LAUSR

Abstract This paper studies the vibration frequency of rippled single-layered graphene sheets (SLGSs). The energy-based analytical model is proposed based on improved continuum mechanics theory (CMT) by considering the variable vibration mass and strain energy. It is found that significant frequency shift on pristine SLGSs can be realized using functional groups, defects, carbon nanotubes and surface wrinkles. Reduction of vibration frequency in SLGSs with random ripples is mainly dominated by the variable mass. Increasing of vibration frequency in continuously rippled SLGSs is highly warranted by the strain energy. A phase diagram which shows the relationship between different factors causing ripples on SLGS and frequency shift can be obtained. Finally, a novel nano device concept can be proposed based on frequency ascension, quality factors and bandwidth. The results obtained in this paper can provide a fundamental understanding of tunable vibration frequency in atomically thin materials and an insight for the next generation nano resonant devices design.