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

感兴趣的主题是涉及具有固有对称性的大型和/或复杂系统的流固相互作用（FSI）。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，圆顶结构，空间结构以及机器喷气发动机等******对称在许多情况下导致高度简化的行为，即使是大型复杂系统。同时，对称性可能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，这些行为很难解释或完全理解。******人们对对称群理论及其在大型复杂工程系统中的应用越来越感兴趣，从空间结构到高速变速器和喷气发动机。然而，系统的开发仍然有限。然而，在许多问题上，对称理论为复杂系统的动力学提供了深刻的见解。旋转机械的模态定位问题现在已经广为人知。这个困扰50年代工程师的问题，可以用对称群理论来解释。******在拟议的研究计划中，将研究与流体流动与结构相互作用有关的附加效应。模态局部化/对称破缺极大地改变了有效振动模态。预计这将显著改变管在轴流作用下的稳定性行为。为了解决大系统复杂性的挑战，本研究计划采用对称群理论为大型复杂系统建立可行的降阶模型。具体解决的问题是在流体结构相互作用领域(i)复杂的流动，如圆形圆柱体后面的尾流和（ii）或大型流动结构系统，如经历流致不稳定性的圆柱体阵列。******除了预测观测到的动力学行为之外，基于对称的模型的一个潜在更重要的贡献是证明了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的倍周期分岔。******卡门尾流的倍周期分岔与强迫扰动与卡门尾流的对称性之间的相对对称性密切相关。其他具有相同相对对称性的物理系统包括具有周期性振荡支撑的钟摆，以及在垂直激励下充满流体的容器。由于相同的对称性破缺不稳定性，系统也表现出周期加倍的不稳定性。***********

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. ***********