Snap-buckling and resonance of functionally graded graphene reinforced composites curved beams resting on elastic foundations in thermal environment

Abstract

This article pays attention to the snap-buckling and resonance behaviors of functionally graded graphene platelets reinforced composites (FG-GPLRCs) curved beams resting on the elastic foundations in a thermal environment. The material properties of the FG-GPLRCs curved beams with immovable clamped-clamped ends are temperature-independent. Considering the influence of von-Kármán nonlinearity, the Euler-Bernoulli beam theory is applied to derive the motion equations. The approximate solutions of nonlinear vibration and snap-through buckling responses of the curved beams under harmonic forces are found with the help of the two-step perturbation method and the modified Lindstedt–Poincaré method. The influences of different parameters including temperature variations, the elastic foundations, the graphene platelets (GPLs) distribution, the weight fraction of GPLs, the number of GPLs layers and the radius of curvature of the curved beams on nonlinear resonance and snap-buckling behaviors are investigated.