Nonlinear free vibration of functionally graded CNT-reinforced composite plates

Abstract

This paper is concerned with the development of a nonlinear numerical method for solving the nonlinear vibration problem and the parametric investigation of nonlinear free vibration characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates. The von Kármán nonlinear vibration problem is numerically formulated in the framework of 2-D natural element method (NEM) and the (1,1,0)* hierarchical model which is equivalent to the first-order shear deformation theory. The selectively reduced integration technique is employed to suppress the shear locking, and the resulting nonlinear modal equation is solved by a three-step direct iterative scheme. The nonlinearity in free vibration is evaluated in terms of the nonlinear to linear fundamental frequency ratio with respect to the relative vibration amplitude. Through the comparison with the other reference methods, the reliability of present nonlinear method is verified with the maximum relative difference less than 8.0%. The nonlinear free vibration characteristics FG-CNTRC plates are parametrically investigated with respect to the gradient pattern and volume fraction of CNTs and the relative thickness and aspect ratio of plates. The gradient pattern gives rise to the significant affect and the relative thickness and the aspect ratio shows the bounded effect, while the variation to the volume fraction of CNTs is found to be insignificant.