两端铰支输流管道在脉动内流作用下的稳定性和参数共振

Stability and Parametric Resonances of a Pinned-Pinned Pipe Conveying Pulsating Fluid

研究了两端铰支输流管道在脉动内流作用下的参数共振问题。用平均法导出了失稳判据和 3种参数共振区域的边界曲线方程 ,并据此讨论了系统参数对不稳定区域的影响。用数值方法分析了各种参数共振的响应曲线 ,其存在区域以及响应频率与脉动流频率之间的关系。研究结果发现 ,组合共振区域内发生两种不同的拟周期运动和组合周期运动 ,而且第 1振型次谐波共振曲线延伸到组合共振区域。因此 ,在同一脉动频率下存在可发生多种不同运动 (第 1振型次谐波振动、拟周期振动和组合周期振动等 )

This paper deals with the stability and parametric resonances of a pinned-pinned pipe conveying pulsating fluid. The stability criterion of the pipe is derived with the method of averaging. According to the criterion, the effect of the physical parameters of the system on the regions of three parametric resonances has been discussed. The amplitude-frequency response curves and their frequency properties of the parametric resonances are investigated by using the method of numerical analysis. The results obtained show that several motions may occur in the region of combination resonance, including two kinds of quasi-periodic vibrations and combined periodic motion. Since the subharmonic resonance curve of the first mode extends as far as the region of combination resonance, there are some parameter regions in which several motions including the first mode subharmonic vibration, quasi-periodic vibration and combined periodic motion may occur corresponding to the same frequency of the pulsating flow.