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Stability analysis of cantilevered cylinder subjected to axial flow

The stability and dynamics of a cantilevered cylinder in axial flow are investigated. The discretized ordinary differential equation of motion is derived by using a four-mode expansion of Galerkin's method with the eigenfunctions of a cantilever beam. The effect of some key parameters, such as the fluid velocity u, the free-end shape parameter f, on the stability is studied and discussed. The diagram of the stability regions and dynamical behavior of the system is presented in a parameter plane. Some complicated dynamical behavior that is found for a higher fixed value of f with increasing u is as follows: (1) the system loses stability by first-mode divergence, (2) it regains stability, (3) it becomes subject to second-mode flutter, (4) it becomes subject to second- and third-mode flutter, (5) the second-mode flutter disappear, and it develops third-mode flutter only, (6) together with divergence instability more complex dynamical behavior then follows.