Comments on the validity of transfer matrix based models for the prediction of the effect of curved sound packages

Abstract

In this paper, the validity of using the Transfer Matrix Method (TMM) to account for the effect of practical curved sound packages (i.e. spring-mass treatment) in vibroacoustic systems is assessed. For this purpose, a sub-structuring method that employs a Patch Transfer Functions (PTF) approach is used to efficiently couple standard Finite Element Method (FEM) of the structure and the acoustic cavity with the sound package model. Three models of the noise control treatment are compared, namely (i) a locally reacting model, (ii) a non-locally reacting (NLR) model based on the TMM, and (iii) a FEM. The FEM model considers the actual curved geometry of the SP in order to estimate its dynamic behavior while the simplified TMM based models assume the SP to be flat (i.e. unwrapped if curvature is present), homogeneous and of infinite lateral extent. In addition, these results are systematically compared to a full Finite Element/Boundary Element Methodology. The accuracy and the limitations of adopting the unwrapped approximation in TMM based models are shown through two parametric studies. The first considers the radius of curvature of the system as a parameter while the SP thickness is constant. The second considers the thickness of the SP as a parameter while the radius of curvature of the system is held fixed. For the considered configurations, the first parametric study allows to conclude that the curvature of the SP does not affect the dynamic behavior of the system due to its large dissipation and softness and it can be practically assumed flat if the NLR model is used to model the SP. However, the second parametric study shows that the thickness of the curved SP may affect the efficiency of the NLR model. Moreover, the limitations of locally reacting models are confirmed.