Dipole relaxation rates of mass-loaded spherical inclusions in elastic matrix materials

Abstract

It is necessary to be aware of the rise times of dominant resonances when tone bursts or wide bandwidth pulses are used to test the acoustic response characteristics of materials containing resonant inclusions. In practice the monopole of a void and the dipole of a mass-loaded inclusion are the most important basic resonances. The dipole center of mass relaxation rate of a mass-loaded, rigid spherical inclusions in an elastic matrix material is analyzed. Inclusion to matrix mass density ratios ranging from one to eight and matrix shear stiffnesses ranging over more than an order of magnitude are considered. It is found that the rise time of center of mass oscillations is much longer than that of cavity oscillations in the case of heavily mass-loaded inclusions in rigid matrix materials. In soft materials, the reverse is true. In terms of the period of oscillation at resonance, the relaxation time of the rigid dipole is less than half a period long. This rate may be viewed as the lower bound on the relaxation rates of mass-loaded viscoelastic inclusions.