Consequences of the Ingard-Myers coupling condition in the case of a low frequency guided acoustic wave convected and coupled with a yielding wall

It is known since long that a plane acoustic guided wave coupled with a vibrating wall could be attenuated in a certain frequency range. From analytical and numerical models, it seems that in presence of a uniform mean flow this attenuation still exists but reduced. The coupling in presence of a flow can be envisaged with various conditions, the most rigorous being that known as the Ingard-Myers condition. Have experimental results obtained by various authors in other acoustic fields been perfectly coherent with this condition, there would have been no choice but to use it. As this is not the case, we are led to build various predicting models and keep that one with the nearest results of those obtained by experiments. The present work stays at the very first modelling stage and focuses on the 2-dimensional configuration where a convected low frequency acoustic wave interacts with a 1-dimensional membrane (a quasi-string). In the absence of a rigorous analytical solution when the 1D-membrane is of finite length, the problem is solved in its weak form within a finite volume via a numerical finite element model and continuities with a plane wave beyond. The differential operator makes it possible to work with linear basis functions, therefore resulting in simple non-classical elementary matrices. Outside the fact that the acoustic wave is not always perfectly plane just in front of the vibrating structure, it will be shown how the attenuation against frequency is modified by the flow, and also how the insertion of the coupling condition that takes into account or not the convection changes the results.