Analysis of the pontoon fluctuations with a seasonally changing parameter of stability on the astir surface of finite water depth
S. V. Cherdantsev1, N. V. Cherdantsev2
1Kuzbass State Technical University, Vesennaya str., 28, Kemerovo, 650026, Russia
2Institute of Coal, Siberian Branch of Russian Academy of Sciences, Leningradskii pr., 10, Kemerovo, 650065, Russia
Keywords: зумпф угольного разреза, понтон, потенциал скоростей, частота волн, ватерлиния, метацентрические высоты, присоединенные массы жидкости, параметрическая качка понтона, уравнение Матье, диаграмма Айнса-Стретта, sump of an open coal mine, pontoon, potential of the velocities, frequency of the waves, waterline, metacentric heights, added masses of liquid, parametric pitching pontoon, Mathieu equation, Inc-Strutt stability diagram
Abstract
It is shown that due to the periodic changes in metacentric heights of a pontoon on the astir surface of liquids in the sump of an open coal mine, the pontoon is capable to produce parametric pitching, both in the longitudinal and in the transverse directions. The equation, describing parametric pitching, is transformed to the Mathieu equation, whose factors depend both on the own frequencies and the pontoon floatability features on «calm water», and on the frequency of fluctuation of a liquid, which, in turn, is defined by the sump size. The installed regularities between parameters, characterizing parametric pitching in the longitudinal and transverse directions, and areas of its instability are revealed.
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