发表机构
University of Michigan（密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文建立二维不可压缩流中可扩展膜的涡脱落模型，发现柔顺性增强启动升力但放大振荡，并揭示张力消失导致的奇异极限与从周期到混沌颤振的转变。
AI 中文摘要
我们开发了一个二维不可压缩模型，用于描述从两个边缘连续脱落涡旋的可扩展膜，该模型与膜方程的弱谱伽辽金离散化耦合，允许在零弯曲刚度下直接计算。将压力跳跃视为束缚涡量的通量，解释了膜如何响应集中的流体载荷。对于固定-固定膜，柔顺性使物体朝向领先边缘涡旋移动，延迟其脱离，并主要在启动阶段增强升力；在周期性脱落发展后，柔顺性主要放大力的振荡而非平均升力。涡旋脱离可以将重载膜卸载至压缩状态，产生弯曲正则化的褶皱。对于$R_2>0$，只要膜保持为浸入，膜方程在张力符号无关的情况下保持适定。释放后缘会产生内在的退化：张力在自由端点消失，使得$R_2=0$问题在形式上欠定，而弱公式选择其有界能量分支。这种张力消失端点捕获压力扰动并驱动快速的尖端弹击；主频率和有效波数接近其零刚度极限，并带有来自奇异贝塞尔分支的逆对数修正。最后，降低拉伸模量会使周期性颤振失稳，反复的流体驱动脱离和弹性返回表明存在同宿缠结，这是从周期性颤振过渡到混沌颤振的基础。
英文摘要
We develop a two-dimensional inviscid model for extensible membranes with continuous vortex shedding from both edges, coupled to a weak spectral Galerkin discretization of the membrane equation that permits direct computation at zero bending rigidity. Viewing the pressure jump as a flux for bound vorticity explains how membranes respond to concentrated fluid loading. For fixed-fixed membranes, compliance draws the body toward the leading-edge vortex, delaying its detachment and enhancing lift primarily during start-up; after periodic shedding develops, compliance mainly amplifies the force oscillations rather than mean lift. Vortex detachment can unload heavy membranes into compression, producing bending-regularized wrinkles. For $R_2>0$, the membrane equation remains well-posed independently of the sign of the tension, provided the membrane remains an immersion. Releasing the trailing edge creates an intrinsic degeneracy: the tension vanishes at the free endpoint, making the $R_2=0$ problem formally underdetermined, while the weak formulation selects its bounded-energy branch. This vanishing-tension endpoint traps pressure disturbances and drives rapid tip-snapping; the dominant frequency and effective wave number approach their zero-rigidity limits with an inverse-logarithmic correction arising from a singular Bessel branch. Finally, decreasing the stretching modulus destabilizes periodic flutter, and the repeated fluid-driven departure and elastic return suggest a homoclinic tangle underlying the transition from periodic to chaotic flutter.
