输流管道在分布随从力作用下的振动和稳定性

VIBRATION AND STABILITY OF PIPES CONVEYING FLUID WITH DISTRIBUTED FOLLOWER FORCE

以Pflüger柱模型和普通输流管道模型为基础,建立了在流动流体和分布随从力共同作用下管道的运动微分方程,并采用Galerkin法进行离散。通过特征值分析,得到了发生发散失稳的临界流速计算公式,以及不同参数下系统复频率随流速的变化曲线。通过Runge-Kutta数值积分法对离散方程组求解,得到了不同参数下管道的位移时程曲线和相图。计算结果表明:分布随从力作用下输流管道发生发散失稳的无量纲临界流速与质量比无关,发生颤振失稳的无量纲临界流速随质量比的增大略微提高;随着分布随从力的增大,发生发散失稳和颤振失稳的临界流速均明显降低;随着质量比的增大,发生发散失稳时管道的位移随时间增加变快,流致振动的振幅增大。在无分布随从力作用和不考虑流体流动两种特殊情况下,所得结果与已有研究一致。

Based on Pfliiger column model and that of a fluid-conveying pipe, the dynamic differential equation for pipes under co-action of distributed follower force and flowing fluid is established, which is then discretized with Galerkin method. By analyzing its eigenvalues, a formula is derived for calculating the critical flow velocity for divergence, and the complex frequencies versus the flow velocity are obtained for different parameters. By solving the discretized equations with Runge-Kutta numerical integration, the displacement time-history and the phase diagrams of the pipes are given for different parameters. The numerical results show that： the dimensionless critical flow velocities for divergence for pipes conveying fluid with distributed follower force are irrelevant to the mass-ratio, and those for flutter increase slightly with increasing mass-ratio; the critical flow velocities for both divergence and flutter decrease notably as the distributed follower force increases; with increasing mass-ratio, the increase-rate of the displacement of pipes in divergence and the amplitude of fluid-induced vibration increase. In the absence of distributed follower force or of flowing fluid, the results are in good agreement with known ones.