›› 2012, Vol. 32 ›› Issue (5): 46-48.DOI: 10.3969/j.issn.1006-1335.2012.05.010

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Bifurcation Analysis of a Constrained Cantilevered Pipe Conveying Fluid under the Harmonic Parametric Excitations

ZHANG  Yan-lei 1,  HUANG  Hui-chun 1, 2,  CHEN  Li-qun 1， 3   

  1. (1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University,            Shanghai  200072,  China;2. Shanghai Second Polytechnic University,  Shanghai  201209,  China3. Department of Mechanics,  Shanghai University,  Shanghai  200444,  China)
  • Received:2011-12-13 Revised:2012-02-07 Online:2012-10-18 Published:2012-10-15

振荡流作用下受约束的悬臂输流管的分岔特性

张艳雷   

  1. ( 1. 上海大学  上海市应用数学和力学研究所，  上海  200072； 2. 上海第二工业大学，  上海  201209；3. 上海大学  力学系，  上海  200444 )
  • 通讯作者: 张艳雷

Abstract: The bifurcation behavior of the cantilevered pipes conveying pulsating fluid is investigated by taking into the nonlinear factors of Dirac delta account. The partial differential equation are discretized via the Galerkin’s method, and lead to a set of ordinary differential equations (ODEs). The ODEs is numerically solved by a fourth order Runge-Kutta scheme. Attention is concentrated on the possible bifurcation of the system with a different govern dimensionless parameters. The route to chaos is shown to be via period-doubling bifurcations. Finally, the cumulative effect of frequency on the dynamics is discussed in the different dimensionless flow velocity.

Key words: vibration and wave , pulsating fluid , Galerkin , Runge-Kutta

摘要： 引入三次方非线性的Dirac delta函数研究约束条件下悬臂输流管中的分岔特性。输流管内流体因振荡流作用而产生自激振动，是分岔与混沌运动的原因。通过迦辽金截断方法使系统变为标准的有限低维离散的系统。运用龙格库塔数值仿真的方法求解低维系统，获得关于振荡流作用下受约束的悬臂输流管的分岔特性。给出具体的数值算例，研究流速及振荡流参数的分岔影响。

关键词: 振动与波, 振荡流, 迦辽金截断, 龙格库塔

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