Energy aspects of wave propagation in the infinite cylindrical shell fully submerged into the liquid

Abstract

The joint non-axisymmetric vibrations of an ideal acoustic liquid and an infinite thin empty cylindrical shell of Kirchhoff type are investigated. The first mode corresponds to this important type of vibrations. Vibrational modes associated with deformation of the cross-section of the shell are also considered. The problem of free vibrations of the shell submerged into the liquid space is studied in the rigorous mathematical statement. The exact analytical solution of this problem is analyzed. The source of vibration and acoustic fields in the system shell-liquid is the wave propagating through the shell from infinity. The high and low frequency asymptotics of the dispersion curves are analyzed. The propagating waves and energy flux in the system shell-liquid are determined. The case of negative group velocity (at positive phase velocity) of the waves and the sign of the energy flux components in the shell are discussed. The energy flux and its component are considered in the vicinity of quasitraverse points of dispersive curves. Different types of these points and their coordinates are asymptotically studied. The influence of relative velocities of the waves in the shell and fluid on the behavior of the entire system is explored. Comparison of various vibration modes is performed from the viewpoint of energy fluxes.