Nonlinear Vibration of Functionally Graded CNT-Reinforced Composite Plate Under Nonuniform In-Plane Loading

Abstract

In this study, a functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plate exposed to uniform and different forms of nonuniform in-plane loadings is analyzed for the determination of plate’s nonlinear vibration behavior (frequency-amplitude curve). Firstly, to guesstimate the effective mechanical properties of the FG-CNTRC plate, the extended rule-of-mixture technique is implemented when CNTs are aligned and distributed throughout the thickness of the plate. The different forms of CNTs distributions are considered, like - uniformly distributed (UD) and functionally Graded (FG-X type and FG-O type). Secondly, the FG-CNTRC is modeled based on higher order shear deformation theory (HSDT) including von-Kármán nonlinearity. Then, the distribution of stresses (σxx, σyy, τxy) within the plate because of nonuniform in-plane loading is estimated by resolving the in-plane elasticity problem using Airy’s stress approach. Thirdly, the governing partial differential equations (PDEs) of the FG-CNTRC plate are derived by employing Hamilton’s principle and solved using Galerkin’s method to convert these PDEs to the nonlinear ordinary differential equations (ODEs). Lastly, the Incremental Harmonic Balance (IHB) method are used to solve these nonlinear ODEs to trace the non-linear vibration behavior (frequency-amplitude curve) of the FG-CNTRC plate. The effect of different parameters like volume fraction of CNT, types of nonuniform loadings, types of CNTs distribution, and dynamic load factors on nonlinear vibration behavior of the FG-CNTRC plate are examined.KeywordsFG-CNTRC plateGalerkin’s methodNonuniform loadingIncremental harmonic balance