Influence of material uncertainties on thermo-elastic vibration characteristics of graphene reinforced functionally graded porous beams

Abstract

This paper aims to study the influence of material uncertainties on thermo-elastic vibration response of functionally graded porous (FGP) beams reinforced with graphene platelets (GPLs) using the perturbation-based stochastic finite element method. The influence of material uncertainty on the vibration behavior of FGP-GPL reinforced beams subjected to thermal loading conditions have been discussed for low variability (randomness) in material design parameters (porosity content, amount of nanofillers) and material properties (Young’s modulus, density of metal matrix, and nanofillers) respectively. A C0 continuous stochastic finite element formulation based on higher-order shear deformation theory has been formulated. The convergence and validation of the present formulation have been compared with a traditional Monte-Carlo simulation to establish the accuracy of the present methodology. The homogenized effective material properties are estimated using the Halpin-Tsai micromechanics model and Voigt’s rule of mixture and are typically assumed to be varying along the thickness direction. The results highlighting the effect of uncertainty in material properties on the thermo-elastic vibration response of FGP-GPL reinforced beams have been discussed thoroughly.