Wave Transmission and Reflection Analysis Based on the Three-dimensional Second Strain Gradient Theory

The scattering of guided waves through a coupling region is crucial information when studying waveguides. In this paper, the second strain gradient theory (SSG) used to describe wave transmission and reflection in three-dimensional micro-sized medium. First, constitutive relation 3D SSG model derived while six quintic Hermite polynomial shape functions are for displacement field. Then Hamilton’s principle weak formulation unit-cell’s stiffness matrix finite element stiffness, mass matrices force vector. Eventually diffusion (i.e. including coefficients) computed discussed various conditions.