Instability and Vibration Analyses of Functionally Graded Carbon Nanotube–Reinforced Laminated Composite Plate Subjected to Localized In-Plane Periodic Loading

Abstract

Carbon nanotubes (CNTs) have attracted many researchers during the last three decades due to their versatile nature and exceptional mechanical properties. In this study, a functionally graded CNT-reinforced laminated composite (FG-CNTRLC) plate subjected to different types of localized in-plane loadings was analyzed semianalytically to determine its dynamic instability and nonlinear vibration characteristics. The effective mechanical properties of the FG-CNTRLC plate were estimated using the extended rule-of-mixture technique. The FG-CNTRLC plate was modeled based on higher-order shear deformation theory (HSDT) in conjunction with von Kármán nonlinearity. The distribution of prebuckling stresses within the plate due to localized in-plane loading was estimated by solving the in-plane elasticity problem using Airy’s stress approach. The nonlinear governing partial differential equations (PDEs) of the FG-CNTRLC plate were derived using Hamilton’s principle. The Galerkin method was used to convert these nonlinear PDEs to the nonlinear ordinary differential equations (ODEs). The nonlinear ODEs were solved using the incremental harmonic balance (IHB) method to obtain the nonlinear vibration response of the FG-CNTRLC plate. After dropping the nonlinear terms, the linear ODEs were solved by the Bolotin method to trace the dynamic instability regions. The effect of different parameters such as volume fraction of CNTs, different types of localized in-plane loadings, types of CNTs distribution, the static and dynamic load factor on the dynamic instability regions, and the nonlinear vibration characteristics of the FG-CNTRLC plate, were examined.