Waves with the Negative Group Velocity in the Cylindrical Shell, Filled with Compressible Liquid

Abstract

The problem of joint oscillations of the infinite thin cylindrical shell filled with acoustical liquid of the Kirchhoff–Love type is considered. Free harmonic vibrations of the system are found. Propagating waves are analyzed. Much attention is given to exploration of waves with negative group velocity in the neighborhood of the bifurcation point of dispersion curves. Dispersion curve asymptotics are used in the neighborhood of the bifurcation point for this case. The ranges of frequencies and wavenumbers where this effect is observed are also estimated. Asymptotics for the regular case and for the case of bifurcation are discussed. Dependence of processes on the relative thickness of the shell and other parameters of the system are viewed. Possible fields of applicability of the effects gained are established.