两端固定输流管道的稳定性和参数共振

研究了两端固定输流管道在脉动内流作用下的参数共振问题。用平均法导出了管道失稳判据和三种参数共振区域的边界曲线方程，讨论了系统参数对失稳区域的影响。用数值方法给出了各种参数共振的响应曲线，分析了其存在区域以及响应频率与脉动流频率之间的关系。研究结果表明，组合共振区域内可发生拟周期运动和组合周期运动；组合共振曲线能延伸到第二振型次谐波共振区域；第一振型次谐波共振曲线能覆盖整个组合共振区域，而且能延伸到第二振型次谐波共振区域。因此，此系统存在同一个脉动频率与多种运动相对应的参数区域。

Stability and Parametric Resonances of a Clamped-Clamped Pipe Conveying Fluid

This paper deals with the stability and parametric resonances of a clamped-clamped pipe conveying pulsating fluid. A criterion of the stability 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 regons of three parametic resonances has been discussed. The amplitude-frequency response curves and the frequency properties of the parametric resonances are investigated by using the method of numerical analysis. The results obtained show that the quasi-periodic and combined periodic motions may occur in the region of combination resonance. Since the subharmonic resonance curve of the first mode and the combination resonance curve extend as far as the region of the second mode resonance, there are some parameter regions in which several motions may occur corresponding to the same frequency of the pulsating flow.