International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 581-586

On the stationary vibrations of a rectangular plate subjected to stress prescribed partially at the circumference

M. G. El Sheikh,1 A. H. Khater,2 and D. K. Callebaut3

1Mathematics Department, Faculty of Science, Ain Shams University, Cairo, Egypt
2Mathematics Department, Faculty of Science, Cairo University, Beni-Suef, Egypt
3Physics Department, University of Antwerp, (U.I.A.), Antwerp B2610, Belgium

Received 16 June 1989; Revised 15 December 1989

Copyright © 1991 M. G. El Sheikh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The stationary periodical problem of a vibrating rectangular plate, stressed at a segment while fixed elsewhere at one of its edges, is considered. Using the finite Fourier transformation, the problem is converted to a singular integral equation that in turn can be reduced to an infinite system of algebraic equations. The truncation of the algebraic system is justified.