Analysis of nonlinear forced vibration of multi-layered graphene sheets

This paper studies nonlinear forced vibration of multi-layered graphene sheets (MLGSs). Emphasis is placed on the anti-phase large-amplitude vibration which has the potential to overcome the van der Waals (vdW) interaction between layers for mechanical exfoliation of MLGSs. In contrast to the existing linear analyses, this paper derives a nonlinear explicit expression for analysis of large-amplitude vibration because the nonlinear term in Taylor expansion of vdW force function cannot be ignored when amplitude of vibration is large. Based on the vdW explicit formulation, a nonlinear continuum model is developed for the vibrations of MLGSs subjected to out of plane harmonic excitation in spectral neighborhood of lower resonances. The corresponding amplitude–frequency relationships are discussed comprehensively. The influence of externally excited loads on forced vibration behavior of MLGSs is also investigated. The theoretical model presented is expected to help analyze separation of MLGSs into a few- or even single-layered graphene sheets.