中文摘要：

应用Galerkin法和复模态法研究Winkler弹性地基上两端铰支输流管道的临界流速问题。将系统偏微分控制方程进行Galerkin离散后,根据系统静态失稳条件求得临界流速,并利用复模态法对偏微分控制方程直接求解加以验证。结果表明：较低阶Galerkin法只适用于弱刚性地基情况,而当地基刚性比较强时,采用较高阶Galerkin法才能得到精确的结果。研究同时发现,临界流速只与地基刚度及管道轴向预紧力有关,而管道黏弹性系数及质量比等参数不会影响临界流速。

英文摘要：

Critical flow velocity of pinned-pinned pipes conveying fluid resting on Winkler foundation is investigated using the Galerkin and complex mode methods.After discretizing the governing equation with the Galerkin method,critical velocity is obtained in terms of the condition of divergence instability.Complex mode method is applied directly in the partial differential governing equation to validate the results.It is concluded that the lower-order Galerkin method is valid only for the case of weak-rigidity foundation.When the rigidity of the foundation is stronger,higher orders are needed for accurate results.It is also found that the critical velocity is always concerned with the foundation rigidity and the axial tension force,however the viscoelastic coefficient and mass ratio have no effect on it.