Post-buckling and vibration analysis of randomly distributed CNT reinforced fibre composite plates under localised heating

Abstract

Present study aims to investigate the non-linear stability and vibration characteristics of randomly distributed carbon nanotube reinforced fiber composites (RD-CNTRFC) under localized heating. The effective material properties of RD-CNT reinforced polymer is determined using Eshelbhy-Mori-Tanaka (EMT) approach and Chamis method is used to estimate the material properties of the RD-CNTRFC plates considering properties to be temperature-dependent. The strain-displacement fields of plates are developed using Reddy’s higher order shear deformation theory and von-Kármán non-linearities. The in-plane pre-buckling stresses within the plates due to localized heating are estimated using Airy’s stress function by satisfying compatibility equation. Galerkin’s approach is adopted to simplify the partial differential equations (PDEs) into non-linear algebraic equations for stability analysis and ordinary differential equations (ODEs) for vibration analysis. The critical temperature of the plates can be obtained using standard eigen value approach and thermal non-linear equilibrium path of plate can be traced using iterative eigen value approach. The present approach is initially verified with the results of published literature. Moreover various parametric studies like agglomeration effect of CNTs, mass fraction of CNT, aspect ratio, width-to-thickness ratio are also carried-out to elucidate their influence on thermal stability and vibration characteristics of RD-CNTRFC plates.