Hostname: page-component-5c6d5d7d68-ckgrl Total loading time: 0 Render date: 2024-08-26T19:26:11.673Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-Linear Vibration Analysis of a Rectangular Plate on a Viscoelastic Foundation

Published online by Cambridge University Press:  07 June 2016

B Kishor  and
J S Rao
B Kishor
Affiliation:
University of Jodhpur
J S Rao
Affiliation:
Indian Institute of Technology, Kharagpur
Get access

Summary

An analysis is presented for the non-linear vibrations of an elastic rectangular plate resting on a viscoelastic foundation. Hamilton’s principle is used for obtaining coupled non-linear partial differential equations of the system. These equations are uncoupled with the help of Berger’s approximation and the Galerkin method is used to obtain the solution of the resulting equations. Particular cases of the plates on an elastic foundation are also discussed.

Type
Research Article
Information
Aeronautical Quarterly , Volume 25 , Issue 1 , February 1974 , pp. 37 - 46
Copyright
Copyright © Royal Aeronautical Society. 1974

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Winkler, E, Die Lehre von der Elasticitët und Festigkeit, pp 182-184. Dominicus, Prague, 1867.Google Scholar
2. Holl, D L, Thin plates on elastic foundations, pp 71-74, Proceedings of the Fifth International Congress of Applied Mechanics, Cambridge, Massachusetts, 1938.Google Scholar
3. Reissner, E, On the theory of the bending of elastic plates. Journal of Mathematics and Physics, Vol 23, pp 184-191, November 1944.CrossRefGoogle Scholar
4. Kaczkowski, Z, Orthotropic rectangular plates with arbitrary boundary conditions, Vol 6, pp 430441. Proceedings of the Ninth International Congress of Applied Mechanics, Brussels, 1957.Google Scholar
5. Mazurkiewicz, Z, Bending vibration and buckling of a rectangular orthotropic plate resting on a non-homogeneous foundation. Bulletin of the Polish Academy of Science, Vol 8, pp 129-133, 1960.Google Scholar
6. Wilde, P, Rectangular anisotropic plates with clamped edges. Archiwum Mechaniki Stoswanej, Vol 12, pp 241-258, 1960.Google Scholar
7. Kundu, B B, The transverse vibrations of a non-isotropie plate of rectangular and elliptic boundaries resting on elastic foundations. Journal of Science and Engineering Research, Vol 11, p 107, January 1967.Google Scholar
8. Hoshkin, B C, Lee, E H, Flexible surfaces on viscoelastic subgrades. Journal of Engineering Mechanics Division, Proceedings American Society of Civil Engineers, Vol 85, No EM4, pp 11-30, October 1959.CrossRefGoogle Scholar
9. Pister, K S, Williams, M L, Bending of plates on a viscoelastic foundation. Journal of Engineering Mechanics Division, Proceedings American Society of Civil Engineers, Vol 86, No EM5, pp 31-44, October 1960.CrossRefGoogle Scholar
10. Kishor, B, Dynamic response of a plate on a viscoelastic subgrade. Bulletin of the Indian Society of Earthquake Technology, September 1972.Google Scholar
11. Kishor, B, Rao, J S, Non-linear transverse vibration analysis of a circular elastic plate resting on a viscoelastic foundation. Sixteenth Congress of the Indian Society of Theoretical and Applied Mechanics, Allahabad, 1972.Google Scholar
12. Berger, H M, A new approach to the analysis of large deflections of plates. Journal of Applied Mechanics, Transactions of the American Society of Mechanical Engineers, Vol 22, pp 465-472, December 1955.CrossRefGoogle Scholar
13. Timoshenko, S P, Woinowski-Krieger, S, Theory of Plates and Shells. McGraw-Hill, New York, 1959.Google Scholar
14. Fung, Y C, Foundations of Solid Mechanics. Prentice-Hall of India, New Delhi, 1968.Google Scholar
15. Stoker, J J, Non-Linear Vibrations. Interscience, New York, 1950.Google Scholar
16. Chu, H, Herrmann, G, Influence of large amplitudes on free flexural vibrations of rectangular elastic plates. Journal of Applied Mechanics, Transactions of the American Society of Mechanical Engineers, Vol 23, No 4, pp 532-540, December 1956.CrossRefGoogle Scholar