Modelling advanced composite plates resting on elastic foundation by using a quasi-3D hybrid type HSDT

This paper presents a free vibration analysis of functionally graded plates (FGPs) resting on elastic foundation by using a generalized quasi-3D hybrid type higher-order shear deformation theory (HSDT). The significant feature of this formulation is that it deals with only 5 unknowns as the first order shear deformation theory (FSDT), instead of 6 as in for example the well-known trigonometric plate theory (TPT). The displacement field is modeled combining hyperbolic and sinusoidal shear strain shape functions in which the stretching effect is included. The elastic foundation follows the Pasternak (two-parameter) mathematical model. The governing equations are obtained through the Hamilton's principle. These equations are then solved via Navier-type, closed form solutions. The fundamental frequencies are found by solving the eigenvalue problem. The accuracy of the current solutions can be visualized by comparing it with the 3D and other closed form solutions available in the literature.