Parametric Instability Analysis of Functionally Graded CNT-Reinforced Composite (FG-CNTRC) Plate Subjected to Different Types of Non-uniform In-Plane Loading

Abstract

Carbon nanotube has attracted many researchers from last two decades due to its exceptional mechanical and multiuse properties. In this article, a semi-analytical study is performed to determine the dynamic instability of a Functionally Graded Carbon Nanotube Reinforced Composite (FG-CNTRC) plate exposed to uniform and various non-uniform in-plane loadings. The efficient mechanical properties for the plate are estimated using rule of mixture where CNTs are distributed aligned and distributed across the plates’ thickness such as Uniformly distributed (UD) and Functionally Graded (FG-X and FG-O). Here, The FG-CNTRC plate is modeled by means of higher order shear deformation theory (HSDT) and the stress distributions (σxx, σyy, τxy) within the plate because of non-uniform loadings are calculated using Airy’s stress method. Then, the Hamilton’s principle is applied to obtain the governing partial differential equations of the FG-CNTRC plate, and which is later solved with the help of Galerkin’s method to convert it to ordinary (Mathieu type) differential equations. Next, these Mathieu type equations are solved employing Bolotin’s method to trace the instability boundaries corresponding to period 2T. At last, the consequence of different parameters like volume fraction of CNT, types of non-uniform loading, static load factor, types of CNTs distribution on instability of the FG-CNTRC plate are examined.