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This paper shows the mechanism of instability and chaos in a cantilevered pipe conveyingsteady fluid.The pipe under consideration has added mass or a nozzle at the free end.The Galerkin methodis used to transform the original system into a set of ordinary differential equations and the standard methodsof analysis of the discrete system are introduced to deal with the instability.With either the nozzle parameteror the flow velocity increasing,a route to chaos can be observed very clearly:the pipe undergoing buckling(pitchfork bifurcation),flutter(Hopf bifurcation),doubling periodic motion(pitchfork bifurcation)andchaotic motion occurring finally.
This paper shows the mechanism of instability and chaos in a cantilevered pipe conveyingsteady fluid. The pipe under consideration has added mass or a nozzle at the free end. The Galerkin methodis used to transform the original system into a set of ordinary differential equations and the standard methodsof analysis of the discrete system are introduced to deal with the instability.With either the nozzle parameteror the flow velocity increasing, a route to chaos can be observed very clearly: the pipe undergoing buckling (pitchfork bifurcation), flutter (Hopf bifurcation), doubling periodic motion (pitchfork bifurcation) andchaotic motion occurring finally.