Atomistic-continuum multiscale-based free vibration analysis of single-layered graphene sheets in pre- and post-buckled states

Abstract

Free vibration of single-layered graphene sheets (SLGSs) subjected to compressive in-plane loads and embedded in a Winkler–Pasternak elastic medium in the pre- and post-buckled configurations is examined herein. To consider both geometric and material nonlinearities and include the size-dependent mechanical behavior of small-scale structures without taking any additional phenomenological parameters into account, the high-order Cauchy-Born (HCB) method, hyperelastic membrane and second gradient elasticity theory are used for providing mathematical formulation. Also, the variational differential quadrature (VDQ) method and Hamilton’s principles are applied to provide a set of discretized governing equations of motion. To evaluate the free vibration of SLGSs in post-buckling domain, first, the post-buckling problem corresponding to the considered system is solved. Then, by assuming a small disturbance about the equilibrium condition, the frequency response of SLGSs is obtained as a function of the applied in-plane load. In numerical results, the effects of various parameters such as geometry, elastic foundation and boundary conditions are highlighted and discussed in detail. © 2023, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.