Nonlinear free flexural vibrations/post-buckling analysis of laminated orthotropic beams/columns on a two parameter elastic foundation

Abstract

Nonlinear free flexural vibrations and post-buckling of laminated orthotropic beams resting on a class of two parameter elastic foundation are studied using a three-noded shear flexible beam element. Geometric nonlinearity is considered using von Karman’s strain–displacement relations. The formulation includes the effects of transverse shear deformation, in-plane and rotary inertia terms. Exact numerical integration is employed for evaluating all the strain energy terms. The nonlinear governing equations are solved by employing the direct iteration technique. Numerical results are obtained for orthotropic and cross-ply laminated beams with simply supported boundary conditions. A detailed study is carried out to highlight the influences of different parameters on frequencies and buckling loads of laminated orthotropic beams.