Nonlinear Vibration Response Analysis on a Composite Plate Reinforced With Carbon Nanotubes

Abstract

In order to compare nonlinear vibration response of the different enabled materials in the matrix of composites, the nonlinear vibrations of a composite plate reinforced with carbon nanotubes (CNT) are studied. In this paper, the carbon nanotubes are supposed to be long fibers. The nonlinear governing partial differential equations of motion for the composite rectangular thin plate are derived by using the Reddy’s third-order shear deformation plate theory, the von Karman type equation and the Hamilton’s principle. Then, the governing equations get reduced to ordinary differential equations in thickness direction with variable coefficients and these are solved by the Galerkin method. The case of 1:1 internal resonance is considered. The asymptotic perturbation method is employed to obtain the four-dimensional averaged equations. The numerical method is used to investigate the periodic and chaotic motions of the composite rectangular thin plate reinforced with carbon nanotubes. The results of numerical simulation demonstrate that there exist different kinds of periodic and chaotic motions of the composite plate under certain conditions. At last, the nonlinear vibration responses of the plate are compared with the same responses of angle-ply composite laminated plates.