Bulk strain solitons in a cylindrical shell

A mathematical model is proposed to describe longitudinal waves in the nonlinearly elastic thin-walled cylindrical shell. In the framework of the model equation of motion for the longitudinal displacement is derived. In the case of the homogeneous shell this equation has the form of the double dispersive equation (DDE) for the linear longitudinal strain component and has a solitary wave solution. Dependence of the parameters of this solution on the elastic and geometric properties of the shell is studied. Results of the experimental observation of the bulk strain soliton in a dust-like shell are presented, and estimation of the wave amplitude and speed is provided. A numerical simulation is performed to study evolution of the strain soliton in a cylindrical shell with variation of cross section.