NONLINEAR DYNAMICS OF BLUFF-BODY WAKES AND FLUID-STRUCTURE INSTABILITIES: A SYMMETRY-GROUP BASED APPROACH

感兴趣的主题是流体-结构相互作用（FSI），涉及大型和/或复杂的系统与固有的对称性。这样的系统在自然界和工程中无处不在。典型的例子包括机械和土木工程结构，如桁架结构，穹顶结构，空间结构以及机器喷气发动机等。在许多情况下，对称性导致高度简化的行为，即使是大型复杂系统。与此同时，对称性可能会导致意想不到的和反直觉的行为，如果不深入研究对称性影响下的系统动力学细节，这些行为可能难以解释或完全理解。** 对称群理论及其在从空间结构到高速喷气发动机等大型复杂工程系统中的应用引起了越来越多的兴趣。然而，系统的开采仍然有限。然而，在许多问题中，对称性理论为复杂系统的动力学提供了深刻的见解。旋转机械中的模态局部化问题现在是公知的和理解的。这个在50年代困扰工程师们的问题可以很方便地用对称群理论来解释。** 在拟议的研究计划中，将研究与结构相互作用的流体流的存在相关的附加效应。模态局部化/破缺极大地改变了有效振动模态。预计这将显著地改变经受轴向流的管的稳定性行为。为了解决大型系统的复杂性的挑战，拟议的研究计划采用对称群理论，为大型复杂系统开发可行的降阶模型（ROM）。所解决的具体问题是在流体-结构相互作用的领域，（i）复杂的流动，如圆柱后面的尾流和（ii）或大型流动-结构系统，如圆柱阵列经历流动诱导的不稳定性。** 除了预测观察到的动力学行为外，基于对称性的模型的一个潜在的更重要的贡献是证明尾流动力学与具有相同对称性的一般物理和数学系统的动力学之间的联系。作为一个具体的例子，卡门尾流经历了高振幅强迫倍周期分岔。** 卡门尾流的倍周期分叉与强迫扰动和卡门尾流对称性之间的相对对称性密切相关。具有相同相对对称性的其他物理系统包括具有周期性振荡支撑的圆柱体和在垂直激励下的流体填充容器。由于对称性破缺不稳定性，系统也表现出倍周期不稳定性。***********

The subject of interest is fluid-structure interaction (FSI) involving large and/or complex systems with inherent symmetry. Such systems are ubiquitous in nature and in engineering. Typical examples include mechanical and civil engineering structures such truss structures, dome structures, space structures as well as machines jet engines etc.******Symmetry in many cases leads to highly simplified behavior, even for large complex systems. At the same time, symmetry may lead to unexpected and counter-intuitive behavior which can be difficult to explain or fully understanding without delving into the details of system dynamics under the influence of symmetry. ******There has been increasing interest in symmetry group theory and its application to large complex engineering systems ranging from space structures to high speed trans and jet engines. However, systematic exploitation remains limited. Yet there are many problems where symmetry theory provides deep insight into the dynamics of complex systems. The problem of mode localization in rotating machines is now well known and understood. This problem, which perplexed engineers in the 50s can very conveniently, explained using symmetry group theory. ******In the proposed research program the additional effects associated with the presence of fluid flow interacting with the structures will be investigated. Mode localization / symmetry-breaking drastically changes the effective vibration modes. This is expected to significantly modify the stability behavior of tubes subjected to axial flow. To address the challenge of complexity in large systems the proposed research program employs symmetry group theory to develop feasible reduced order models (ROMs) for large and complex systems. The specific problems addressed are in the area of fluid-structure interactions for (i) complex flows such as wake flows behind circular cylinders and (ii) or large flow-structure systems such as cylinder arrays undergoing flow-induced instabilities. ******Besides the predicting the observed dynamical behavior, a potentially more important contribution of the symmetry based model is the demonstration of the link between the wake flow dynamics and the dynamics of the general class of physical and mathematical systems having the same symmetry. As a specific example, the Karman wake undergoes a period-doubling bifurcation for high amplitude forcing. ******The period-doubling bifurcation of the Karman wake is intimately related to the relative symmetry between the forcing perturbation and the symmetry of the Karman wake flow. Other physical systems having the same relative symmetries include pendulums with periodically oscillating support, and fluid-filled vessels under vertical excitation. The systems also exhibit period-doubling instabilities due to the same symmetry breaking instability. ***********