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

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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Main Authors: Lukovsky, I., Ovchynnykov, D., Timokha, A.
Format: Article
Language:English
Published: Інститут математики НАН України 2011
Series:Нелінійні коливання
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/175504
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spelling irk-123456789-1755042021-02-02T01:28:25Z Asymptotic nonlinear multimodal method for liquid sloshing in an upright circular cylindrical tank. Part 1: Modal equations Lukovsky, I. Ovchynnykov, D. Timokha, A. 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. Комбiнуючи варiацiйний метод Луковського – Майлса та асимптотику Нарiманова – Моiсеєва, побудовано нелiнiйну модальну систему, що описує резонанснi коливання рiдини у вертикальному круговому цилiндричному резервуарi. Коливання вiдбуваються завдяки перiодичному чи майже перiодичному збуренню з частотою, близькою до першої власної частоти. На вiдмiну вiд iснуючих нелiнiйних модальних систем, якi базуються на асимптотичних спiввiдношеннях Нарiманова – Моiсеєва, побудованi модальнi рiвняння: (i) включають всi необхiднi (нескiнченну кiлькiсть) узагальненi координати другого та третього порядку, (ii) утримують винятково ненульовi гiдродинамiчнi коефiцiєнти, для яких (iii) знайдено достатньо простi обчислювальнi формули. Як наслiдок, модальнi рiвняння можна використати в аналiтичних дослiдженнях нелiнiйних явищ, що буде продемонстровано в наступнiй частинi 2. 2011 Article 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. 1562-3076 http://dspace.nbuv.gov.ua/handle/123456789/175504 517.9 en Нелінійні коливання Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description 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.
format Article
author Lukovsky, I.
Ovchynnykov, D.
Timokha, A.
spellingShingle Lukovsky, I.
Ovchynnykov, D.
Timokha, A.
Asymptotic nonlinear multimodal method for liquid sloshing in an upright circular cylindrical tank. Part 1: Modal equations
Нелінійні коливання
author_facet Lukovsky, I.
Ovchynnykov, D.
Timokha, A.
author_sort Lukovsky, I.
title Asymptotic nonlinear multimodal method for liquid sloshing in an upright circular cylindrical tank. Part 1: Modal equations
title_short Asymptotic nonlinear multimodal method for liquid sloshing in an upright circular cylindrical tank. Part 1: Modal equations
title_full Asymptotic nonlinear multimodal method for liquid sloshing in an upright circular cylindrical tank. Part 1: Modal equations
title_fullStr Asymptotic nonlinear multimodal method for liquid sloshing in an upright circular cylindrical tank. Part 1: Modal equations
title_full_unstemmed Asymptotic nonlinear multimodal method for liquid sloshing in an upright circular cylindrical tank. Part 1: Modal equations
title_sort asymptotic nonlinear multimodal method for liquid sloshing in an upright circular cylindrical tank. part 1: modal equations
publisher Інститут математики НАН України
publishDate 2011
url http://dspace.nbuv.gov.ua/handle/123456789/175504
citation_txt 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.
series Нелінійні коливання
work_keys_str_mv AT lukovskyi asymptoticnonlinearmultimodalmethodforliquidsloshinginanuprightcircularcylindricaltankpart1modalequations
AT ovchynnykovd asymptoticnonlinearmultimodalmethodforliquidsloshinginanuprightcircularcylindricaltankpart1modalequations
AT timokhaa asymptoticnonlinearmultimodalmethodforliquidsloshinginanuprightcircularcylindricaltankpart1modalequations
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last_indexed 2023-10-18T22:39:02Z
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