Forced Vibration of a Pipe Conveying Fluid due to the External Excitation

Linear stability of a pipe conveying fluid has been studied as a classical problem of the elastic stability problem. The straight position of a pipe can be destabilized by Hopf bifurcation. The critical value of the fluid velocity at which the straight position of a pipe loses its stability is called critical flow velocity. When the fluid velocity is slightly smaller than its critical value for the Hopf bifurcation, the damping ratio of a certain mode becomes very small. In such region, the forced vibration of a pipe comes up as a problem, when subjected to the external excitation. In this paper, we theoretically investigate the frequency response of forced vibration of a pipe which is subjected to the external excitation