In this paper, the 5000 m mining pipe is taken as the research object, and the transverse and longitudinal vibration laws of the pipe under different working conditions are analyzed. Based on the finite element method (FEM), the pipe is discretized and calculated by the Wilson-θ integral method; finally, the corresponding vibration laws of the mining pipe are obtained. The research shows that the mining pipe vibration responses are irregular motion, with the obvious oscillation phenomenon, and the overall vibration trend decreases first and then increases from the top to the bottom; the maximum vibration response occurs at the pipe top. Under the same working conditions, increasing the towing velocity will decrease the overall longitudinal vibration amplitude and increase the overall transverse vibration amplitude. While the ore bin weight will increase the longitudinal vibration amplitude and decrease the transverse vibration amplitude, increasing the mining pipe large diameter stepped section length and damping will decrease the longitudinal and transverse vibration simultaneously. When the towing velocity is between 0–2.8 m/s, the longitudinal vibration intensity is large, which is the main vibration mode. When the towing velocity is 2.8 m/s, the critical point is reached, and the longitudinal and transverse vibrations have the same intensity. When the towing velocity is greater than 2.8 m/s, the transverse vibration intensity is gradually greater than the longitudinal vibration intensity; at this time, the control of the transverse vibration should be appropriately increased.

中文翻译：

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远洋采矿管纵横向振动特性对比分析

本文以5000 m矿管为研究对象，分析了不同工况下矿管的横向和纵向振动规律。基于有限元法（FEM），通过Wilson- θ对管道进行离散化计算积分法；最终得到相应的矿管振动规律。研究表明，矿管振动响应为不规则运动，振荡现象明显，整体振动趋势自上而下先减小后增大；最大的振动响应发生在管道顶部。在相同工况下，增加拖曳速度会降低整体纵向振幅，增加整体横向振幅。而矿仓重量会增加纵向振动幅值并减小横向振动幅值，而增加矿管大直径阶梯段长度和阻尼会同时减小纵向和横向振动。拖曳速度在0~2.8 m/s之间时，纵向振动强度大，是主要的振动模式。当牵引速度为2.8 m/s时，达到临界点，纵向和横向振动强度相同。当拖曳速度大于2.8 m/s时，横向振动强度逐渐大于纵向振动强度；此时应适当加大对横向振动的控制。横向振动强度逐渐大于纵向振动强度；此时应适当加大对横向振动的控制。横向振动强度逐渐大于纵向振动强度；此时应适当加大对横向振动的控制。