Dynamics of an Axially Moving Bernoulli-Euler Beam: Spectral Element Modeling and Analysis

  • Hyungmi Oh (Graduate School, Department of Mechanical Engineering, Inha University) ;
  • Lee, Usik (Department of Mechanical Engineering, Inha University) ;
  • Park, Dong-Hyun (Department of Industrial Engineering, Inha University)
  • Published : 2004.03.01

Abstract

The spectral element model is known to provide very accurate structural dynamic characteristics, while reducing the number of degree-of-freedom to resolve the computational and cost problems. Thus, the spectral element model for an axially moving Bernoulli-Euler beam subjected to axial tension is developed in the present paper. The high accuracy of the spectral element model 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, wave characteristics, and the static and dynamic stabilities of a moving beam are investigated.

Keywords

References

  1. Al-Jawi, A. A. N., Pierre, C. and Ulsoy, A. G., 1995, 'Vibration Localization in Dual-Span Axially Moving Beams, Part I : Formulation and Results,' Journal of Sound and Vibration, Vol. 179, No. 2, pp. 243-266 https://doi.org/10.1006/jsvi.1995.0016
  2. Bisplinghoff, R. L. and Ashley, H., 1962, Principles of Aeroelasticity, Dover Publication, New York
  3. Blevins, R. D., 1979, Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold Company, New York
  4. 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
  5. Doyle, J. F., 1997, Wave Propagation in Structures : Spectral Analysis Using Fast Discrete Fourier Transforms, Springer-Verlag, New York
  6. Hwang, S. J. and Perkins, N. C., 1992, 'Supercritical Stability of An Axially Moving Beam,' Journal of Sound and Vibration, Vol. 154, No. 3, pp. 381-409 https://doi.org/10.1016/0022-460X(92)90774-R
  7. 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
  8. Lee, U. and Lee, J., 1998, 'Vibration Analysis of the Plates Subject to Distributed Dynamic Loads by Using Spectral Element Method,' KSME International Journal, Vol. 12, No. 4, pp. 565-571
  9. 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
  10. Lee, U., Kim, J. and Leung, A. Y. T., 2001, 'Vibration Analysis of the Active Multi-Layer Beams by Using Spectrally Formulated Exact Natural Modes,' KSME International Journal, Vol. 15, No. 2, pp. 199-209
  11. 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
  12. Newland, D. E., 1993, Random Vibrations, Spectral and Wavelet Analysis, 3rd ed., Longman, New York
  13. Oz, H. R., 2001, 'On the Vibrations of An 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
  14. Pellicano, F. and Vestroni, F., 2001, 'Nonlinear Dynamics and Bifurcations of An Axially Moving Beam,' Journal of Vibration and Acoustics, Vol. 22, pp. 21-30 https://doi.org/10.1115/1.568433
  15. Petyt, M., 1990, Introduction to Finite Element Vibration Analysis, Cambridge University Press, New York
  16. 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
  17. 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
  18. Wickert, J. A. and Mote, C. D., 1988, 'Current Research on the Vibration and Stability of Axially Moving Materials,' Shock and Vibration Digest, Vol. 20, pp. 3-13 https://doi.org/10.1177/058310248802000503
  19. Wickert, J. A. and Mote, C. D., 1990, 'Classical Vibration Analysis of Axially Moving Continua,' Journal of Applied Mechanics, Vol. 57, pp. 738-744 https://doi.org/10.1115/1.2897085