Hopf bifurcation and chaotic motions of a tubular cantilever subject to cross flow and loose support

The Hopf bifurcation and chaotic motions of a tubular cantilever impacting on loose support is studied using an analytic model that involves delay differential equations. By using the damping-controlled mechanism, a single flexible cantilever in an otherwise rigid square array of cylinders is analyzed. The analytical model, after Galerkin discretization to five d.o.f., exhibits interesting dynamical behavior. Numerical solutions show that, with increasing flow beyond the critical, the amplitude of motion grows until impacting with the loose support placed at the tip end of the cylinder occurs; more complex motions then arise, leading to chaos and quasi-periodic motions for a sufficiently high flow velocity. The effect of location of the loose support on the global dynamics of the system is also investigated.