Analytical Behavior of Rectangular Plates Under in-Plane and Lateral Dynamic Loads

摘要

Analytical behavior of rectangular plates with semi-rigid boundary conditions under in-plane and lateral dynamic loads of constant thickness resting on the Winkler foundation is analyzed using a modified Bolotin method. The presentation of the semi-rigid isotropic plate's frequency in a form analogous to the corresponding frequency of a simply supported plate is postulated, considering the wave numbers as unknown quantities. These two equations are determined from a system of two transcendental equations, obtained from the solution of two auxiliary Levy-type problems. The method was shown to be remarkably accurate when used to determine the natural frequencies of plates with non-simply supported boundary conditions. A natural extension of this research is related to the buckling and lateral vibration of isotropic plates subjected to in-plane forces which are time invariant and constant over the area of the plate, with their principal directions parallel to the plate edges and the dynamic lateral force. It is the purpose of this paper to illustrate this extension and to demonstrate its applicability by the presentation of numerical results for a particular plate.