Comparative Study of Free Vibration for Carbon Nanotube-Reinforced Composite Plates Based on Various Higher-Order Plate Theories

A comparative investigation is made on the free vibration behavior of a carbon nanotube-reinforced composite (CNTRC) plate based on various higher-order shear deformation plate theories (HSDTs). For the CNTRC plates, uniformly distributed (Type UD) and functionally graded (Type Λ) reinforcements are considered where the material properties of CNTRC plates are assumed to be graded in the thickness direction and estimated through the rule of mixture. A set of unified nonlinear dynamics governing equations of the CNTRC rectangular plate considering different shear deformation function forms are established based on von Kármán-type geometric nonlinearity. Then by applying Galerkin discretization method, the nonlinear governing equations of a simply-supported CNTRC plate are simplified into a set of ordinary differential equations involving independent time variable. Finally by using the harmonic balance method, the influences of the parameters such as nanotube volume fraction, the plate width-to-thickness ratio and the plate aspect ratio on the natural frequencies and nonlinear free vibration behaviors of CNTRC plates with various higher-order plate theories are analyzed comparatively.