Response regimes in equivalent mechanical model of moderately nonlinear liquid sloshing

摘要

The paper considers stationary and nonstationary responses in reduced-order model (ROM) of partially liquid-filled tank under external forcing. The model involves one common degree of freedom for the tank and the non-sloshing portion of the liquid, and the other one-for the sloshing portion of the liquid. The coupling between these degrees of freedom is nonlinear, with the lowest-order potential dictated by symmetry considerations. Since the mass of the sloshing liquid in realistic conditions does not exceed 10% of the total mass of the system, the ROM turns to be formally equivalent to well-studied oscillatory systems with nonlinear energy sinks (NES). Exploiting this analogy, and applying the methodology known from the studies of the systems with NES, we predict a multitude of possible nonstationary responses in the considered ROM. These responses conform, at least on the qualitative level, to the responses observed in experimental sloshing settings, multimodal theoretical models and full-scale numeric simulations.