Nonlinear forced vibration analysis of FG-CNTRC plates based on the 3D elasticity

Abstract

In this article, an efficient numerical approach is developed to study the primary resonant dynamics of rectangular plates with arbitrary boundary conditions made of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs). The problem is formulated in the context of three-dimensional (3D) elasticity theory. Also, a variational approach based on Hamilton’s principle together with the variational differential quadrature (VDQ) method is proposed to obtain the discretized governing equations on space domain. Then, the solution procedure on the time domain is completed using the numerical Galerkin method, time periodic discretization method and pseudo arc-length continuation algorithm in order to find the frequency-response curves. It is considered that CNTs are distributed in the thickness direction based on an FG manner considering different patterns. After testing the convergence and validity of developed approach, numerical results are presented to investigate the influences of geometrical properties, CNT’s volume fraction and distribution pattern on the nonlinear forced vibration response of plates.