Vibration analysis of multi-phase nanocrystalline silicon nanoplates considering the size and surface energies of nanograins/nanovoids

Nanocrystalline nanoplates are composed from three phases which are nano-grains, nano-voids and interface. This paper develops a higher order refined plate model with a sinusoidal shear strain function for vibration analysis of porous nanocrystalline nanoplates based on modified couple stress theory. Nano-voids or porosities inside the material have a stiffness-softening impact on the nanoplate. Modified couple stress theory is employed to capture grains rigid rotations. The governing equations obtained from Hamilton's principle are solved applying Galerkin's method which satisfies various boundary conditions. The reliability of present approach is verified by comparing obtained results with those provided in literature. Finally the influences of couple stress parameter, grain size, porosities and shear deformation on the vibration characteristics of nanocrystalline nanoplates have been explored.