Scattering of Sound by Finite Elastic Surfaces Bounding Ducts or Cavities Near Resonance

A finite membrane is set in one of the infinite plane rigid walls of a two-dimensional duct and the whole is immersed in a stationary acoustic medium. A plane wave is incident onto the elastic surface and the sound field is examined in the limit of small fluid loading. Leading-order asymptotic solutions for the potential in the duct break down near both duct and membrane resonances, but improved estimates are derived which include the effect of the small, but finite, radiation damping in the system. The method is valid for a wide range of geometries and is performed on the problem with an elastic plate bounding one side of a cavity.