A mixed approach for studying size effects and connecting interactions of planar nano structures as resonant mass sensors

Present paper investigates the potential application of planar nano structures with attached nano particles as nano resonant sensors by introducing a nonlocal plate model which considers size effects. To take into account an elastic connection between the nano plate and the attached nanoparticle, the nano particle is considered as a mass-spring system. Then, a mixed approach based on pseudo-spectral and integral quadrature rule is implemented to numerically determine the frequency shift caused by the attached mass-spring system. 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 with concentrated objects. Results show that for soft connections with small values of spring constant the predicted frequency shift is greater than rigid connections. It means that considering a rigid connection instead of elastic one will underestimate the frequency shift of nano resonant sensors. Also, it is shown that neglecting size effects results in overestimating the frequency shift of nano resonant sensors. Furthermore, nano plates with greater aspect ratios offer smaller dimensionless frequency shifts and the maximum belongs to a square one. The presented results could be useful as a guideline for designing nano resonant sensors of plane shapes like graphene based mass sensors.