Investigation of Vortex Induced Excitation Employing Nonlinear Dynamics and Chaos Theory

该项目涉及涡-结构相互作用动力学的深入研究。对升力振荡器模型概念进行了回顾和扩展。在这项工作中提出的新方法中的Hartlen&Currie（HC）模型的邻域中的参数空间进行搜索。连续分析，相当于数值展开，表明HC模型的邻域，包含模型揭示意想不到的物理意义的动态。研究了刚性结构涡激与柔性结构涡激之间的联系，指出了分叉与连续分析是寻找可行动力学模型的有效工具。本文第二部分对升力振子进行了扰动分析，结果表明，升力振子的锁定行为是普遍存在的。2/1锁定占主导地位。此外，对截断形式的Navier-Stokes方程的分析证实，平面二维无粘流可以表现出由2/1分量主导的三维二次不稳定性，这与扰动分析定性一致。最后，对上述发现进行了实验验证。流场可视化与热膜风速仪相结合，显示了令人信服的证据，即占主导地位的不稳定性实际上是由流体结构系统的物理表现。

This project involved an in depth investigation of the dynamics of vortex-structure interaction. The lift oscillator model concept was reviewed and expanded. In the new approach proposed in this work the parameter space in the neighborhood of the Hartlen＆Currie (HC) model was searched. Continuation analysis, equivalent to numerical unfolding, showed that the neighborhood of the HC models, contains models revealing unexpected physically meaningful dynamics. A connection between vortex excitation of rigid structures and their flexible counterparts was found. Bifurcation and continuation analysis was found to be an effective tool in the search for feasible dynamical models. Peturbation analysis of the lift oscillator in the second part of this work showed that lock-in behavior was prevalent. The 2/1 lock-in was dominant. Furthermore, an analysis of a truncated form of the Navier-Stokes equations confirmed that a planar 2D inviscid flow can exhibit 3D secondary instabilities dominated by the 2/1 component, in qualitative agreement with the perturbation analysis. Finally, the foregoing findings were tested experimentally. Flow visualization coupled with hot-film anemometry showed convincing evidence that the dominant instabilities are actually physically manifested by the fluid-structure system.