Cellular Models of a Viscoelastic Medium with Solid Spherical Inclusions

The study calculates the acoustic characteristics of a composite medium in the form of rubber with solid inclusions, which was previously proposed as a sound-absorbing material with hydrostatic-pressure-independent properties. The calculation is based on the application of cellular models of monodisperse suspensions with the boundary conditions on the cell surface in the form of a thin rigid shell or the Happel condition to such a composite medium. The transition to a viscoelastic medium is performed by replacing the viscosity of the suspension by a quantity that is proportional to the complex shear modulus of rubber. Only shear losses in rubber are taken into account. The calculation is valid in a wide frequency range for arbitrary volume concentrations of inclusions. The calculated data and experimental data that are available from the literature are compared. Variants of layered sound absorbers consisting of a set of rubber-coated solid balls of different sizes that are placed in a low-viscosity compressible polymethylsiloxane liquid are considered.