This article considers the dynamically stress-strain state of two-layer viscoelastic cylinders under internal (or kinematic) excitation. The relationship between stress and strain is satisfied by the Boltzmann-Volterra integral relations. The problem is reduced to a plane problem of the theory of viscoelasticity. The stated problem is solved by the Green-Lamb potential method. The resulting integro-differential equations in partial derivatives are solved using special Bessel and Hankel functions of the 1st and 2nd kind of the nth order. Solutions are expressed in terms of special functions of the complex argument. To determine the integral constants, a system of algebraic equations with complex coefficients is obtained. Numerical solutions are obtained and an analysis is made. The relevance of the study of the stress-strain state of structures under the action of dynamic loads, taking into account the viscoelastic properties of the material, is due to their widespread use in modern mechanical engineering. A typical example of such structures is a viscoelastic cylinder with a centrally located channel (cylindrical or non-trivial geometry). The body is made of materials with high specific strength. Composite materials are used depending on the purpose of the rocket, its size and operating loads.

kinematic, dynamic,, deformation

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