Nonlinear vibration and dynamic response of simply supported shear deformable laminated plates on elastic foundations

Nonlinear vibration and dynamic response are presented for a simply supported, shear deformable laminated plate subjected to a transverse dynamic load combined with initial in-plan static loads and resting on a two-parameter (Pasternak-type) elastic foundation. The formulations are based on Reddy’s higher order shear deformation plate theory and general von Kármán-type equation, which includes the plate-foundation interaction. Two cases of the in-plane boundary conditions are considered. The equations of motion are solved by means of a perturbation technique to determine nonlinear frequencies and dynamic responses of symmetric cross-ply and antisymmetric angle-ply shear deformable laminated plates. The effects of amplitude ratio, foundation stiffness and initial in-plane loads on frequency ratios and dynamic responses are also studied. The results show that the foundation stiffness and initial in-plane loads have a significant effect on the nonlinear to linear frequency ratios as well as dynamic response of shear deformable laminated plates.