Surface tension effects on fluid sloshing in a tank subjected to external excitation has been less studied. This work aims at understanding this phenomenon in order to derive practical solutions to problems faced in several engineering. A tank containing a fluid with a free surface is submitted to gravity and capillary forces and subject to external dynamic excitation. Introduction of vertical sinusoidal dynamical excitation leads to a problem of paramtric oscillations governed by the Mathieu equation. Analysis of the Mathieu equation shows the existence of stable and unstable regions in the stability diagram. Some results induced by harmonic excitations on the fluid sloshing are presented. When the external dynamical excitation amplitude ε is small, periodic solutions appear in stable regions and when ε increases, the fluid behavior is not perfectly periodic and the amplitudes are not regular. Nonlinear effects make the behavior of the fluid complicated and render it almost unpredictable. In stable regions, the solution remains bounded at any time. When changing the perturbation parameter ε, the phase difference increases and also with the increase of the surface tension.

中文翻译：

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毛细作用对正弦垂直动力激励下矩形容器中流体的晃动

表面张力对受外部激励作用的储罐中流体晃荡的影响研究较少。这项工作旨在了解这种现象，以便为几种工程中面临的问题提供切实可行的解决方案。装有自由表面流体的储罐会受到重力和毛细作用力的作用，并受到外部动力的激励。垂直正弦动态激励的引入导致由Mathieu方程控制的参数振动问题。对Mathieu方程的分析显示，稳定性图中存在稳定和不稳定区域。提出了由谐波激励引起的流体晃动的一些结果。当外部动力激励振幅ε小时，周期解出现在稳定区域中，而当ε增大时，流体行为不是完美的周期性，振幅也不规则。非线性效应使流体的行为变得复杂，并使流体几乎不可预测。在稳定区域中，解决方案随时都保持有界。当改变扰动参数ε时，相位差增加，并且也随着表面张力的增加而增加。