Dynamic Viscoelastic Effects on Sound Wave Diffraction by Spherical and Cylindrical Shells Submerged in and Filled with Viscous Compressible Fluids

Abstract

An analysis for sound scattering by fluid-filled spherical and cylindrical viscoelastic shells immersed in viscous fluids is outlined. The dynamic viscoelastic properties of the scatterer and the viscosity of the surrounding and core fluids are rigorously taken into account in the solution of the acoustic scattering problem. The novel features of Havriliak-Negami model for viscoelastic material dynamic behaviour description along with the appropriate wave-harmonic field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in form of infinite series. Subsequently, the associated acoustic field quantities such as the scattered far-field pressure directivity pattern, form function amplitude, transmitted intensity ratio, and acoustic force magnitude are evaluated for given sets of medium physical properties. Numerical results clearly indicate that in addition to the traditional fluid viscosity-related mechanisms, the dynamic viscoelastic properties of the shell material as well as its thickness can be of major significance in sound scattering. Limiting cases are examined and fair agreements with well-known solutions are established.