Dynamic Instability of CNT-Reinforced Composite Plate Under Non-uniform In-plane Loading

Abstract

An analytical study is conducted to define the dynamic instability of the carbon nanotubes-reinforced composite (CNTRC) plate under the action of different kinds of non-uniform loadings. The efficient mechanical properties of the lamina are calculated using the Eshelby–Mori–Tanaka scheme, where CNTs are distributed randomly within the epoxy. Hence, the CNT-embedded matrix is considered isotropic. The CNTRC plate is modeled as per higher-order shear deformation theory (HSDT). Due to the non-uniform nature of loading, the distribution of stresses (σxx, σyy, τxy) within the CNTRC plate is derived by solving the in-plane elasticity problem using Airy's stress method. Hamilton's principle is implemented to derive the partial differential equations (PDEs) of the CNTRC plate using the derived stresses. These PDEs are solved to obtain the ordinary differential (Mathieu type) equations using the Galerkin method. Subsequently, Mathieu type equations are solved using the Bolotin method to find the boundaries of instability corresponding to periods T and 2 T. Finally, the effect of changed parameters such as the mass fraction of CNT, CNT agglomeration, static and dynamic load factors, and various non-uniform in-plane loadings on the dynamic instability of the CNTRC plates is examined.