# Asymptotic nonlinear multimodal modeling of liquid sloshing in an upright circular cylindrical tank. I. Modal equations

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Combining 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 small-amplitude periodic or an almost-periodic 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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