(1. 北京科技大学 土木与资源工程学院，北京 100083；
2. 北京科技大学 金属矿山高效开采与安全教育部重点实验室，北京 100083)
摘 要: 充填管路末端水平管段的振动会极大地影响充填效果和充填效率，针对这一问题，为探究管道振动状态随管内膏体平均流速变化的规律，结合现场实际，构建管道振动分析模型，建立了水平输送管段的三维非线性振动控制方程组。采用伽辽金法和Runge-Kutta法进行数值求解，得到了输送管道自由端的动力学响应，并通过时间历程图、分岔图、相平面图和运动轨迹图进行呈现。结果表明：管内膏体无量纲流速uf在增大的过程中存在一个临界流速ucr，且两个方向上的临界流速不同，η1方向上ucr=10.55，η2方向上ucr=0.001。当uf＜ucr时，管道最终会稳定下来；当uf＞ucr，管道自由端会发生颤振失稳，其运动形式表现为周期振动和概周期振动，且随着uf的增大，管道的振动幅度也会不断增大。
关键字: 膏体输送；管道三维振动；非线性；平均流速
（1. School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China;
2. State Key Laboratory of High-Efficient Mining and Safety of Metal Mines, Ministry of Education, University of Science and Technology Beijing, Beijing 100083, China）
Abstract:In the process of paste-filling, the violent vibration of the horizontal pipeline conveying paste close to paste-filling area tends to affect the effect of filling and efficiency greatly. To investigate the effect of paste average flow velocity on vibration, the analysis model was obtained for the horizontal pipeline conveying paste according to the actual condition on site. Based on this, the governing equations for nonlinear three-dimensional dynamics were deduced. By the Galerkin discretization and the Runge-Kutta algorithm, the equations were solved numerically and the dynamic responses of free-end which were presented by time trace, bifurcation diagram, phase-plane diagram and oscillation trajectories were obtained. The numerical results show that there is a critical flow velocity which is different in two dimensions when non-dimensional velocity of paste uf increases, and ucr is 10.55 in η1, ucr is 0.001 in η2. It also shows that the pipe is stable as uf＜ucr. When uf＞ucr, the pipe loses stability via flutter, meanwhile, the period and quasi-period vibration are observed. Moreover, the amplitude of vibration increases as uf increases.
Key words: paste transportation; three-dimensional vibration of pipeline; nonlinear; average flow velocity
