Waves with negative group velocity in cylindrical shell filled with liquid
The problem of joint oscillations of an infinite thin cylindrical shell filled with liquid is investigated in the framework of the Kirchoff-Love model, which is often used for modeling various pipelines. The waves caused by different sources of vibrations can produce vibrations of supports and connections in the pipelines, which may affect the strength properties of the system. Special attention is given to the waves with negative group velocity. The time dependence of the processes under study is supposed to be harmonic. Joint oscillations of the shell and the fluid are considered. The free vibrations of the system are determined. An exact dispersion equation that is based on the exact analytical solution of the problem is used. This equation is asymptotically explored in the neighborhood of the point where it has multiple roots. The propagating waves are analyzed. Much attention is given to studying the 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 bifurcation point for this case. The difference between the types of asymptotics for the regular case and for the case of bifurcation is discussed. The analysis of arising effects is fulfilled in terms of kinematic and dynamic variables and in terms of wave group velocity. The relative advantages and disadvantages of these approaches are discussed. The dependence of dynamic and kinematic variables on the relative thickness of the shell, the mode number and other parameters of system is viewed. The possible fields of applicability of the gained effects are established.