Transverse vibration of circular graphene sheet-based mass sensor via nonlocal Kirchhoff plate theory

Abstract

The potential of circular graphene sheet (GS) as a mass sensor is explored. A circular GS carrying a nanoparticle at an arbitrary position is modeled as a circular nanoplate with a concentrated micro-mass for clamped and simply supported boundary conditions. Based on the nonlocal Kirchhoff plate theory which incorporates size effects into the classical theory, the natural frequencies of the mass sensor are derived using the Galerkin method. The effects of mass and position of the nanoparticle on the frequencies and frequency shifts are discussed. The frequencies reduce to the results of the classical model for the absence of the small scale effect, which maintain in accordance with those available in literatures. Numerical results show that when the mass of the attached nanoparticle increases or its location is closer to the plate center, the natural frequency decreases, but frequency shift increases. Small scale effect diminishes the frequencies strongly, but has less effect on the frequency shifts. When the radius of the nanoplate decreases, the frequency shift increases. The results are helpful to design circular GS-based resonators as nanomechanical mass sensor.