A computational procedure for analyzing acoustical scattering by multilayer concentric spherical scatterers having an arbitrary mixture of acoustic and elastic materials is proposed. The procedure is then used to analyze the scattering by a spherical scatterer consisting of a solid shell and a solid core encasing an electrorheological (ER) fluid layer, and the tunability in the scattering characteristics afforded by the ER layer is explored numerically. Tunable scatterers with two different ER fluids are analyzed. One, corn starch in peanut oil, shows that a significant increase in scattering cross-section is possible in moderate frequencies. Another, fine poly-methyl methacrylate (PMMA) beads in dodecane, shows only slight change in scattering cross-sections overall. But, when the shell is thin, a noticeable local resonance peak can appear near ka=1, and this resonance can be turned on or off by the external electric field.

Scattering is the most fundamental problem in the research on phononic crystals and acoustic metamaterials; and scattering in a three-dimensional space poses challenging issues; and yet, the most challenging of all, is the scattering by elastic objects since an acoustic wave splits into different types of waves, propagating at different speeds, when it enters an elastic object. In this paper, a unified formalism is developed to analyze the scattering of an acoustic wave by a multilayer spherical object that is made of a mixture of an arbitrary number of concentric layers of elastic and acoustic media. Using this formalism, acoustical scattering by a multilayer spherical scatterer encasing an electrorheological (ER) fluid layer in an underwater environment is studied. Numerical examples show that ER fluids can alter the scattering characteristics above the first resonant frequency, which itself can be tuned by the applied electric field.