Skip to main content
SpringerLink
Log in

Nonlinear Oscillations of Viscoelastic Rectangular Plates

  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Nonlinear oscillations of viscoelastic simply supported rectangular plates are studied by assuming the Voigt–Kelvin constitutive model. Using Hamilton's principle in conjunction with the kinematics associated with Kirchhoff's plate model, the governing equations of motion including the effect of damping are represented in terms of the transversal deflection and a stress function. Utilizing the Bubnov–Galerkin method, the nonlinear partial differential equations are reduced to an ordinary differential equation which is studied geometrically by approximate construction of the Poincaré maps. Explicit expressions are given for periodic solutions.

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. Hadian, J. and Nayfeh, A. H., 'Modal interaction in circular plates', Journal of Sound and Vibration 142(2), 1990, 279–292.

    Article  Google Scholar 

  2. Lu, C. H., Mao, R., and Evan-Iwanowski, R. M., 'Non-stationary parametric responses of shear deformable orthotropic plates', Journal of Sound and Vibration 184(2), 1995, 239–342.

    Google Scholar 

  3. Xia, Z. Q. and Lukasiewicz, S., 'Nonlinear, free, damped vibrations of sandwich plates', Journal of Sound and Vibration 175(2), 1994, 219–232.

    Google Scholar 

  4. Xia, Z. Q. and Lukasiewicz, S., 'Nonlinear damped vibrations of simply-supported rectangular sandwich plates', Nonlinear Dynamics 8, 1995, 417–433.

    Google Scholar 

  5. Chia, C. Y., Nonlinear Analysis of Plates, McGraw-Hill, New York, 1980.

    Google Scholar 

  6. Nayfeh, A. H. and Mook, D. T., Nonlinear Oscillations, Wiley-Interscience, New York, 1979.

    Google Scholar 

  7. Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, Berlin, 1990.

    Google Scholar 

  8. Fung, Y. C., Foundations of Solid Mechanics, Prentice-Hall, Englewood Cliffs, New Jersey, 1965.

    Google Scholar 

  9. Reddy, J. N., Applied Functional Analysis and Variational Methods in Engineering, McGraw-Hill, New York, 1986.

    Google Scholar 

  10. Hartman, P., Ordinary Differential Equations, Wiley, New York, 1964.

    Google Scholar 

  11. Esmailzadeh, E. and Jalili, N., 'Parametric response of cantilever Timoshenko beams with tip mass under harmonic support motion', International Journal of Non-Linear Mechanics 33(5), 1998, 765–781.

    Google Scholar 

  12. Esmailzadeh, E. and Shahani, A. R., 'Longitudinal and rotational coupled vibration of viscoelastic bars with tip mass', International Journal of Non-Linear Mechanics 34(1), 1999, 111–116.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Sharif University of Technology, P.O. Box 11365-9567, Azadi Avenue, Tehran, Iran

    E. Esmailzadeh

  2. Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-159, Gava Zang, Zanjan, Iran

    M. A. Jalali

Authors
  1. E. Esmailzadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. A. Jalali
    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

Esmailzadeh, E., Jalali, M.A. Nonlinear Oscillations of Viscoelastic Rectangular Plates. Nonlinear Dynamics 18, 311–319 (1999). https://doi.org/10.1023/A:1026452007472

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1026452007472

Search

Navigation