A new semi-analytical approach for nonlinear vibration behavior of porous graphene platelet reinforced circular plates and spherical caps with stepped spiderweb stiffeners

This paper investigates the nonlinear vibration responses of porous graphene platelet reinforced composite (PGPLRC) circular plates and spherical caps with stepped spiderweb stiffeners resting on elastic foundations and under harmonic external pressure in the thermal environment. The material properties of both the shell skin and the spiderweb stiffeners are assumed to be graded in the thickness direction according to the continuous change of the foam volume fractions. Governing equations are based on Donnell shell theory, taking into account von Karman nonlinearities, initial imperfection, and visco-elastic foundation. Approximate solutions can be chosen in polynomial forms, and the Euler–Lagrange equations are applied to derive nonlinear motion equations of structures. The Runge–Kutta method is applied, and the time-amplitude vibration behavior can be obtained; meanwhile, the fundamental frequencies are explicitly investigated. The effects of geometrical, material, foundation parameters, and stepped spiderweb stiffeners on the nonlinear vibration behavior of PGPLRC circular plates and spherical caps with stepped spiderweb stiffeners are investigated and discussed in detail. The results demonstrate that the effectiveness of the spiderweb stiffeners and suitable porosity distribution significantly improves the stiffness and vibration resistance of the structures. The effectiveness and reliability of the present approach in analyzing nonlinear vibration responses of the considered structures with intricate material and geometry can also be observed.