Acoustic resonance scattering by viscoelastic objects

Abstract

In this paper acoustic scattering from a viscoelastic sphere accurately modeled by means of the Kelvin–Voigt model is studied. The approach based on a single impedance-type or Cauchy boundary condition used in the past to account for losses in the body, is reconciled with the exact approach of viscoelasticity, which accounts for material losses via complex field equations, complex propagation vectors, and a set of three realistic boundary conditions on the surface of the sphere. Using the exact approach of viscoelasticity theory, the effect of viscoelastic losses on the various quantities of interest is determined. The Resonance Scattering Theory (RST) is ideally suited to isolate features of the acoustic spectrum which are dependent upon material composition. In order to use the RST for the combination of a viscoelastic object in a liquid medium, an impedance-matched background is required, and it is developed here for the first time. Subtraction of this background successfully isolates the resonances in the present case. Finally, an exact expression for the specific surface impedance of the sphere, which depends in a complicated way on frequency, on mode order, and on the four parameters controlling the viscoelastic properties of the sphere is derived. The effect of all these quantities on the sonar cross section of the sphere, or on the modal contributions contained within it is studied, and many pertinent results are displayed.