Skip to main content
SpringerLink
Log in

Parametrically Excited Non-Linear Traveling Beams with and without External Forcing

  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

The effects of parametric excitation on a traveling beam, both with and without an external harmonic excitation, have been studied including the non-linear terms. Non-linear, complex normal modes have been used for the response analysis. Detailed numerical results are presented to show the effects of non-linearity on the stability of the parametrically excited system. In the presence of both parametric and external harmonic excitations, the response characteristics are found to be similar to that of a Duffing oscillator. The results are sensitive to the relative strengths of and the phase difference between the two forms of excitations.

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

  1. Wickert, J. A. and Mote Jr., C. D., ‘Current research on the vibration and stability of axially moving materials’, Shock and Vibration Digest 20(5), 1988, 3‐13.

    Google Scholar 

  2. Naguleswaran, S. and Williams, C. J. H., ‘Lateral vibrations of band-saw blades pulley belts and like’, International Journal of Mechanical Science 10, 1968, 239‐250.

    Google Scholar 

  3. Asokanthan, S. F. and Ariaratnam, S. T., ‘Flexural instabilities in axially moving bands’, ASME Journal of Vibration and Acoustics 116, 1994, 275‐279.

    Google Scholar 

  4. Pakdemirli, M., Ulsoy, A. G., and Ceranoglu, A., ‘Transverse vibration of an axially accelerating string’, Journal of Sound and Vibration 169(2), 1994, 179‐196.

    Google Scholar 

  5. Nayfeh, A. H. and Mook, D. T., Nonlinear Oscillations, Wiley, New York, 1979.

    Google Scholar 

  6. Mockenstrum, E. M., Perkins, N. C., and Ulsoy, A. G., ‘Stability and limit cycles of parametrically excited, axially moving strings’, ASME Journal of Vibration and Acoustics 118, 1996, 346‐350.

    Google Scholar 

  7. Troger, H. and Hsu, C. S., ‘Response of a nonlinear system under combined parametric and forcing excitation’, ASME Journal of Applied Mechanics 44, 1977, 179‐181.

    Google Scholar 

  8. Zavodney, L. D., Nayfeh, A. H., and Sanchez, N. E., ‘The response of a single-degree-of-freedom system with quadratic and cubic non-linearities to a principal parametric resonance’, Journal of Sound and Vibration 129(3), 1989, 417‐422.

    Google Scholar 

  9. Chakraborty, G., Mallik, A. K., and Hatwal, H., ‘Normal modes and near-resonance response of beams with non-linear effects’, Journal of Sound and Vibration 210(1), 1998, 19‐36.

    Google Scholar 

  10. Chakraborty, G., Mallik, A. K., and Hatwal, H., ‘Non-linear vibration of a traveling beam’, International Journal of Non-Linear Mechanics (in press).

  11. Thurman, A. L. and Mote Jr., C. D., ‘Free periodic non-linear oscillations of an axially moving strip’, ASME Journal of Applied Mechanics 36, 1969, 83‐89.

    Google Scholar 

  12. MoteJr., C. D., ‘A study of band saw vibrations’, Journal of Franklin Institute 279, 1965, 430‐444.

    Google Scholar 

  13. Wang, K. W. and Mote Jr., C. D., ‘Vibration coupling analysis of band/wheel mechanical systems’, Journal of Sound and Vibration 109, 1986, 237‐258.

    Google Scholar 

  14. Al-Jawi, A. A. N., Pierre, C., and Ulsoy, A. G., ‘Vibration localization in dual span axially moving beams. Part I: Formulation and results; Part II: Perturbation analysis’, Journal of Sound and Vibration 179(2), 1995, 289‐312.

    Google Scholar 

  15. Hwang, S.-J. and Perkins, N. C., ‘High speed stability of coupled band/wheel systems: theory and experiment’, Journal of Sound and Vibration 169, 1994, 459‐483.

    Google Scholar 

  16. Hwang, S.-J. and Perkins, N. C., ‘Super-critical stability of an axially moving beam. Part I: Model and equilibrium analysis; Part II: Vibration and stability analysis’, Journal of Sound and Vibration 154, 1992, 381‐409.

    Google Scholar 

  17. Wang, K. W., ‘Dynamic stability analysis of high speed axially moving bands with end curvature’, ASME Journal of Vibration and Acoustics 113, 1991, 62‐68.

    Google Scholar 

  18. Wickert, J. A. and Mote Jr., C. D., ‘Classical vibration analysis of axially moving continua’, ASME Journal of Applied Mechanics 57, 1990, 738‐744.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology, Kanpur, U.P. –, 208016, India

    G. Chakraborty & A. K. Mallik

Authors
  1. G. Chakraborty
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. K. Mallik
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chakraborty, G., Mallik, A.K. Parametrically Excited Non-Linear Traveling Beams with and without External Forcing. Nonlinear Dynamics 17, 301–324 (1998). https://doi.org/10.1023/A:1008391503175

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008391503175

Search

Navigation