横向受迫超临界输液管道的振动分析

Transverse Forced Vibrations Analysis of Pipes Conveying Fluid in the Supercritical Regime

当输液管道内流体的速度超过临界流速时,管道的静平衡位形会发生屈曲变形,形成一组对称的非零静平衡解。通过坐标变换,可以确定横向受迫管道关于非零静平衡解的扰动方程。通过迦辽金截断方法使系统变为标准的有限维离散陀螺系统。运用离散多尺度方法以及陀螺系统的可解性条件,获得关于横向弱受迫主共振的幅值与相角方程,从而建立振动幅值频率的调谐关系。通过给出超临界条件下的输液管道的数值算例,研究各种参数对前两阶主共振的幅值的影响。此外,研究结果还表明离散多尺度方法适用于分析超临界问题。

When the flow speed is larger than the critical value, the equilibrium configuration bifurcate into two possible curved equilibrium configurations. The main emphasis is placed on the vibration analysis of the pipes conveying fluid with forced excitation around each bifurcated equilibrium. The disturbance equa- tion is derived from the governing equation via a coordinate transform. The equation is cast in the stand- ard form of a gyroscopic system via the Galerkin method. The set of first-order ordinary differential equa- tions governing the modulation is derived by multi-scales lustrating the influence of the parameters. method. The dynamical behavior is observed illustrating the influence of the parameters.