Nonlinear frequency and chaotic motion of the honeycomb higher-order disk with graphene nanoplatelets face sheets subjected to harmonic excitation via two-dimensional analysis

Abstract

Honeycomb structures are one type of structure that has the geometry of a honeycomb to allow the minimization of the amount of used material to reach minimal material cost and minimal weight. For this issue, in the current analysis, an attempt is made to develop the nonlinear mathematical model for the chaotic and large-amplitude motions of a sandwich disk with graphene nanoplatelet face sheets honeycomb core and subjected to external excitation. Using Hamilton’s principle, higher-order shear deformation theory (HSDT), and the Von-Karman nonlinear theory, the nonlinear governing equation is derived. The generalized differential quadrature method (GDQM) and perturbation approach (PA) are eventually used to develop a precise solution approach. This article’s fundamental and golden results are that for clamped–clamped boundary conditions, the softening of the system in zone 2 is less than zone 1, whereas the instable responses in zone 2 are more than zone 1. Also, for the sandwich disk with clamped–clamped boundary conditions, the system’s dynamic behavior tends to be more harmonious and less chaotic as the fiber’s angle increases. Therefore, increasing the fiber angle reduces the system’s chaos with clamped edges, which is very important for future works.