Behaviors of dynamics and stability standard of graphene nanoplatelet reinforced polymer corrugated plates resting on the nonlinear elastic foundations

摘要

The dynamical analyses of functionally graded graphene nanoplatelet reinforced composite (FG-GPLRC) trapezoidally and sinusoidally corrugated plates on the nonlinear elastic foundations are investigated in this paper. The FG-GPLRCs are assumed to be distributed uniformly and functionally graded through the thickness. The material properties are estimated through the Halpin-Tsai micromechanical model, while the Poisson's ratio and density mass are implemented by the rule of mixtures. The mathematical model rests upon the classical theory and Von Karman-Donnell geometrical nonlinearity assumption. The dynamical responses of the simply-supported FG-GPLRC corrugated plates are obtained by employing a homogenization-based analytical model and the Galerkin's method. The effects of the environment, GPLs weight fraction, GPLs distribution patterns, geometric parameters are carried out in detail in the paper. The amplitude of the critical force of periodic and chaotic status can be found by applying the bifurcation diagrams 3D and 2D. With the selected critical values, time history, phase plane graphs, Poincare maps, maximum Lyapunov exponent, and Fourier spectrum are presented to observe the periodic and chaotic status of corrugated plates. The obtained results are also compared and validated with those of other studies.