Nonlinear dynamics of functionally graded graphene nanoplatelet reinforced polymer doubly-curved shallow shells resting on elastic foundation using a micromechanical model

Abstract

The paper focuses on the nonlinear vibration of functionally graded graphene nanoplatelet reinforced composite doubly curved shallow shells resting on elastic foundations. The graphene nanoplatelet reinforced composites are assumed to be distributed uniformly and functionally graded through the thickness. The material properties are assumed to be temperature-dependent and are estimated through the Halpin–Tsai micromechanical model, while the Poisson’s ratio, density mass, and thermal expansion are implemented by the rule of mixtures. The mathematical formulation is developed based on the classical shell theory and Von Karman-Donnell geometrical nonlinearity assumption. The dynamical responses of a simply supported functionally graded-graphene nanoplatelet reinforced composite doubly curved shallow shells are obtained by employing the Airy’s stress function and the Galerkin’s method. The responses of nonlinear vibration as time history, frequency-amplitude curve, phase plane graphs, and Poincare maps are carried out in this paper. In addition, the effects of the environment, graphene nanoplatelets weight fraction, graphene nanoplatelets distribution patterns, and thickness-to-length ratio are scrutinized. The obtained results are also compared and validated with those of other studies.