Propagation of internal waves in dissipative layered cylindrical bodies

In the paper the problems of propagation of internal waves in dissipative layered cylindrical bodies interacting with deformable (viscoelastic) media is discussed. The dynamic behavior of cylindrical bodies is described by equations of continuum mechanics. The spectral problem is reduced to solving a system of ordinary differential equations of the first order with variable complex coefficients. The solution of differential equations is expressed by special cylindrical Bessel and Hankel functions. The frequency equations are solved numerically by Muller's and Gaussian methods. The change in the natural frequency and phase velocity as a function of the wave number is investigated. For inhomogeneous dissipative mechanical systems nonmonotonic dependence of the imaginary part of the phase velocity of the wave numbers is discovered.