Abstract
<jats:p>The work considers an infinitely long circular cylinder, generally consisting of an arbitrary number of coaxial viscoelastic layers, surrounded by a viscoelastic medium. It is assumed that the layered package consists of thick-walled and thin-walled layers of the cylinder. When describing the motion of thin-walled elements, the equations of the theory of such shells are used, which are based on the Kirchhoff-Love hypotheses. For thin-walled layers, the initial equations are the linear theory of elasticity. The problem is solved by the Green-Lamb method. The displacement potentials are determined from the solutions of the Helmholtz equation. Arbitrary constants are determined from the boundary conditions that are placed between the bodies. As a result, the problem posed is reduced to a system of inhomogeneous algebraic equations with complex coefficients, which is solved by the Gauss method with the selection of the main element. Analytical expressions for dynamic displacements and stresses of layers and the environment are obtained through special Bessel and Hankel functions. It was found that for $R_1/r_0>50$ , the effect of a cylindrical source is decomposed as a plane wave, i.e. the radius of curvature of the wave can be ignored.</jats:p>