Multiple Scattering and Visco-Thermal Effects on 2D Phononic Crystal

TL;DR

This study investigates how visco-thermal and multiple scattering effects influence acoustic wave propagation in a 2D phononic crystal, revealing a broad frequency range where both effects coexist.

Contribution

The paper extends numerical methods to include visco-thermal losses and compares results with experiments and homogenization theory to analyze regime transitions.

Findings

Identifies a large frequency domain with coexistence of visco-thermal and multiple scattering effects.

Provides numerical extension using Schlömilch series for visco-thermal losses.

Validates findings through comparison with experimental data.

Abstract

In this paper, we are interested in the transition between regimes here either visco-thermal or multiple scattering effects dominate for the propagation of acoustic waves through a 2D regular square array of rigid cylinders embedded in air. An extension of the numerical method using Schl\"omilch series is performed in order to account for visco-thermal losses. Comparison withexperimental data and results from classical homogenization theory allows to study the transition between a low frequency limit (where viscous and thermal effects dominate) and a high frequency regime (where multiple scattering effects become predominant). For this particular geometry, a large frequency domain where visco-thermal and multiple scattering effects coexist is found.