A consideration on pre- and post-instability of an axisymmetric elastic beam subjected to axial leakage flow

The dynamical behavior of an axisymmetric elastic beam subjected to axial leakage flow is investigated numerically and experimentally. The coupled equations of motion for a fluid and a beam structure are derived using the Navier–Stokes equation for an axial leakage flow-path and the Euler–Bernoulli beam theory. Performing complex eigenvalue analysis, the variation of the dynamic behavior during pre- and post-instability is investigated with respect to increasing axial leakage flow velocity. Also, an experiment was performed to determine the critical velocity of the unstable dynamic behavior of an axisymmetric elastic beam confined in a concentric cylinder subjected to axial leakage flow through a small annulus, and to measure the variation of the dynamic behavior on pre- and post-instability when the unstable phenomenon with the lower predominant frequency is shifted to the higher one. The relationships between the axial flow velocities and the unstable phenomena are clarified for the transition from the lower mode to the higher mode by comparing the theoretical calculations with experimental observations. Especially, the generation of traveling waves and the energy balance for the distortion of vibration response in the axial direction are discussed and considered at the transition region of the complex coupled vibration response of an axisymmetric elastic beam subjected to an axial leakage flow. Numerical and experimental results are found to be in quite good agreement.