On static and dynamic snap-throughs of the imperfect post-buckled FG-GRC sandwich beams

Abstract Post-buckled beams have been the basic elements of many mechanical devices used for energy harvesting, low-frequency vibration isolation, etc. This paper focuses on the theoretical analysis of nonlinear bending and forced vibration of the post-buckled sandwich beams with graphene reinforced composites (GRC) face sheets. It is assumed that the graphene nanoplatelets are directional in the beam's length and piecewise functionally graded (FG) along with the thickness. Also, the initial imperfection is supposed to possess the same shape as the first-order vibration mode and the material properties are temperature dependent. Based on a modified higher-order shear deformation zig-zag theory, the governing equations considering the thermal effects are derived. To obtain the closed form solutions of the strongly nonlinear system, a combination of the two-step perturbation with the modified Lindstedt-Poicare method is proposed. The accuracy of the results based on the current models and computation methods is validated. Subsequently, the imperfection sensitivity of bending and principal resonance characteristics under different axial compressions is also discussed. Numerical results reveal the static and dynamic snap-through behaviors and provide the optimal graphene reinforcement type of sandwich beams under different core-to-face sheet thickness ratios.