Bifurcation and chaos analysis of cantileuer pipeline conveying fluid with nonlinear spring support

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Journal of Vibration and Shock ›› 2011, Vol. 30 ›› Issue (8) : 269-274.

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Bifurcation and chaos analysis of cantileuer pipeline conveying fluid with nonlinear spring support

TANG Ye1; FANG Bo1; ZHANG Ye -wei1; LI Qing-fen2

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Abstract

The nonlinear behaviors of cantilever pipeline conveying fluid system, under the excitation of pulsating fluid and harmonic motion of the base are investigated to find out the law of system motion. The differential equation of cantilever pipeline conveying fluid motion with nonlinear spring support is established, and the nonlinear differential equation of motion is discretized by the Ritz-Galerkin method based on the natural frequency and eigenfunctions of cantilever beam which is regarded similarly under the linear spring support condition. Through numerical calculations, the nonlinear dynamic responses of system are analyzed by bifurcation diagrams, phase portraits and power-spectrum portraits. The laws that the average velocity of fluid and the mass ratio of fluid and pipeline have an important effect on the periodic motion and the chaotic motion of system are obtained. The results obtained show that the behavior of system response is the periodic motion when the average velocity of fluid is relatively little. The response of system gets into the chaotic motion via series of period-doubling bifurcations, and it changes into the periodic motion via series of inverse period-doubling bifurcations with increase in the average velocity of fluid. When the system turns up the chaotic motion, the critical value which is the average velocity of fluid decreases with decrease in the mass ratio of fluid and pipeline. This shows that the vibration mode of system can be controlled by changing the parameters for mass ratio of fluid and pipeline.

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nonlinear / spring support / pipeline conveying fluid / bifurcation / chaos

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TANG Ye;FANG Bo;ZHANG Ye -wei;LI Qing-fen . Bifurcation and chaos analysis of cantileuer pipeline conveying fluid with nonlinear spring support[J]. Journal of Vibration and Shock, 2011, 30(8): 269-274