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

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