Response of Symmetric Cross-Ply Laminated Plates With Levy-Type Boundary Conditions Under Random Loads

Abstract

A generalized modal approach utilizing a set of adjoint eigenfunctions is presented to solve the forced vibration problem of symmetric cross-ply laminated composite plates which are simply supported at two opposite sides and have arbitrary boundary conditions at the remaining two supports. The first and third order shear deformation theories are used to include the effect of shear deformations in the equations of motion of the plates. The autocorrelation function of the response caused by spatially and temporally correlated random loads is obtained. The numerical results obtained for the third order, first order and classical lamination theories are compared to demonstrate the importance of shear deformations in the dynamic analysis of composite plates. It is shown that shear deformations cannot be ignored even for moderately thick plates. Significant differences are also observed in the magnitude and distribution of the normal and shear stresses near the clamped edges, calculated by the third order theory and the classical and first order theories.