Buckling and Vibration of Thick Laminates on Pasternak Foundations

Abstract

This paper investigates buckling, free vibration, and vibration with initial in-plane loads for moderately thick, simply supported symmetric cross-ply rectangular laminates on Pasternak foundations. The total potential energy functional is derived based on the first-order shear deformation plate theory. The differential equations, which govern the vibration and buckling behavior of the plate are then derived from the potential energy functional. Employing the Navier solution procedure, closed-form buckling and vibration solutions have been obtained and are presented in tables and figures. Extensive parametric studies have been carried out to investigate the effects of plate geometry, in-plane load ratio, and foundation parameters on the buckling and vibration behavior of the plate system. Sets of first-known closed-form buckling and vibration results are presented for simply supported symmetric cross-ply laminates on Pasternak foundations. These results may be useful to engineers in engineering practice and to researchers in checking numerical models.