Attenuation of sound in multi-element acoustically lined rectangular ducts in the absence of mean flow☆

Abstract Extensions of the ordinary Wiener-Hopf technique are outlined and applied to the solution of sound attenuation in multi-element ducts with acoustically absorbing liners in series as well as in parallel combination. For demonstration purposes the simplest case of engineering interest is chosen: namely, a rectangular channel at zero convection velocity. Extensions to circular and annular geometries as well as to mean flow situations are possible. In the absence of a realistic source model acoustic power attenuation results are presented for an incoming fundamental mode only, to show the influence of major design parameters for point reacting liners. The broad band-width attenuation capacity of some liner configurations as well as the necessity to include wave reflections at liner discontinuities for multi-element liners is clearly demonstrated. For a given acoustic source a multi-mode solution can be found by summing the contributions of each incoming unattenuated mode.

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