深海采矿扬矿管的纵向振动分析

为研究深海采矿系统扬矿管的纵向振动规律,通过振动理论建立了扬矿管的纵向振动的偏微分方程,并对该方程进行求解,得到了扬矿管的固有频率、振型函数以及振动响应函数的理论解。随后用MATLAB进行仿真,从扬矿管上选取3个不同位置,分别绘制了有阻尼系统响应和无阻尼系统响应时绝对位移与相对位移随时间的变化曲线。在此基础上,对扬矿管的轴向应力进行研究。结果表明:两种情况下,扬矿管振幅随着水深的增加而增加,在3 000 m以后的振动幅值变化很小,有阻尼系统响应的变化规律类似于简谐运动;且在扬矿管顶端,有阻尼系统响应时所受的轴向应力要比无阻尼时的轴向应力减少25.5%,在大部分时刻,轴向应力随着深度的增加而减少。

Longitudinal Vibrations Analysis of Lifting Pipe in Deep-sea Mining

This paper targets at the vertical vibration rule of the lifting pipe in deep sea mining system. In order to do the research, the partial differential equation is established according to theories of vibration mechanics. Then, based on the equation, the research gets the data of the natural frequency, the vibration mode function and response function of the pipe. Only data is not quite convincing. Thus, by using MATLAB, three positions from different water depth on the mining pipe were selected to do the following research, shaping evolving curves of the absolute displacement and the relative displacement with time. Based on these results, the study of the axial stress of the mining pipe shows that, with the damping or without, the amplitude of the pipe increases with the increase of water depth, but, under 3000m, the amplitude changes very little; and at the top of the pipe, he axial pressure under damping is less 25.5% than without damping. To sum up, in most cases, the axial stress decreases with the increase of water depth.