Theoretical Analysis of Vibration Frequency of Graphene Sheets Used as Nanomechanical Mass Sensor

Nanoelectromechanical resonator sensors based on graphene sheets (GS) show ultrahigh sensitivity to vibration. However, many factors such as the layer number and dimension of the GSs will affect the sensor characteristics. In this study, an analytical model is proposed to investigate the vibration behavior of double-layered graphene sheets (DLGSs) with attached nanoparticles. Based on nonlocal continuum mechanics, the influences of the layer number, dimensions of the GSs, and of the mass and position of nanoparticles attached to the GSs on the vibration response of GS resonators are discussed in detail. The results indicate that nanomasses can easily be detected by GS resonators, which can be used as a highly sensitive nanomechanical element in sensor systems. A logarithmically linear relationship exists between the frequency shift and the attached mass when the total mass attached to GS is less than about 1.0 zg. Accordingly, it is convenient to use a linear calibration for the calculation and determination of attached nanomasses. The simulation approach and the parametric investigation are useful tools for the design of graphene-based nanomass sensors and devices.