The energy flux analysis of the backwards waves in a cylindrical shell with spring-type boundary condition on the outer surface

The problem of free harmonic vibrations of an infinite circular cylindrical shell with spring-type boundary condition on the outer surface, analogous to Winkler foundation for a plate, is studied. The shell is considered of Kirchhoff-Love type. The dispersion equation is derived on the base of the exact analytical solution. The propagating waves are analyzed. The energy flux and its components corresponding to different types of shell motion is calculated in the frequency ranges where the backwards waves arise. The comparison of different mechanisms of energy transmission in the shell is fulfilled. It is shown that the negative character of the energy flux is due to the negative character of its longitudinal and torsional components with dominating of the torsion one.