Nonlocal Galerkin Strip Transfer Function Method for Vibration of Double-Layered Graphene Mass Sensor

Abstract

Double-layered graphene sheets (DLGSs) can be applied to the development of a new generation of nanomechanical sensors due to their unique physical properties. A rectangular DLGS with a nanoparticle randomly located in the upper sheet is modeled as two nonlocal Kirchhoff plates connected by van der Waals forces. The Galerkin strip transfer function method which is a semi-analytical method is developed to compute the natural frequencies of the mass-plate vibrating system. It can give exact closed-form solutions along the longitudinal direction of the strip. The results obtained from the semi-analytical method are compared with the previous ones, and the differences between the single-layered graphene sheet (SLGS) and the DLGS mass sensors are also investigated. The results demonstrate the similarity of the in-phase mode between the SLGS and DLGS mass sensors. The sensitivity of the DLGS mass sensor can be increased by decreasing the nonlocal parameter, moving the attached nanoparticle closer to the DLGS center and making the DLGS smaller. These conclusions are helpful for the design and application of graphene-sheet-based resonators as nano-mass sensors.