Effect of thermal pre/post-buckling regimes on vibration and instability of graphene-reinforced composite beams

Abstract

The aim of this research is to analyze the natural frequencies and instability of laminated nanocomposite beams in thermally pre/post-buckled configurations. The thick beam consists of ten composite layers, each reinforced with graphene platelets (GPLs). It is also assumed that the beam is in contact with a generalized linear/nonlinear elastic medium. Different patterns are used to simulate selected distribution profiles of material properties through the beam thickness. Reddy’s third-order shear deformation theory within the framework of the von-Kármán assumption is implemented to derive the kinematic relation. Hamilton’s principle is used to derive the equations of motion for the uniformly heated graphene-reinforced composite beam. In the absence of an external pressure load, the Duffing-type equation is obtained and solved for the nonlinear vibration problem of the beam. The analytical solutions for the vibration and stability problems of the thermally buckled beam are obtained using the perturbation-based method. This study presents new insights into the vibration and stability problems of laminated nanocomposite beams. The influence of important parameters of the nanocomposite beam such as the weight fraction of nanofillers, the distribution pattern of GPLs, slenderness ratio, temperature variation and foundation components on the nonlinear behavior of the beam is numerically presented and discussed.