Abstract
Abstract In work questions of distribution of characteristic waves in the dissipative stratified cylindrical bodies interacting with deformable (viscoelastic) environments are considered. The dynamic behavior of cylindrical bodies is described by the equations of a mechanics of continua. The spectral task comes down to the solution of system of ordinary differential equations of first order with variable complex coefficients. The solution of system of differential equations is expressed by means of Bessel and Hankel’s cylindrical higher transcendental functions. The frequenciest equations are solved numerically by methods of Müller and Gauss. Change of a natural frequency and phase speed depending on a wave number is investigated. For dissipative heterogeneous mechanical systems nonmonotone dependence of imaginary parts of phase speeds on wave numbers is found.