A Transfer-Matrix-Based Approach to Predicting Acoustic Properties of a Layered System in a General, Efficient, and Stable Way

Layered materials are one of the most commonly used acoustical treatments in the automotive industry, and have gained increased attention, especially owing to the popularity of electric vehicles. Here, a method to model and couple layered systems with various layer types (i.e., poro-elastic layers, solid-elastic layers, stiff panels, and fluid layers) is derived that makes it possible to stably predict their acoustical properties. In contrast with most existing methods, in which an equation system is constructed for the whole structure, the present method involves only the topmost layer and its boundary conditions at two interfaces at a time, which are further simplified into an equivalent interface. As a result, for a multi-layered system, the proposed method splits a complicated system into several smaller systems and so becomes computationally less expensive. Moreover, traditional modeling methods can lose stability when there is a large disparity between the magnitudes of the waves within the layers (e.g., at higher frequencies, for a thick layer, or for extreme parameter values). In those situations, the contribution of the most attenuated wave can be masked by numerical errors, hence inducing instability when inverting the system. Here, the accuracy of the wave attenuation terms is ensured by decomposing each layer’s transfer matrix analytically and reformulating the equation system. Therefore, this method can produce a stable prediction of acoustical properties over a large frequency and parameter region. The fact that the proposed method can couple different layer types in a general, efficient, convenient, and stable way is beneficial, for example, when numerically optimizing the design of the acoustical treatments. The predicted acoustic properties of layered systems calculated using the proposed method have been validated by comparison with those predicted by previously existing methods. Further, an optimal design exercise is performed to find a lightweight layered dash panel treatment.