AI 中文总结
研究旋转弹性盘在粘性流体中的弹流动力学不稳定性，结合线性化方程与剪应力导出稳定性问题，经线性稳定性分析，通过无量纲参数确定屈曲起始，发现盘屈曲模式及逆行行波，揭示流体剪切使旋转弹性结构失稳的机制。
AI 中文摘要
在粘性流体中旋转的柔软薄弹性盘，会经历由旋转产生的离心张力以及周围流动产生的粘性剪切力。离心张力使盘的扁平状态稳定，而粘性剪切力则可能使其失稳。我们将旋转弹性盘的线性化Föppl-von Kármán方程与经典von Kármán涡旋流产生的剪应力相结合，推导出一个弹流动力学稳定性问题。线性稳定性分析通过两个无量纲控制参数确定屈曲的起始，这两个参数衡量离心加强和流体诱导剪切。超过阈值时，盘屈曲成方位角周期性的鞍状模式，其波数随旋转张力增加而增加。屈曲构型还支持比物质框架旋转更慢的逆行行波。这些结果确定了一种流体剪切使旋转弹性结构失稳的简单机制。
英文摘要
A soft thin elastic disk spinning in a viscous fluid experiences centrifugal tension generated by rotation together with viscous shear generated by the surrounding flow. While the former stabilizes the flat state, the latter can destabilize it. We combine the linearized Föppl-von Kármán equations for a rotating elastic disk with the shear stresses arising from the classical von Kármán swirling flow to derive an elastohydrodynamic stability problem. Linear stability analysis identifies the onset of buckling in terms of two dimensionless control parameters measuring centrifugal stiffening and fluid-induced shear. Above threshold the disk buckles into azimuthally periodic saddle-like modes whose wavenumber increases with increasing rotational tension. The buckled configuration also supports retrograde traveling waves that rotate more slowly than the material frame. These results identify a simple mechanism whereby fluid shear destabilizes rotating elastic structures.
Comments8 pages, 4 figures
