参-强激励联合作用下输流管的分岔和混沌行为研究

研究输送脉动流的两端固定输流管道在其基础简谐运动激励下的分岔和混沌行为,考虑管道变形的几何非线性和管道材料的非线性因素,推导了系统的非线性运动方程,并应用Galerkin方法对其进行了离散化处理。通过采用数值模拟方法,对系统的运动响应进行仿真,重点探讨了流体平均流速、流速脉动振幅以及基础简谐运动激励振幅对系统动态特性的影响。结果表明,系统在不同的参数下会发生围绕不同平衡点的周期和混沌等运动,并在系统中发现了两条通向混沌运动的途径:倍周期分岔和阵发混沌运动。

Bifurcation and Chaotic Motion of Fluid-Conveying Pipe under Combined Parametric and Forcing Excitations

The stability and dynamics of a pipe conveying pulsating fluid with both ends fixed, excited by the harmonic base motion normal to the pipe span, were investigated. Considered the nonlinear effects of deflection and material, the differential equations of motion were derived, and discretized with Galerkin method. The motions of pipe were analyzed by means of numerical simulations, the effects of the average velocity of fluid, the pulsating amplitude of the velocity and the exciting amplitude of harmonic motion on the dynamics of pipe were discussed emphatically. The result shows that the pipe may undergo periodic and chaotic motions around different equilibrium in certain parameter regions, and two routes to chaos via periodic doubling and intermittent chaos respectively in this system are found out.