Asymptotic nonlinear multimodal method for liquid sloshing in an upright circular cylindrical tank. Part 1: Modal equations - Lukovsky, I.; Ovchynnykov, D.; Timokha, A. (Нелінійні коливання, 2011)
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.