弹性地基上分布随从力作用下含裂纹输流管道的稳定性

Stability of Cracked Fluid-conveying Pipeline on Elastic Foundation Under Distributed Follower Forces

将分布随从力、winker地基等效刚度k作为输流管道运动微分方程新增参数纳入考虑,新的振动微分方程由此产生,离散并且求解采用Galerkin法。频率特征值源于频率扫描(frequency scanning)及传递弯矩法。具体分析了在考虑分布随从力(跟随力),裂纹存于管跨上不同位置、不同大小弹性地基刚度支承管道时,其失稳形式的变化。研究显示弹性地基存在对保持含裂纹管道的稳定性起部分作用,需重视裂纹开口深度及裂纹所处管跨位置对管道稳定性的影响。

The differential equation of fluid-conveying pipes considering distributed follower force and elastic foundation is established. The equation is discreted and solved by Galer- kin method and the frequency characteristic values are solved by bending moment transfer method. The effects of crack location and elastic foundation stiffness to the form of instabili- ty of the pipes under the distributed follower force are analyzed. Results show that the elas- tic foundation stiffness can enforce the stability of the pipes effectively, and the effects are more obvious when the crack location is closer to the middle of the pipe.