Integral Equation Method for Free Vibration of Annular Plates with Elastic Supports

Abstract:

Annular plates are commonly found in the fields of engineering. The present study is concerned with the integral equation method for the free vibrations of annular plates with elastic supports. A set of complete systems of orthogonal functions, which is constructed by Bessel functions of the first and the second kind is used to construct the Green's function of annular plates. The eigenvalue problem of free vibration of annular plates with Elastic Supports is transformed into the eigenvalue problem of integral equation. And then, the problem of integral equation is transformed into a standard eigenvalue problem of a matrix with infinite order. Numerical example shows the significant advantages of the present method.

• Periodical: Applied Mechanics and Materials (Volumes 52-54)
• Pages: 573-577
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.52-54.573
• Online since: March 2011
• Authors: Gang Cheng, Wei Dong Wang, Quan Cheng
• Keywords: Annular Plate, Green's Function, Integral Equation Method, Natural Frequency, Vibration

References

[1] D.A. Vega, P.A.A. Laura and S.A. Vera: Journal of Sound and Vibration Vol. 233 (2000), p.171.

[2] C.M. Wang and V. Thevendran: Journal of Sound and Vibration Vol. 163 (1993), p.137.

[3] S. Kukla and M. Szewczyk: Journal of Sound and Vibration Vol. 300 (2007), p.387.

[4] T.S. Shih and D. Allaei: Journal of Sound and vibration Vol. 140 (1990), p.239.

[5] C. Shu, W.X. Wu, H. Ding and C.M. Wang: Comput. methods appl. Mech. Engrg Vol. 196(2007), p.1330.