Abstract An experimental investigation is presented of an oscillating disk submerged in water. The system is adapted from one modeled by the Bagley-Torvik equation, being modified to more closely approximate idealizations in the derivation. The modified system eliminates alignment problems that would violate the assumption of fluid forces being due only to shear in the fluid. An implicit finite difference model based on the Riemann-Liouville fractional derivative was used to model the observed oscillatory free response resulting from a non-homogeneous initial condition. The numerical model accounted for motion well until the amplitude was small.

中文翻译：

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振动盘中分数阶行为的实验研究

摘要 对浸入水中的振动盘进行了实验研究。该系统改编自由 Bagley-Torvik 方程建模的系统，在推导过程中被修改为更接近理想化。修改后的系统消除了对齐问题，这些问题会违反流体力仅由流体中的剪切力的假设。基于 Riemann-Liouville 分数阶导数的隐式有限差分模型用于模拟由非均匀初始条件引起的观察到的振荡自由响应。数值模型很好地解释了运动，直到振幅很小。