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This paper proposes a new method for investigating the Hopf bifurcation of a curvedpipe conveying fluid with nonlinear spring support.The nonlinear equation of motion is derived byforces equilibrium on microelement of the system under consideration.The spatial coordinate ofthe system is discretized by the differential quadrature method and then the dynamic equation issolved by the Newton-Raphson method.The numerical solutions show that the inner fluid velocityof the Hopf bifurcation point of the curved pipe varies with different values of the parameter,nonlinear spring stiffness.Based on this,the cycle and divergent motions are both found to existat specific fluid flow velocities with a given value of the nonlinear spring stiffness.The results areuseful for further study of the nonlinear dynamic mechanism of the curved fluid conveying pipe.
This paper proposes a new method for investigating the Hopf bifurcation of a curved pipe conveying fluid with nonlinear spring support. The nonlinear equation of motion is derived byforces equilibrium on microelement of the system under consideration. The spatial coordinate of the system is discretized by the differential quadrature method and then the dynamic equation is released by the Newton-Raphson method. Numerical solutions show that the inner fluid velocity of the Hopf bifurcation point of the curved pipe varies with different values of the parameter, nonlinear spring stiffness. Based on this, the cycle and divergent motions are both found to existat specific fluid flow velocities with a given value of the nonlinear spring stiffness.The results areuseful for further study of the nonlinear dynamic mechanism of the curved fluid conveying pipe.