Wave Propagation in a Composite Material Containing Dispersed Rigid Spherical Inclusions
A dynamic model of the effects of stress waves on composite materials with rigid spheres in an elastic matrix, such as plastics with small particle fillers to increase stiffness and sound absorption, or metal solutions that separate during solidification into, say, steel-carbide spheroids in a ferrite matrix. In a dilute suspension with randomly distributed particles, multiple interactions between inclusions can be neglected; and the dispersion and attenuation of waves in the medium can be found in terms of the local scattering processes at each inclusion. Coupled equations of motion for both matrix and inclusions were derived through a variational technique. Results show the well-known fourth-power dependence of attenuation on frequency. Since the dynamics of wave scattering introduce inertia effects not explained by the mass and diameter of the inclusions alone, a constitutive equation involving the velocities must be specified.