Propagation of non-stationary waves in three-layer cylindrical bodies from local loads

The work is devoted to the study of wave processes in three-dimensional viscoelastic three-layer cylindrical bodies under the influence of non-stationary loads. A detailed analysis of well-known works devoted to this problem is given. The work developed a mathematical model, methodology, algorithm and computer program for the study of wave processes in three-dimensional multilayer cylindrical bodies under local and uniform unsteady influences. When developing a methodology for the solution, methods of separation of variables and orthogonal sweep were used. The distribution of the stress wave in three-layer cylindrical bodies was investigated under non-stationary actions from various profiles. The main attention is paid to the construction of stable algorithms for solving these three-dimensional three-layer problems. It was found that, with the same loading characteristics, stress waves are formed in the material of the outer layer. Also, locally loaded stress leads to the appearance of tensile stresses comparable in magnitude with compressive, tensile stresses already loaded in the first moments. An increase in stresses at the entrance of a wave into a cylinder with a denser material and a number of other effects were found.