Vibration of a Multilayered Graphene Sheet With Initial Stress

Abstract

This paper reports an investigation on the vibration of an individual multilayered graphene sheet with initial stress, based on an elastic plate model and membrane model with simply supported ends, considering the van der Waals force interaction between all layers of graphene sheets. The effect of initial stress is more obviously with an increase of half wave numbers m and n. This investigation indicates that the stiffness D, effected by thickness choose, plays a dominant role in the lowest natural frequencies, and much weaker role in high order natural frequencies. The influence of the stiffness is more significant for all natural frequencies with an increase of half wave numbers m and n. The lowest natural frequency of a multilayered graphene sheet for a given combination of m and n is independent of the van der Waals interaction but all of the other higher natural frequencies are significantly dependent on this interaction.