分析弹性支承输流管道的失稳临界流速

研究了两端弹性支承输流管道静态失稳和动态失稳临界流速. 根据梁模型横向弯曲振动模态 函数，由两端弹性支承的边界条件得到了其模态函数的一般表达式. 根据特征方程具体分析 了弹性支承刚度、质量比、流体压力和管截面轴向力等主要参数对失稳临界流速的影响. 数 值计算结果表明，管道在弹性支承下的动力稳定性比较复杂，在较小的弹性支承刚度和较小 的参数范围内，管道主要表现为动态颤振失稳；在较大的弹性支承刚度和较大的参数作用下， 管道的失稳形式主要表现为静态失稳；并且失稳临界流速随流体压力和管截面轴向压力的增 加而下降，随管截面轴向拉力的增加而上升.

Analysis of Critical Instability Flowrate of Pipeline Conveying Fluid with Elastic Supports

The dynamic stability of pipes conveying fluid with both ends supported elastically is investigated. The vertical vibration modal function of pipeline supported elastically on two ends is derived from the boundary condition of the elastic supported beam.The effect of supporting elastic coefficient,mass ratio,fluid pressure and axial force on critical instability flowrate is calculated and analyzed based on the eigenequation.The numerical results show that the stability of pipe is complicated because the dynamic stability varies with different elastic supporting coefficients and parameters acting on the pipe.Dynamic flutter instability will occur with a certain low elastic coefficient and in some parameter ranges and the static instability will happen under a high elastic coefficient and high parameters acting on the pipe.The critical instability flowrate is proportional conversely to fluid pressure and axial compression force of pipe section,but is proportional to the axial tensile force.