 57, pp. 738-744 https://doi.org/10.1115/1.2897085
  21. Riedel, C. H. and Tan, C. A., 1998, 'Dynamic Characteristics and Mode Localization of Elastically Constrained Axially Moving Strings and Beams,' Journal of Sound and Vibration, Vol. 215, No. 3, pp. 455-473 https://doi.org/10.1006/jsvi.1998.1643
  22. Pellicano, F. and Vestroni, F., 2001, 'Non-linear Dynamics and Bifurcations of an Axially Moving Neam,' Journal of Vibration and Acoustics, Vol. 122, pp. 21-30 https://doi.org/10.1115/1.568433
  23. Lee, H. P., 1993, 'Dynamics of a Beam Moving over Multiple Supports,' International Journal of Solids and Structures, Vol. 30, No. 2, pp. 199-209 https://doi.org/10.1016/0020-7683(93)90060-K
  24. Stylianou, M. and Tabarrok, B., 1994, 'Finite Element Analysis of an Axially Moving Beam, part I: Time Integration,' Journal of Sound and Vibration, Vol. 178, No. 4, pp. 433-453 https://doi.org/10.1006/jsvi.1994.1497
  25. Wang, K. W. and Mote, C. D., Jr., 1986, 'Vibration Coupling Analysis of Band/Wheel Mechanical Systems,' Journal of Sound and Vibration, Vol. 102, No. 1, pp. 1-9 https://doi.org/10.1016/S0022-460X(86)80006-2
  26. Wickert, J. A. and Mote, C. D., Jr., 1988, 'Current Research on the Vibration and Stabaility of Axially Moving Materials,' Shock and Vibration Digest, Vol. 20, pp. 3-13 https://doi.org/10.1177/058310248802000503
  27. International Journal of Solide & Structures v.34 no.24 Stability and Vibration Characteristics of Axially Moving Plates Lin,C.C. https://doi.org/10.1016/S0020-7683(96)00181-3