I.O.Lukovsky, D.V.Ovchynnykov, O.M.Timokha A complete tree-order asymptotic nonlinear modal system describing the liquid sloshing in a vertical circular cylindrical tank |
Acoustic bulletin, Vol. 14 ¹ 2, (2011) |
| A nonlinear asymptotic modal system describing the resonant sloshing in a vertical circular cylindrical tank due to horizontal excitation with forcing frequencies close to the lowest natural sloshing frequency is derived using the variational modal method by Lukovsky and the Moiseev asymptotics. It couples the two dominant generalized coordinates responsible for two lowest natural modes (characterized by the same natural frequency), as well as infinite number of generalized coordinates of the second and third orders. The derived modal system is a generalization of existing nonlinear modal systems based on the Moiseev asymptotics including the classical five-mode Lukovsky system, since the above systems neglected the contribution of the higher natural modes of the second and third orders. For the model problem on the steady-state resonant sloshing regimes with a finite liquid depth, we demonstrate the effect of the higher natural modes on the response curves and show that consideration of these modes does not qualitatively change the frequency ranges and bifurcation points of the "planar" and "swirling" wave regimes, in comparison with the results by the five-mode Lukovsky system. Nevertheless, in frequency ranges where the steady-state regimes are unstable and one can expect for chaotic liquid motions, the secondary (internal) resonances may occur. Their existence indicates the necessity of revision of the Moiseev asymptotics. |
|
KEY WORDS: liquid sloshing in the tank, the Lukovsky variational method, the Moiseev asymptotics, modal system, nonlinearity |
| TEXT LANGUAGE: Ukrainian |