Chaotic responses and nonlinear dynamics of the graphene nanoplatelets reinforced doubly-curved panel

Abstract

In this article, a mathematical derivation is made to develop a nonlinear dynamic model for the nonlinear frequency, and chaotic responses of the graphene nanoplatelet (GPL) reinforced composite (GPLRC) doubly-curved panel subject to an external harmonic load. Using Hamilton's principle and the Von-Karman nonlinear theory, the nonlinear governing equations are derived. For developing an accurate solution approach, generalized differential quadrature method (GDQM) and perturbation approach (PA) are finally employed. The results show that GPL's pattern, radius to length ratio, harmonic load, and thickness to length ratio have important role in the chaotic motion of the doubly-curved panel. The fundamental and golden results of this paper is that the chaotic motion and nonlinear frequency of the panel is hardly dependent on the value of the smaller radius to length ratio (R1/a parameter) and viscoelastic foundation. It means that by increasing the value of R1/a parameter, and taking into account the viscoelastic foundation, the motion of the system tends to show the chaotic motion. Moreover, for GPL-A, GPL-V, and GPL-UD patterns, when the value of the R1/a parameter or the curvature shape of the doubly-curved panel increases, the chaoticity in motion response improves while for the GPL-O pattern, this matter reverses.