The influence of temperature variations on large-amplitude vibration of functionally graded metallic foam arches reinforced with graphene platelets

This paper aims to study the influence of temperature variations on the large-amplitude free vibration behaviour of functionally graded (FG) metallic foam arches reinforced with graphene platelets (GPLs) using finite element methodology. The temperature-dependent material properties are considered, and the homogenized effective material properties are estimated using the Halpin-Tsai micromechanics model and Voigt's rule of mixture. The present formulation is based on higher-order shear deformation theory in conjunction with geometric nonlinearity for the structural analysis. A C-0 finite element model is implemented to develop the system of nonlinear governing equations, which are solved numerically using the direct-iterative procedure. The material properties are assumed to be varying along the thickness direction. A convergence and validation study has also been performed to validate the accuracy of the present nonlinear finite element formulation. Various design parameters such as porosity index, the weight fraction of GPLs, porosity distributions, opening angle, temperature dependency and independency etc. are considered for the detailed parametric study. New insights pertaining to the effect of temperature on nonlinear frequencies and mode shapes at higher amplitudes are discussed in detail.