Bifurcations and chaotic motions in the autonomous system of a restrained pipe conveying fluid

The stability and dynamics of a cantilevered pipe conveying fluid with motion-limiting constraints and a linear spring support have been investigated. Emphasis is placed on analyzing local qualitative behavior of the system in the neighborhood of a doubly degenerate point. Using some qualitative reduction methods of dynamical system theory, the four-dimensional differential equation of motion is reduced to a two-dimensional one, and then the possible motions of the pipe are predicted through analyzing bifurcations of the solution to the reduced equation of motion. The unfolding result is found to be in good agreement with the result obtained using the numerical method. It is also found that there exist the quasi-periodic motions and route to chaos through breakup of the quasi-periodic torus surface in some parameter region of the system, which differs from that of periodic-doubling bifurcation route found earlier in this system. Numerical simulations have been performed using the four-dimensional equation of motion to confirm the analytical results.