A general and stable approach to modeling and coupling multilayered acoustical systems with various types of layers

In this article, a general method is proposed to model layered acoustical systems with two-by-two transfer matrices, and further, to solve for their acoustic absorption, reflection, and transmission coefficients. Since the proposed method uses the matrix representation of various layers and interfaces, as in the Transfer Matrix Method (TMM), the equation system can be established efficiently. However, the traditional TMM can become unstable when there is a large disparity between the magnitudes of the waves traveling in opposite directions within the layers (i.e., at higher frequencies, for a thick layer, or for extreme parameter values). In such cases, the contribution of the most attenuated wave can be masked by numerical errors and can induce instability when solving the system. Therefore, in the proposed method, the accuracy of the wave attenuation terms is ensured by decomposing each layer’s transfer matrix and reformulating the equation system. This method can be used to couple different layer types in a general way and is easy to assemble and implement with numerical code. The predicted acoustic properties of layered systems calculated using the proposed method have been validated by comparison with those predicted by previously-existing methods.