Nonlinear deformation waves in a geometrically and physically nonlinear viscoelastic cylindrical shell containing viscous incompressible fluid and surrounded by an elastic medium

The present study is devoted to analysis of nonlinear deformation of longitudinal waves in a cylindrical shell surrounded by an elastic medium and containing viscous incompressible fluid inside. The physical properties of the shell are defined by the equations of quadratic theory of viscoelasticity, which takes into account the linear elastic volume strain. The problem of wave propagation in viscoelastic and nonlinear thin-walled structures, including cylindrical shells, without interaction with the viscous incompressible fluid are considered from the perspective of earlier theory of solitons. The presence of fluid requires the development of new mathematical models and computer simulation of the processes occurring in the system.