Frequency analysis of free torsional vibrations of a three-layer cylindrical viscoelastic shell

The article investigates the frequency analysis in partial torsional vibrations of the elastic shell of a three-layer cylindrical joint. It is assumed that the outer layers of the shell are made of elastic material, and the middle layer is made of viscoelastic material. The equations derived by the authors in earlier works were used as the equations of Torsional vi-brations of a cylindrical shell, frequency equations were obtained from them for the case when the shell surface is free from external forces, and they were solved using the Maple 17 program. The obtained numerical solutions are used to plot the dependence of the oscillation frequency on the number of waves. The graphs were analyzed for cases when the materials and thickness of the edge and middle layers differed.