This work proposes a numerical investigation on the occurrence of parametric excitation in the classical Benjamin problem, when the support of the articulated chain of pipes is subjected to a prescribed oscillatory motion. Equations of motion for an articulated chain composed of two rigid pipes ejecting fluid are derived. Floquet theory is applied to the linearized mathematical model, and curves of instability as functions of the parametric excitation (amplitude and frequency) are obtained for selected internal flow velocities. In addition to the linear analysis, maps (showing the post-critical response as a function of some control parameters) are computed using numerical integrations of the nonlinear model. Among other findings, this paper reveals that the presence of the internal flow significantly affects the stability of the trivial solution. Furthermore, the concomitant parametric excitation and internal flow effects lead to maps of post-critical response with a marked erosion, i.e., small variations in the parameters of the mathematical model have significant effects in the observed response.

这项工作提出了一个关于经典本杰明问题中参数激励发生的数值研究，当铰接的管道链的支座受到规定的振荡运动时。推导了由两个喷射流体的刚性管组成的铰接链的运动方程。将浮球理论应用于线性数学模型，并针对选定的内部流速获得了不稳定性随参数激励函数（振幅和频率）变化的曲线。除了线性分析之外，还使用非线性模型的数值积分来计算映射图（显示临界后响应作为某些控制参数的函数）。除其他发现外，本文还揭示了内部流动的存在会显着影响琐碎溶液的稳定性。