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

Abstract

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