振荡流作用下受约束的悬臂输流管的分岔特性

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

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。

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.