This paper deals with bifurcations and chaos of a cantilevered pipe conveying a steady fluid clamped at one end and having a nozzle and subjecting to nonlinear constraints at the free end. Nozzle parameter, flow velocity and linear stiffness of the pipe are taken as the variable parameters. The system is transformed into four-order ordinary differential equation using the Galerkin method. The static stability is studied in terms of some basic mathematical approaches. The method of averaging is employed to investigate the stability of the period motions. Three critical values are obtained. The system loses the static stability by saddlenode bifurcation and the dynamical stability by Hopf bifurcation. The period motions of the system lose the stability by a pitch-fork bifurcation and the system form the doubling-period motions.
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