A simple finite element procedure for free vibration of rectangular thin and thick plates

Abstract

A simple finite element procedure is introduced and developed to solve the free vibration problem of rectangular plates. The proposed method first reduces the original plate problem to two simple beam problems. Each beam problem is then discretized separately with the help of one-dimensional finite element method (FEM). Since only the one-dimensional FEMs are dealt with in the proposed approach, the implementation of the proposed approach is much easier than the case where the two-dimensional FEM is applied to the problem. The reliability and applicability of the proposed method are demonstrated herein through the solution of some illustrative problems, including the vibration problems of thin and thick rectangular plates. The simulations have been done for plates with different boundary conditions including the simply supported, clamped, and free boundary conditions. The results generated by the proposed method are compared with analytical and numerical results available in the literature and excellent agreement is achieved.