A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation

This work presents a dynamic investigation of functionally graded (FG) plates resting on elastic foundation using a simple quasi-3D higher shear deformation theory (quasi-3D HSDT) in which the stretching effect is considered. The culmination of this theory is that in addition to taking into account the effect of thickness extension (ez ≠ 0), the kinematic is defined with only 4 unknowns, which is even lower than the first order shear deformation theory (FSDT). The elastic foundation is included in the formulation using the Pasternak mathematical model. The governing equations are deduced through the Hamilton's principle. These equations are then solved via closed-type solutions of the Navier type. The fundamental frequencies are predicted by solving the eigenvalue problem. The degree of accuracy of present solutions can be shown by comparing it to the 3D solution and other closed-form solutions available in the literature.