Quasi-resonances in sound-insulating coatings

This paper is concerned with the radiation of sound waves from a submerged cylindrical body which is coated by an imperfect elastic layer; that is, the coating only covers part of the cylinder. The focus of the study is to quantify the effect of the gap in the elastic layer on the radiated acoustic power. A finite element method is employed to determine the acoustic pressure field in the fluid and the displacement field in the coupled layer. This reveals that the effect of a modest sized gap in the coating does not markedly alter the radiated field except at distinct frequencies, at which values the coating exhibits strong fluid-coupled oscillations. We develop a simple analytical model to explain the resonance phenomenon and show that quasi-resonances arise when the wavelength of the deformation pattern ‘matches’ the azimuthal length of the surface of the coating. This resonant behaviour is conveniently captured by a single parameter Q, which is the ratio of the typical inertial fluid pressure induced by the wall oscillation to the stiffness of the elastic coating. For each choice of material parameters, there is shown to be an infinite set of values of Q corresponding to distinct quasi-resonance mode numbers. The effects on the radiated field due to variations in various physical parameters, such as acoustic wavenumber and elastic layer inertia, are also discussed.