非线性弹簧支承悬臂输液管道的分岔与混沌分析

唐 冶;方勃;张业伟;李庆芬

振动与冲击 ›› 2011, Vol. 30 ›› Issue (8) : 269-274.

PDF(1864 KB)
PDF(1864 KB)
振动与冲击 ›› 2011, Vol. 30 ›› Issue (8) : 269-274.
论文

非线性弹簧支承悬臂输液管道的分岔与混沌分析

  • 唐 冶1; 方勃1; 张业伟1; 李庆芬2
作者信息 +

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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摘要

研究悬臂输液管道系统在自激励、参数激励和外激励联合作用下的非线性动力学行为,揭示系统运动的规律。建立了非线性弹簧支承悬臂输液管道的运动微分方程,以线性弹簧支承条件下悬臂梁的固有频率和振型函数作为近似,采用李兹-伽辽金方法对非线性运动微分方程进行离散化,经过数值计算,利用分岔图、相图和功率谱图分析系统的非线性动力学响应,得到了流体平均流速和流体与管道质量比对系统周期运动和混沌运动的影响规律。研究结果表明,当流体平均流速较小时,系统的响应首先表现为周期运动,随着流体平均流速的增大,系统的响应通过系列倍周期分岔而进入混沌运动,又经由系列倍周期倒分岔转化为周期运动。随着流体与管道质量比的减小,系统出现混沌运动的临界流体平均流速值减小,这说明通过改变流体与管道质量比参数可以控制系统的振动形态。

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.

关键词

非线性 / 弹簧支承 / 输液管道 / 分岔 / 混沌

Key words

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

引用本文

导出引用
唐 冶;方勃;张业伟;李庆芬. 非线性弹簧支承悬臂输液管道的分岔与混沌分析[J]. 振动与冲击, 2011, 30(8): 269-274
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

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