Investigating the Nonlinear Vibration Characteristics of a GNP-Reinforced Honeycomb Sandwich Doubly Curved Shell Resting on Nonlinear Foundation

Abstract

Effect of the nonlinear strain terms and nonlinear foundation is studied on the nonlinear vibration-based characteristics of a honeycomb shell reinforced with graphene nanoplatelets (GNPs) face–sheets. The governing motion’s equations are derived using Hamilton’s principle, in which the von Karman geometric nonlinear kinematic terms are used and a third-order nonlinear foundation. After extending the required relations for the effective characteristics of the honeycomb core as well as GNPs-reinforced face–sheets using Gibson’s formula and Halpin–Tsai, the constitutive relations are developed using the curvilinear coordinate system. After derivation of the time-dependent Partial Differential Equations (PDEs) of motion, Galerkin’s scheme is developed to arrive at a time Differential Equation (DE). To solve the nonlinear time-dependent differential equation, the perturbation technique and the modified Poincare–Lindstedt method are used to arrive at nonlinear results. After a comprehensive verification of literature results, the authors present a comprehensive parametric analysis to investigate the impact of various classes of parameters such as material, geometric and foundation on the nonlinear responses. The results of this research can be used in the design of novel structures in aerospace engineering and defense technology equipment.