The Stability of a Cantilever Beam Subjected to One-Dimensional Leakage Flow

The stability of a cantilever beam subjected to one-dimensional leakage flow is investigated. The motion of such a beam is expressed as the sum of the first few eigenfunctions of a cantilever beam. The critical flow velocities and the natural frequencies on the neutral stability are determined as a function of gap width. Experimental results are in agreement with analytical ones. The complex frequency of the four lowest modes of the system is calculated in several representative cases as a function of flow velocity. In the case that the beam is clamped at the upstream end, the system is found to lose stability by coupled-mode flutter. On the other hand, in the case that the beam is clamped at the downstream end, the system is found to lose stability by divergence first, and successively lose stability by flutter with increasing flow velocity.