Vibration analysis of multi-phase nanocrystalline material nanoshells using strain gradient elasticity

Abstract

This paper studies the free vibrational behavior of porous nanocrystalline silicon nanoshells using strain gradient theory. Nanocrystalline materials are multi-phase composites with the contribution of nanopores, nanograins and interface phase. Because of experimental observation of strain gradients near the interface phase, the nanoshell is modeled via strain gradient theory. A micromechanical model based on the Mori–Tanaka scheme is employed to incorporate the size of nanograins/nanopores and their surface energies. The nanoshell is modeled via first order shear deformation theory and Galerkin’s method is implemented to obtain vibration frequencies. Shape functions that satisfy available classical and non-classical boundary conditions in strain gradient theory are proposed. It is shown that the vibrational behavior of the nanoshell is influenced by the porosity percentage, nanograin size, strain gradient coefficient, boundary conditions, and the surface phase of nanograins/nanopores.