Physically Admissible and Inadmissible Exact Localized Solutions in Problems of Nonlinear Wave Dynamics of Cylindrical Shells

It is shown that, when studying nonlinear longitudinal deformation waves in cylindrical shells, it is possible to obtain physically admissible solitary wave solutions using refined shell models. In the article, a physically admissible exact localized solution based on the Flügge – Lurie – Byrne model is constructed. An analysis of the influence of the external nonlinear elastic medium on the exact solutions obtained is carried out. It is established that the use of quadratic and cubic nonlinear deformation laws leads to nonintegrable equations with exact soliton-like solutions. However, the amplitudes of the exact solutions exceed the values of permissible dis- placements corresponding to the maximum points on the curves of the deformation laws of the external medium, which leads to the physical inadmissibility of these solutions.