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Article information
2015 , Volume 20, ¹ 2, p.79-90
Cherdantsev S.V., Cherdantsev N.V.
Analysis of the mathematical model for stability of a pontoon in process of the vertically-lateral fluctuations in the sump of an open coal mine
Sumps in the soil faces are constructed to prevent flooding of coal mines faces by ground and underground water. As sump is filled with water, water is then pumped out, to do that a floating dewatering plants are placed directly to the sump. They float with the help of pontoons equipped with the drainage equipment. Safe operation of the pontoons on the cuts can be achieved by correctly calculating their buoyancy, static stability and sustainable modes of motion. Buoyancy and static stability has been discussed by the authors in a number of papers, and sustainable modes of motion was only partially discussed. In particular, a number of works of authors demonstrated that different modes of movement of the pontoon can be identified as part of the solution of the Cauchy problem for a system of ordinary differential equations of the 2nd order with constant coefficients that describe the vertical, lateral and pitching pontoon occurring independently of each other. In this article, we found that if a heave pontoon gets a small roll, it will start to make side and lateral pitching. These motions are independent of each other. The authors showed that the joint vertical lateral pitching can be described by a differential equation of the 2nd order with variable coefficients (Mathieu equation), depending on the ratio of the natural frequencies of the two types of pitching and the characteristics of the buoyancy of the pontoon on the “calm water”. The most significant results of this paper the authors are as follows: - graphs and relations between parameters of the pontoon and variable coefficients Mathieu equation; - we found that under the assumption of small amplitude, heave motion of all pontoons with the sizes considered in this paper are stable under the vertical side pitching.
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Keywords: pontoon, floatability, metacentric height, added masses of liquid, vertical and lateral pitching pontoon, Mathieu equation, stability diagram Ince - Strutt
Author(s):
Cherdantsev Sergey Vasilievich
Dr. , Associate Professor
Position: Professor
Office: T.F. Gorbachev Kuzbass State Technical University
Address: 650000, Russia, Kemerovo, ul. Vesennyaya 28
Phone Office: (3842) 39 69 55
E-mail: svch01@yandex.ru
Cherdantsev Nikolay Vasilievich
Dr. , Associate Professor
Position: Head of Laboratory
Office: Institute of Coal Siberian branch to Russian Academy of the Sciences
Address: 650065, Russia, Kemerovo, Leningrad avenue, 10
Phone Office: (3842) 39 69 55
E-mail: nvch2014@yandex.ru
References:
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Bibliography link:
Cherdantsev S.V., Cherdantsev N.V. Analysis of the mathematical model for stability of a pontoon in process of the vertically-lateral fluctuations in the sump of an open coal mine // Computational technologies. 2015. V. 20. ¹ 2. P. 79-90
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