Diffusion based homogenization method for 1D wave propagation

Abstract

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.