Vibration of single-layered graphene sheet-based nanomechanical sensor via nonlocal Kirchhoff plate theory

The potential of single-layered graphene sheet (SLGS) as a nanomechanical sensor is explored. A simply supported SLGS carrying a nanoparticle at any position is modeled as a rectangular nanoplate with a concentrated micro-mass. Based on the nonlocal Kirchhoff theory of plates which incorporates size effects into the classical theory, the natural frequencies of a nanomechanical sensor are derived using the Galerkin method. The effects of the mass and position of the nanoparticle on the frequency shift are discussed. In the absence of the nonlocal parameter, the frequencies reduce to the results of the classical model, in agreement with those using the finite element method. The obtained 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 frequency shift. Decreasing the plate side length also increases the frequency shift. Obtained results are helpful to the design of SLGS-based resonator as nanomechanical mass sensor.