A Wave Based Method to predict the absorption, reflection and transmission coefficient of two-dimensional rigid frame porous structures with periodic inclusions

This paper presents an extension to the Wave Based Method to predict the absorption, reflection and transmission coefficients of a porous material with an embedded periodic set of inclusions. The porous unit cell is described using the Multi-Level methodology and by embedding Bloch-Floquet periodicity conditions in the weighted residual scheme. The dynamic pressure field in the semi-infinite acoustic domains is approximated using a novel wave function set that fulfills the Helmholtz equation, the Bloch-Floquet periodicity conditions and the Sommerfeld radiation condition. The method is meshless and computationally efficient, which makes it well suited for optimisation studies.