Nonlinear Stability of a Fluid-Conveying Cantilevered Pipe With End Mass in Case of Horizontal Excitation at the Upper End

Nonplanar vibrations of a cantilevered pipe with an end mass is studied. We have already clarified the nonplanar vibrations with a single frequency component when the pipe conveys fluid whose velocity is slightly over the critical value, above which the lateral vibration of the pipe is self-excited due to the internal flow. Moreover, for the case that the upper end of the pipe is excited periodically in the horizontal direction, we have shown in the previous paper that the nonplanar limit cycle motions start complex spatial transients and settle down to stationary planar forced-excited vibration when the excitation frequency is near the nonplanar limit cycle frequency. The purpose of this paper is to examine the stability of the nonplanar pipe vibrations when the nonplanar self-excited pipe vibrations are subjected to the excitation at the upper end. A set of ordinary differential equations, which govern the amplitudes and phases of unstable mode vibration and contain the effect of excitation at the upper end are derived. Stability analysis of these equations clarifies the nonlinear interactions between nonplanar self-excited pipe vibrations and the forced excitation. Second, the experiments are conducted with a silicon rubber pipe conveying water, confirming the dynamic features of pipe vibrations for the horizontal excitation.