Journal of Applied Mathematics
Volume 2007 (2007), Article ID 56360, 12 pages
doi:10.1155/2007/56360
Research Article
Finite Element Formulation of Forced Vibration Problem of a Prestretched Plate Resting on a Rigid Foundation
Mathematics Department, Faculty of Science and Letters, Sakarya University, Esentepe Campus, Sakarya 54187, Turkey
Received 27 April 2007; Revised 21 June 2007; Accepted 3 September 2007
Academic Editor: Heinz H. Bauschke
Copyright © 2007 M. Eröz and A. Yildiz. 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.
Abstract
The three-dimensional linearized theory of elastodynamics mathematical formulation of the forced vibration of a prestretched plate resting on a rigid half-plane is given. The variational formulation of corresponding boundary-value problem is constructed. The first variational of the functional in the variational statement is equated to zero. In the framework of the virtual work principle, it is proved that appropriate equations and boundary conditions are derived. Using these conditions, finite element formulation of the prestretched plate is done. The numerical results obtained coincide with the ones given by Ufly and in 1963 for the static loading case.