Nonlinear forced vibration of higher-order shear deformable FG-GPLRC spherical shell caps with parallel stiffeners on nonlinear elastic foundation

Abstract

A semi-analytical approach to investigate the nonlinear forced vibration behavior of functionally graded graphene platelet-reinforced composite (FG-GPLRC) circular plates and shallow spherical shell caps reinforced with parallel stiffeners is presented in this paper under time-dependent radial loading. The higher-order shear deformation theory is applied to establish the governing equations taking into account the von Kármán nonlinearity assumption, while a model of nonlinear visco-elastic foundation is considered to account for elastic, shear, and damping effects. The parallel stiffeners are modeled using a higher-order smeared stiffener technique. Clamped and immovable boundary conditions are assumed for both plates and shells. The total potential energy is formulated via the Lagrange approach, and the Rayleigh dissipation function is applied to model the foundation’s damping. The resulting nonlinear motion equations are obtained by applying the Euler-Lagrange formulation. Time-domain responses are computed by the Runge-Kutta method, whereas frequency-amplitude characteristics are determined using the harmonic balance method. Parametric studies elucidate the significant influences of geometric parameters, material distribution, stiffener configuration, and foundation nonlinearity on the vibration behavior.