Thermal Effect on Vibration Responses of Double-Layered Graphene Sheet–Based Nanomechanical Resonators Based on Galerkin Strip Transfer Function Method

Abstract

Thermal effect on mass detection sensitivity of double-layered graphene sheet (DLGS) resonators based on their nonlocal vibration is investigated. A rectangular DLGS with a nanoparticle anywhere at the upper sheet is modeled as two nanoplates connected by van der Waals force. Based on the nonlocal Kirchhoff theory of plates which incorporates size effects into the classical theory, Galerkin strip transfer function method (GSTFM), which is a semi-analytical method, is developed to solve the characteristic equations and in settling the semi-analytical solutions of the frequency shift of the mass-plate vibrating system. It can give exact closed-form solutions along the strip longitudinal direction. Obtained results from the semi-analytical solutions are in good agreement with the available data in literature. Parametric studies on the natural frequency shift including the temperature changes, the nonlocal parameter and the location of the attached nanoparticle are discussed. The obtained results show that an increase of the temperature difference yields to reduction of fundamental frequency, and the DLGS-based nanomechanical resonator became more sensitive at a negative temperature change. Those conclusions are helpful to the design and application of GS-based resonator as nanomass sensor.