Effects of in-plane loads on vibration of laminated thick rectangular plates resting on elastic foundation: An exact analytical approach

In this article, an exact analytical solution for vibration and buckling of symmetrically laminated thick rectangular plates on elastic foundation subjected to different types of in-plane loading is presented. It is assumed that the laminated rectangular plate is symmetric and composed of transversely isotropic layers. Based on the third order shear deformation plate theory, three coupled partial differential governing equations of motion of the plate are obtained. Doing some mathematical manipulations, these equations are converted into a sixth order and a second order decoupled partial differential equations. By applying different types of in-plane loading and using the Levy solution, vibration and buckling of symmetric laminated rectangular plate resting on two-parameter elastic foundation is solved analytically. The accurate natural frequencies of the laminated rectangular plates with six different boundary conditions are presented for several thickness–length ratios, some aspect ratios, different elastic foundation parameters and various in-plane loading ratios. The results show that the in-plane loading can increase or decrease the natural frequency of laminated rectangular plate depending on the boundary condition and the type of loading. Finally, the mode shape contour plots are depicted for a laminated rectangular plate with various boundary conditions and different in-plane loadings.