The coupled motion of shallow-water sloshing in a horizontally translating upright annular vessel is considered. The vessel’s motion is restricted to a single space dimension, such as for Tuned Liquid Damper systems. For particular parameters, the system is shown to support an internal 1 : 1 resonance, where the frequency of coupled sloshing mode which generates the vessel’s motion is equal to the frequency of a sloshing mode which occurs in a static vessel. Using a Lagrangian Particle Path formation, the fully nonlinear motion of the system is simulated using an efficient numerical symplectic integration scheme. The scheme is based on the implicit-midpoint rule which conserves energy and preserves the energy partition between the fluid and the vessel over many time-steps. Linear and nonlinear results are presented, including those showing the system transitioning to higher-frequency eigenmodes as the fluid depth is reduced.

中文翻译：

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耦合浅水流体在直立环形容器中的晃动

考虑了水平平移直立环形船中浅水晃荡的耦合运动。容器的运动仅限于单个空间维度，例如调谐液体阻尼器系统。对于特定参数，系统显示支持内部 1:1 共振，其中产生船舶运动的耦合晃动模式的频率等于发生在静态船舶中的晃动模式的频率。使用拉格朗日粒子路径形成，使用有效的数值辛积分方案模拟系统的完全非线性运动。该方案基于隐式中点规则，该规则保存能量并在许多时间步长内保持流体和容器之间的能量分配。呈现线性和非线性结果，