This work provides comparative modeling approaches to determine the velocities and frequencies of various bioinspired plunge-diving systems. A nonlinear reduced-order model is developed and utilized to analyze the dive at impact considering both Timoshenko and Euler-Bernoulli beam theories. Using Hamilton's principle, the equations of motion are first derived. Then, static and dynamic buckling analyses are conducted. For this study, a geometrically simplified cone-beam system is considered, where the cone represents the head and the beam represents both the neck and body of the plunge-diving systems. The first study is to analyze the effects different diving drone materials and cone dimensions play on the sensitivity of the system. The second study applies real bird parameters to the cone-beam system, namely, a plunge-diving bird (Northern gannet) and a surface-diving bird (Double-crested cormorant). The results show that choosing a material with a higher Young's modulus and a cone with a smaller half angle delay the velocity at which buckling occurs. The buckling velocities of the predicted Northern gannet model reveal to be much greater than the average recorded diving speeds, validating the bird's ability to plunge-dive. The natural frequencies are found for various plunge-diving systems to predict failure if any external frequencies are known to act on the system while on a mission, i.e. climate or environment conditions. It is shown in all buckling studies that the Euler-Bernoulli beam theory consistently overestimates the responses when compared with the Timoshenko beam theory. In the dynamic responses, Euler-Bernoulli beam theory overestimates for the pre-buckling region, then underestimates at the start of the post-buckling region until a point where the two theories cross paths. The amount of error with Euler-Bernoulli beam theory depends greatly on the slenderness ratio of the beam due to the theory being a simplification of the Timoshenko beam theory.

中文翻译：

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潜水启发系统进入水中时的屈曲和动力学研究。

这项工作提供了比较建模方法，以确定各种生物启发式跳水潜水系统的速度和频率。建立了非线性降阶模型，并利用Timoshenko和Euler-Bernoulli梁理论来分析冲击下的俯冲。使用汉密尔顿原理，首先导出运动方程。然后，进行静态和动态屈曲分析。对于本研究，考虑了几何简化的锥束系统，其中锥代表跳水潜水系统的头部，而射束代表跳水潜水系统的颈部和身体。第一项研究是分析不同潜水无人机材料和锥体尺寸对系统灵敏度的影响。第二项研究将实鸟参数应用于锥束系统，即 跳水跳水的鸟（北塘鹅）和跳水跳水的鸟（双冠cor）。结果表明，选择具有较高杨氏模量的材料和具有较小半角的圆锥体会延迟屈曲的速度。预测的北塘鹅模型的屈曲速度显示出比记录的平均潜水速度大得多，这证明了鸟类的跳水潜水能力。如果已知有任何外部频率在执行任务（例如气候或环境条件）时会作用于系统，则可以为各种跳水潜水系统找到固有频率，以预测故障。在所有屈曲研究中都表明，与Timoshenko束理论相比，Euler-Bernoulli束理论始终高估了响应。在动态响应中，欧拉-伯努利梁理论高估了前屈曲区域，然后低估了后屈曲区域的开始，直到两个理论交叉的点。Euler-Bernoulli光束理论的误差量在很大程度上取决于光束的细长比，因为该理论是对Timoshenko光束理论的简化。