Eigenwaves propagation in three-layer cylindrical viscoelastic shells with a filler non-uniform in thickness

The paper provides the statement of the problem, the development of a calculation method and an algorithm to solve the problems of propagation and absorption of non-axisymmetric natural waves in layered dissipative-inhomogeneous viscoelastic three-layer cylindrical bodies. A detailed analysis of well-known publications devoted to this problem is given. The paper posed the problem of non-axisymmetric natural wave propagation in three-layer cylindrical shells with fillers, taking into account the theory of hereditary viscoelasticity. Dispersion equations were obtained and the dependence of the phase velocity on the wavenumber for the three-layer shells was constructed. A calculation method was developed based on the Muller, Gauss, and orthogonal sweep methods. The program (in C⁺⁺ language) was compiled based on the developed algorithm. Numerical results were obtained for the complex phase velocity depending on various wavenumbers and parameters of an axisymmetric cylindrical mechanical system for the Kirchhoff-Love and Timoshenko hypotheses. The change in the real and imaginary parts of the complex phase velocity under various parameters of the system was investigated for structurally homogeneous and inhomogeneous mechanical systems. The results obtained by the Kirchhoff-Love and Timoshenko hypotheses are in good agreement but differ in the wave absorbing abilities. It was found that a decrease in filler thickness at a rigid inner shell leads to a rapid increase in the real and imaginary parts of the vibration frequencies.