Nonlinear structural and vibration analysis of graphene sheets

Abstract

A nonlinear differential quadrature based method is developed and successfully applied to structural and vibration analyses of general multi-layered graphene sheets in the presence of geometrical nonlinearities and nonlinear van der Waal forces. Important nonlinear displacement characteristics of multi-layered graphene sheets have first been established. Due to relatively large magnitudes of van der Waal forces, different layers of graphene undergo similar deflections under external loadings and nonlinearities in van der Waal forces do not contribute much to the overall nonlinear structural behaviour. In the case of vibration analysis, two groups of modes each having its own unique characteristics have been identified and are defined as the lower classical bending modes and the higher van der Waal enhanced modes. For lower classical bending modes, the layers vibrate in phase and their natural frequencies are only affected by geometrical nonlinearities but decoupled from nonlinear van der Waal forces. For higher van der Waal enhanced modes however, the nonlinear vibration characteristics are dictated by the nonlinear van der Waal forces. These observations are valid for different boundary conditions and different layers of graphene sheets that have been investigated. Van der Waal forces and their effects are properly modelled and examined, together with effects of key physical parameters. The results presented for the first time provide accurate and wholesome studies on the nonlinear structural and vibration characteristics of graphene sheets. These results are important to structural designs of graphene sheets which are increasingly being deployed for innovative engineering applications such as nano-electro-mechanical systems (NEMS).