Vibration analysis of porous functionally graded nanoplates

In this paper, a general nonlocal strain-gradient (NSG) elasticity model is developed for vibration analysis of porous nano-scale plates on an elastic substrate. The present model incorporates two scale coefficients to examine the vibration characteristics much accurately. The application of present nanoplate model as nano-mechanical mass sensors is also investigated. Porosity-dependent material properties of the nanoplate are defined via a modified power-law function and Mori-Tanaka model. Based on Hamilton's principle, the governing equations of the nanoplate on the elastic substrate under hygro-thermal loading are obtained. These equations are solved for hinged nanoplates via Galerkin's method. It is demonstrated that nano-pores, temperature change, humidity change, nonlocal-strain gradient parameters, gradient index and attached nanoparticle have a remarkable influence on vibration frequencies of nanoscale plates.