Large Amplitude Vibration Analysis of Graphene Sheets as Resonant Mass Sensors Using Mixed Pseudo-Spectral and Integral Quadrature Methods

The present paper investigates the potential application of graphene sheets with attached nanoparticles as resonant sensors by introducing a nonlocal shear deformation plate model. To take into account an elastic connection between the nanoplate and the attached nanoparticle, the nanoparticle is considered as a mass-spring system. Then, a combination of pseudo-spectral and integral quadrature methods is implemented to numerically determine the frequency shift caused by the attached mass-spring system for both clamped and simply supported boundary conditions. The obtained results are in a good agreement with those available in the literature, which reveals that the proposed combined method provides accurate results for structural problems related to concentrated objects. The results show that for soft connections with small spring constant values, the predicted frequency shift is greater than for rigid connections. This means that considering a rigid connection instead of elastic one will underestimate the frequency shift of nano resonant sensors. Additionally, it is shown that neglecting nonlocal small scale parameter results in overestimating the frequency shift of nano resonant sensors. The presented results can be useful as a guideline for designing plane shape nano resonant sensors like graphene-based mass sensors.