Frequency analysis of nanoporous mass sensors based on a vibrating heterogeneous nanoplate and nonlocal strain gradient theory

A new modeling of nano-mechanical mass sensors constructed from porous nanomaterials is presented based on generalized nonlocal strain gradient theory (NSGT). In this model, true small size effects including softening and hardening mechanisms are considered for more reliable analysis of mass nanosensors. The present biomass nanosensor is based on an oscillating higher order nanoscale plate in contact with an elastic substrate. Nano-pores or nano-voids are incorporated to the model based on a modified rule of mixture. According to the Hamilton's principle, the formulation of nano-mass sensor is derived. Applying Galerkin's method, the frequency shift due to the mass sensing is obtained. It is indicated that the mass detection of nano-mechanical sensors is significantly influenced by the porosities, nanoparticle mass, nanoparticle numbers, nonlocal parameter, strain gradient parameter, material gradation, elastic foundation and geometrical parameters.