本文首先建立了非线性弹性地基上悬臂输流管在振荡流作用下的运动方程，应用Galerkin方法将运动控制偏微分方程离散成常微分方程组。采用数值方法着重讨论了平均流速、脉动幅值、脉动频率和地基剪切刚度等参数对系统动力学行为的影响。 结果表明：以平均流速为分岔参数系统会出现拟周期运动，然后是周期运动， 接着出现混沌运动；以脉动幅值为分岔参数系统发生周期2，周期4，周期8，然后进入混沌运动；以脉动频率为分岔参数系统先发生拟周期运动，然后在二阶次谐波附近发生混沌运动。另外，地基剪切刚度对系统地周期运动和混沌有抑制作用，随着剪切刚度增大，系统从混沌状态演化到周期状态，直至稳态。
Abstract
The motion equation of cantilevered pipe conveying pulsating fluid on the nonlinear el-
astic foundation is constructed, and is discretized into ordinary differential equations by the Galerkin method. The effect of parameters including mean flow velocity, fluctuation amplitude, fluctuation frequency and shear stiffness on the nonlinear behavior of system is discussed by the numerical method. The results show that by mean flow velocity as the bifurcation parameter the system can present quasi periodic motion, periodic motion, and chaotic motion; by fluctuation amplitude as bifurcation parameter the system presents the period-2, period-4, period-8, and chaotic motion; by fluctuation frequency as bifurcation parameter the system firstly shows quasi-periodic motion, then chaotic motion nearby second sub harmonic. Furthermore, foundation shear stiffness can suppress the period motion and chaotic motion of system. With shear stiffness increasing, chaos state of system gradually changed into periodic motion until the stable state is obtained.
关键词
悬臂输流管 /
弹性地基 /
周期运动 /
混沌运动
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Key words
cantilevered pipe conveying fluid /
elastic foundation /
period motion /
chaotic motion
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