Propagation of Own Non- Axisymmetric Waves in Viscoelastic Three-Layered Cylindrical Shells

Abstract

The relevance of the study of the dynamic movements of structures consisting of a thin-walled shell and a viscoelastic cylindrical cavity mounted on it is due to their widespread application in modern technology. The mechanical system under consideration consists of two concentric cylindrical shells with a viscoelastic filler (or cylinder) between the shells. The filler and shell can be firmly attached to the outer and inner shells along the entire cylindrical surface. The basic equations of small oscillations of the shell theory and the three-dimensional viscoelasticity theory are used to describe the oscillations of the “shell-filler-shell” system with the exact satisfaction of the contact boundary. The main purpose of the work is to develop a method and algorithm for calculating the problems of propagation and absorption of natural waves in a mechanical "shell-filler-shell" mechanical system. A calculation method based on Müller, Gauss and orthogonal running methods was developed. The Kirchhoff-Love and Tymoshenko hypotheses are used for the cylindrical shell. For dissipative homogeneous and non-homogeneous mechanical systems, the variation of the real and imaginary parts of the complex phase velocity from different system parameters was studied. For sufficiently long waves, Kirchhoff-Love and Tymoshenko hypothesized that the phase velocities of the first form were found to be well matched. It was also found that it is possible to use shell equations for shortwave, taking into account the compression of the filler. It was found that the increase in filler thickness was particularly significant for the relatively small thickness of the filler.