Nanoparticle mass detection by single and multilayer graphene sheets: Theory and simulations

The discovery of graphene opened up a new field of research and led to the development of various nanosensors and actuators that form new classes of nano electro mechanical systems (NEMSs) called graphene based nano resonators (GBNRs). Recently, GBNRs have been used in mass detection applications. In such applications and others, single-layer graphene sheets play a fundamental role. However, the synthesis of monolayer graphene is usually challenging and expensive. This makes the commercial use of multilayer graphene systems more attractive and necessary. Moreover, it is now more possible to control the number of layers in large-size graphene systems, and thus the theoretical design tools could help the engineers develop more efficient graphene-based sensors for everyday applications. This paper introduces a non-local elasticity theory for the general configurations of carbon atoms that could form carbon nanotubes (CNTs), nanosheets (graphene) and nanospheres (fullerenes) by means of the laminated plate theory. The problem is solved by the generalized differential quadrature element method (GDQEM). Then, a molecular dynamics approach is used in conjunction with the operational modal analysis (OMA) to perform a nano metric modal analysis. Several comparisons are presented to validate the introduced approaches; and finally, the effects of the number of layers and of nanoparticle mass and position on the frequency shift and sensitivity of the designed sensors are studied. It is demonstrated that the frequency shift decreases slightly and the sensitivity increases by increasing the number of graphene layers. It is also demonstrated that, depending on the positions of nanoparticles in a senor, various mode shapes of a graphene sheet could be excited; and consequently, the shift of the first natural frequency may not be appropriate for particles far from the middle of graphene sheet.