The Research On Dynamics Of Cantilevered Cylinders In Axial Flow

The stability and dynamics of a cantilevered cylinder in axial flow are investigated in this paper. In the equation of motion the inviscid fluid dynamic force, the normal and longitudinal viscous forces, and the hydrostatic forces are mainly considered, seperatly, for the fluid dynamic forces correct to third order 0 (ε3).The four-mode discretized ordinary differential equation of motion is derived by using Galerkin's method with the cantilever beam eigenfunctions. The effect of some key parameters, such as the fluid velocity u , the free-end shape parameter f , the mass ratioβ, the friction ratio b0 and some other parametersχandγ, on the stability is discussed.Some possible complicated motions are studied with two-mode discretized equation in the neighborhood of the degenerate point where coupled flutter and divergence instability occur. The normal form equation is derived using the theory of dynamical systems, and the behavior of the codimension two bifurcation is determined in the neighborhood of the degenerate point. Numerical simulations are performed to confirm the analytical results. Numerical simulations are also carried out in the neighborhood of the corresponding degenerate point which is determined using the four-mode discretized equation. The results of the four-mode equation are well agreement with those obtained using the two-mode equation.