Energy analysis of waves with negative group velocity in cylindrical shell

Abstract

The problem of joint oscillations of a thin infinite cylindrical Kirchoff-Love shell is considered. The free vibrations of the system are found. The propagating waves and energy flux are analyzed. Much attention is given to the exploration of waves with negative group velocity in the neighborhood of the bifurcation point of dispersion curves. The asymptotics of dispersion curves are used in the neighborhood of the bifurcation point for this case. The interval of system parameters (the relation of lengths of circle waves and lengths of waves along cylinder to the relative thickness of the cylinder) is estimated when the negative group velocity arises. The range of frequencies and wavenumbers where this effect is observed is also estimated. The difference in the kinds of asymptotics for the regular case and the case of bifurcation is discussed. The analysis of arising effects is carried out in terms of kinematic and dynamic variables and in terms of energy flux. Relative advantages and disadvantages of these approaches are discussed. Comparison of the contributions of various mechanisms of energy transmission in the shell to the integral energy flux is performed. A special role of the rotational component in the occurrence of a subzero integrated energy flux is analyzed. The dependence of subzero energy flux and dynamic and kinematic variables on the relative thickness of the shell, the mode number and other parameters of the system is considered. The proportionality of the energy flux and its components for various modes is analyzed. The possible fields of application of the obtained effects are established.