Dynamic modeling and vibration analysis of double-layered multi-phase porous nanocrystalline silicon nanoplate systems

Nanocrystalline materials (NcMs) are multi-phase composites containing nanograins, nanovoids and interface. A softening mechanism due to the interface phase and nanovoids is observed in NcMs. For the first time, vibration behavior of double-layered nanocrystalline silicon nanoplates on elastic substrate is analyzed based on a two-variable refined plate model. Due to the experimentally observation of grains micro-rotation and strain gradients near interfaces, the strain gradient based couple stress theory is employed to describe the size-dependent behavior of the nanocrystalline nanoplate. A micromechanical model is employed to incorporate the effects of inclusions and their surface energies. Galerkin's method is implemented to obtain the natural frequencies of nanocrystalline nanoplate with different boundary conditions. One can see that the nanograins size, nanograins surface energy, nanovoids size, void percentage, interface region, scale parameter, foundation constants and boundary conditions have a great influence on the vibration behavior of a double-layered nanocrystalline nanoplate.