Asymptotic nonlinear multimodal modeling of liquid sloshing in an upright circular cylindrical tank. I. Modal equations
 I. Lukovsky,
 D. Ovchynnykov,
 A. Timokha
 … show all 3 hide
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Get AccessCombining the Lukovsky–Miles variational method and the Narimanov–Moiseev asymptotics, we deduce a nonlinear modal system describing the resonant liquid sloshing in an upright circular cylindrical tank. The sloshing occurs due to a smallamplitude periodic or an almostperiodic excitation with forcing frequency close to the lowest natural sloshing frequency. In contrast to the existing nonlinear modal systems based on the Narimanov–Moiseev asymptotic intermodal relations, the derived modal equations (i) contain all necessary (infinitely many) generalized coordinates of the second and third orders and (ii) include exclusively nonzero hydrodynamic coefficients, for which (iii) fairly simple computational formulas are found. As a consequence, the modal equations can be used in analytical studies of nonlinear sloshing phenomena, which will be demonstrated in the forthcoming Part II.
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 Title
 Asymptotic nonlinear multimodal modeling of liquid sloshing in an upright circular cylindrical tank. I. Modal equations
 Journal

Nonlinear Oscillations
Volume 14, Issue 4 , pp 512525
 Cover Date
 20120401
 DOI
 10.1007/s1107201201735
 Online ISSN
 15360059
 Publisher
 Springer US
 Additional Links
 Topics
 Authors

 I. Lukovsky ^{(1)}
 D. Ovchynnykov ^{(1)}
 A. Timokha ^{(1)}
 Author Affiliations

 1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine