Static and dynamic rectangular finite elements for plate vibration analysis

Sa？etak Nowadays dynamic finite elements with frequency dependent unified stiffness matrix are considered in order to reduce finite element mesh density, and, consequently, system of algebraic equations in eigenvalue formulation. In this paper, an attempt to develop a 4-noded rectangular finite element for thin plate bending is presented. Since there is no simple general analytical solution of plate vibrations for arbitrary boundary conditions, dynamic shape functions are assumed as products of beam shape functions in longitudinal and transverse direction. Dynamic finite element with frequency dependent stiffness and mass matrix is derived by energy approach. Convergence of results is checked and it is found that such finite element formulation is not suitable for wider use. Therefore, strip finite element for vibration analysis of rectangular plate with simply supported two opposite edges is developed, which gives exact results. Application of both finite elements is illustrated by several numerical examples