(1. 北京科技大學 土木與資源工程學院，北京 100083；
2. 北京科技大學 金屬礦山高效開采與安全教育部重點實驗室，北京 100083)
摘 要: 充填管路末端水平管段的振動會極大地影響充填效果和充填效率，針對這一問題，為探究管道振動狀態(tài)隨管內膏體平均流速變化的規(guī)律，結合現(xiàn)場實際，構建管道振動分析模型，建立了水平輸送管段的三維非線性振動控制方程組。采用伽遼金法和Runge-Kutta法進行數(shù)值求解，得到了輸送管道自由端的動力學響應，并通過時間歷程圖、分岔圖、相平面圖和運動軌跡圖進行呈現(xiàn)。結果表明：管內膏體無量綱流速uf在增大的過程中存在一個臨界流速ucr，且兩個方向上的臨界流速不同，η1方向上ucr=10.55，η2方向上ucr=0.001。當uf＜ucr時，管道最終會穩(wěn)定下來；當uf＞ucr，管道自由端會發(fā)生顫振失穩(wěn)，其運動形式表現(xiàn)為周期振動和概周期振動，且隨著uf的增大，管道的振動幅度也會不斷增大。
關鍵字: 膏體輸送；管道三維振動；非線性；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
