Asymptotic nonlinear multimodal method for liquid sloshing in an upright circular cylindrical tank. Part 1: Modal equations

Combining the variational method by Lukovsky – Miles and the Narimanov – Moiseev asymptotics, a nonlinear modal system describing the resonant liquid sloshing in an upright circular cylindrical tank is derived. Sloshing occurs due to a small-amplitude periodic or almost-periodic excitation with the...

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Збережено в:
Бібліографічні деталі
Дата:2011
Автори: Lukovsky, I., Ovchynnykov, D., Timokha, A.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2011
Назва видання:Нелінійні коливання
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/175504
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Asymptotic nonlinear multimodal method for liquid sloshing in an upright circular cylindrical tank. Part 1: Modal equations / I. Lukovsky, D. Ovchynnykov, A. Timokha // Нелінійні коливання. — 2011. — Т. 14, № 4. — С. 482-495. — Бібліогр.: 41 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Резюме:Combining the variational method by Lukovsky – Miles and the Narimanov – Moiseev asymptotics, a nonlinear modal system describing the resonant liquid sloshing in an upright circular cylindrical tank is derived. Sloshing occurs due to a small-amplitude periodic or almost-periodic excitation with the forcing frequency close to the lowest natural sloshing frequency. In contrast to the existing nonlinear modal systems based on the Narimanov – Moiseev asymptotic intermodal relationships, the derived modal equations: (i) contain all the necessary (infinitely many) generalized coordinates of the second and the third orders, (ii) include exclusively nonzero hydrodynamic coefficients for which (iii) rather simple computational formulas are found. As a consequence, the modal equations can be used in analytical studies of nonlinear sloshing phenomena that will be demonstrated in the forthcoming Part 2.