Flutter and Chaotic Motions of a Cantilevered Pipe Conveying Fluid

The dynamics of a cantilevered pipe conveying fluid with a spring support and motion-limiting constraints has been investigated. Attention in the study was paid to the effect of the spring constant and some other parameters on the dynamics of the system, and was concentrated especially on the behavior of the pipe in the region of dynamic instability. The results obtained show that for small flow velocities the trivial equilibrium (i.e. the undeformed configuration of the pipe) is always stable for any values of spring constant. But, when the flow velocity is relatively large, the pipe loses its stability either by divergence if the values of spring constant are relatively large, or by flutter if they are relatively small. Several motions, including chaotic motions as the result of a sequence of period doubling bifurcations, are found in the ‘flutter region’ by using the method of numerical simulations. The local codimension -2 bifurcation phenomenon of the system near a doubly degenerate point, on which the system possesses a zero eigenvalue and a pair of pure imaginary eigenvalues, that is, coupled flutter and divergence bifurcation, is also investigated with the aid of some qualitative reduction theory for dynamical systems. It is shown that the unfolding result is in good agreement with the one obtained by the numerical method. Besides, the quasiperiodic motions are found in the system in our theoretical analysis, and then verified by using the method of numerical simulations in a certain region of parameter space.