@ARTICLE{Sobota_Jerzy_Dynamic_2021,
 author={Sobota, Jerzy and Jianxin, Xia and Kirichenko, Evgeniy},
 volume={vol. 66},
 number={No 3},
 journal={Archives of Mining Sciences},
 pages={385-392},
 howpublished={online},
 year={2021},
 publisher={Committee of Mining PAS},
 abstract={The transport pipeline of lifting the underwater minerals to the surface of the water onto the ship during the movement of the vessel takes in the water a curved deformed shape. Analysis of the state of stability of the pipeline showed that if the flow velocity of fluid in the pipeline exceeds a certain critical value Vkr, then its small random deviations from the equilibrium position may develop into deviations of large amplitude. The cause of instability is the presence of the centrifugal force of the moving fluid mass, which occurs in places of curvature of the axis of the pipeline and seeks to increase this curvature when the ends of the pipeline are fixed. When the critical flow velocity is reached, the internal force factors become unable to compensate for the action of centrifugal force, as a result of that a loss of stability occurs. Equations describing this dynamic state of the pipeline are presented in the article.},
 type={Article},
 title={Dynamic States Equations of Transport Pipeline in Deep-Sea Mining},
 URL={http://journals.pan.pl/Content/120846/Archiwum-66-3-04-Sobota.pdf},
 doi={10.24425/ams.2021.138595},
 keywords={deep-sea mining, vertical pipelines, stability of deep-sea pipelines},
}