Stability of Subharmonic Oscillations in a Pipe Conveying Fluid under Harmonic Excitation

The existence and stability of subharmonic oscillations in a two end-fixed fluid conveying pipe whose base is subjected to a harmonic excitation are investigated. A Galerkin approach is utilized to reduce the equation of motion to a second order nonlinear differential equation. The conditions for the existence of subharmonic oscillations are given by using Melnikov method. The stability of subharmonic oscillations is discussed in detail by using action-angle variable and averaging method. It is shown that the velocity of fluid plays an important role in the stability of subharmonic oscillations.