In this study, the vibrational properties of single- and double-layer graphene sheets (GSs) with attached nanoparticles are analyzed based on the nonlocal elasticity theory. The potential applications of atomic-scale mass sensing are presented using GSs with simply supported boundary condition. The frequency equation for GSs with an attached nanoparticle is derived to investigate the vibration frequency of the GSs under thermal environment. Using the proposed model, the relationship between the frequency shifts of graphene-based mass sensor and the attached nanoparticles is obtained. The nonlocal effect and the temperature dependence on the variation of frequency shifts with the attached nanomass and the positions on the GS are investigated and discussed in detail. The obtained results show that the nanomass can be easily detected by using GS resonator which provides a highly sensitive nanomechanical element in sensor systems. The vibrational frequency shift of GS increases with increasing the temperature dependence. The double-layer GSs (DLGSs) have higher sensitivity than the single-layer GSs (SLGSs) due to high frequency shifts.
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