A new semi-analytical approach for nonlinear dynamic responses of functionally graded porous graphene platelet-reinforced circular plates and spherical shells

This paper presents the semi-analytical approach for nonlinear dynamic responses of porous graphene platelet-reinforced circular plates (CiPs) and spherical shells (SpSs) resting on the Pasternak foundation in thermal environment. The graphene platelets (GPLs) are distributed in the functionally graded (FG) distribution patterns and uniform distribution pattern through the CiP and SpS thickness direction. The governing equations of the GPL-reinforced structures subjected to time-dependent external pressure respected to the harmonic and linear functions of time are established based on the geometrically nonlinear higher-order shear deformation theory. A simple and effective semi-analytical solution for the considered problem is established using the Euler-Lagrange equations, and the damping viscosity of the foundation can be counted using the Rayleigh dispassion function. The Runge-Kutta method is employed to determine the dynamic responses of the GPL-reinforced structures, while the fundamental frequencies of free and linear vibration, and frequency-amplitude curves are obtained in explicit form. The numerical results obtained reveal that the GPL and porous distributions, geometrical and material properties can significantly affect the frequency-amplitude curves, and dynamic responses of harmonically loaded and linearly loaded structures, specially, the dynamic buckling phenomenon is clearly observable with the SpSs but not with the CiPs.