Diffusion based homogenization method for 1D wave propagation

Abstract

The implementation of increasingly complex periodic structures for vibro-acoustic purposes in civil engineering and transportation industry creates new modeling and computational challenges, mainly due to the multi-scale nature of the structures. Homogenization techniques able to describe the local dynamics effects appearing in periodic structures have therefore received significant attention in the past years. In this paper, a homogenization technique is proposed for 1D periodic media, where the equivalent material properties are determined using the local wave scattering characteristics of the periodic medium. A Wave Finite Element scheme is used to retrieve the multi-modal interface diffusion coefficients based on a unit-cell FE model of the periodic structure. The homogenized model is then used to derive wavenumbers and Frequency Response Function of the waveguide. Four examples are proposed, including a 3D periodic waveguide exhibiting locally resonant bandgaps. Good agreement is observed. Also limitations of the method are discussed.

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

“…The resulting stiffness and mass matrices are post processed to offer the dynamic stiffness matrix. The dynamical properties of the periodic structure can be reflected through the spectral analysis of the unit cell [17,21]. The main objective of this work is, firstly, to calculate the multi mode propagation in a 3D periodic waveguide by SSG theory, and, secondly, to confirm the wave diffusion under a complex coupling condition.…”