A stable method to model the acoustic response of multilayered structures

Abstract

A general approach to determine the acoustic reflection and transmission coefficients of multilayered panels is proposed in this paper. Contrary to the Transfer Matrix Method (TMM), this method does not become unstable for high frequencies or large layer thicknesses. This method is shown to be as general as the TMM and mathematically equivalent. Its principle is to consider a so called Information Vector which contains all the information necessary to deduce the State Vector through a Translation Matrix. The Information Vector is of reduced length compared to that of the State Vector and can be propagated in any layer without involving exponentially growing terms. In addition, this method enables the coupling between any type of physical media as far as proper boundary relations can be written. Moreover, the method does not lead to an enlargement of the systems’ size in the case of interfaces between media of different physical type. Finally, this method can be easily implemented in numerical codes. The method is validated on three cases classically encountered in acoustic problems. However, it is general enough to model any type of multilayered problems in any field of applied physics.