Acoustic scattering from viscoelastically coated spheres and cylinders in viscous fluids

An analysis for sound scattering by simple compound viscoelastic structures immersed in viscous fluids is outlined. The dynamic viscoelastic properties of the scatterer and the viscosity of the surrounding fluid are rigorously taken into account. The Havriliak–Negami model for viscoelastic material behaviour along with the appropriate wave-harmonic field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in form of an infinite series. Subsequently, the associated acoustic field quantities such as the scattered farfield pressure and the form function amplitude are evaluated for given sets of viscoelastic material properties. Numerical results reveal that the scattered farfield pressure directivity patterns are highly dependent on the coating thickness, especially for the low-damping polymeric coating at small and intermediate non-dimensional frequencies. At these frequencies, the high-damping polymeric coating leads to very uniform pressure patterns for essentially all coating thicknesses. Furthermore, numerical solution of the associated eigenfrequency equation confirms that the comparatively high (moderate) scattered farfield pressure amplitudes corresponding to the high-damping (low-damping) polymer at low and intermediate frequencies is due to the fact that the eigenfrequencies associated with the viscoelastic resonances predominantly fall inside this frequency range. Limiting cases are examined and fair agreements with well-known solutions are established.