Dissipation and dispersion properties of microinhomogeneous media

The propagation of a harmonic elastic wave in a microinhomogeneous (defect-containing) medium is considered in the framework of the rheological model that reperesents the medium in the form of a one-dimensional chain of masses connected by purely elastic elements and by Kelvin-Voigt viscoelastic elements. Analytical expressions are derived for the dissipation and dispersion characteristics of this medium for various distributions of the parameters of the viscoelastic elements. The dissipation and dispersion properties are found to obey the Kramers-Kronig relations. It is also shown that the damping decrement of the wave is almost constant, and the phase velocity monotonically increases in a sufficiently wide range of parameters of the viscoelastic elements in a wide frequency band. The derived expressions for the dispersion and dissipation are used to simulate the propagation of broadband pulses in this kind of medium.