Vibration analysis of functionally graded graphene platelet-reinforced FG plates supported by viscoelastic foundations using an integral HSDT

This work examines the free vibration behaviors of functionally graded graphene platelet-reinforced ceramic-metal (FG-GPLRCM) plates supported by viscoelastic substrates. The analysis uses the integral higher-order shear deformation theory (HSDT), with only four unknowns, satisfying the boundary conditions and capturing transverse shear effects, obviating the need for shear correction factors. The constituents’ effective elastic properties are predicted using analytical models combining the rule of mixtures with the Halpin-Tsai approach. The virtual work principle is employed to derive the governing equations, and then Navier’s technique is applied to derive their solution. Some examples are introduced and solved to validate the proposed theory’s accuracy and efficiency in predicting vibration responses of FG-GPLRCM plates. The parametric analysis investigates how the geometry and size of the plate, as well as the foundation parameters and material gradient index, affect the vibration behavior of an FG-GPLRCM plate. Additionally, the study examines the impact of the GPL’s aspect ratio, thickness ratio, weight fraction, and dispersion type. The results indicate that increasing the weight fraction of the GPL leads to higher vibration frequencies. Furthermore, incorporating stiffness and damping parameters with various types of substrates results in higher frequencies.