Nonlinear vibrations of a reinforced composite plate with carbon nanotubes

The nonlinear vibration behaviors of a reinforced composite plate with the carbon nanotubes (CNT) under combined the parametric and forcing excitations are studied in this paper for the first time. Based on the Mori-Tanaka method and the method of calculating the average stress of composite materials, the effective modules for the carbon nanotubes are obtained. The carbon nanotubes are supposed to be long hollow cylindrical structures. The nonlinear partial differential governing equations of motion for the CNT reinforced composite thin plate are derived by using the Reddy's third-order shear deformation plate theory and the geometric nonlinearity of von Karman. The governing equations are discrete to a set of ordinary differential equations by using the Galerkin method. A perturbation method is then employed to obtained the four-dimensional averaged equations of the CNT reinforced composite thin plate under the cases of 1:1 internal resonances. The nonlinear resonant responses of the CNT reinforced composite rectangular thin plate are analyzed under combined the parametric and forcing excitations. The effects of the forcing excitations on the different kinds of the periodic and chaotic motions of the CNT reinforced composite rectangular thin plate are investigated through a comprehensive parametric study. (C) 2015 Elsevier Ltd. All rights reserved.