Skip to main content
SpringerLink
Log in

Dynamics of an axially moving Bernoulli-Euler beam: Spectral element modeling and analysis

  • Published:
KSME International Journal Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Al-Jawi, A. A. N., Pierre, C. and Ulsoy, A. G., 1995, “Vibration Localization in Dual-Span Axially oving Beams, Part I: Formulation and Results,”Journal of Sound and Vibration. Vol. 179, No. 2, pp. 243–266.

    Article  Google Scholar 

  • Bisplinghoff, R. L. and Ashley. H., 1962,Principles of Aeroelasticity, Dover Publication, New York.

    Google Scholar 

  • Blevins, R. D., 1979,Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold Company, New York.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Doyle, J. F., 1997.Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms, Springer-Verlag, New York.

    Book  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Newland, D. E., 1993,Random Vibrations, Spectral and Wavelet Analysis, 3rd ed., Longman, New York.

    Google Scholar 

  • Öz, 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Petyt, M., 1990,Introduction to Finite Element Vibration Analysis, Cambridge University Press, New York.

    Book  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Wickert, J. A. and Mote, C. D., 1990, “Classical Vibration Analysis of Axially Moving Continua,”Journal of Applied Mechanics, Vol. 57, pp. 738–744.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School, Department of Mechanical Engineering, Inha University, 402-751, Incheon, Korea

    Hyungmi Oh

  2. Department of Mechanical Engineering, Inha University, 253 Yonghyun-Dong, Nam-Ku, 402-751, Incheon, Korea

    Usik Lee

  3. Department of Industrial Engineering, Inha University, 402-751, Incheon, Korea

    Dong-Hyun Park

Authors
  1. Hyungmi Oh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Usik Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dong-Hyun Park
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Usik Lee.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Oh, H., Lee, U. & Park, DH. Dynamics of an axially moving Bernoulli-Euler beam: Spectral element modeling and analysis. KSME International Journal 18, 395–406 (2004). https://doi.org/10.1007/BF02996105

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02996105

Key Words

Search

Navigation