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Large numbers of fluid elastic structures are part of many power plant systems and vibration of these systems sometimes are responsible for plant shut downs. Earlier research at Cornell in this area had centered on nonlinear dynamics of fluid-elastic systems with low degrees of freedom. The focus of current research is the study of the dynamics of thousands of closely arrayed structures in a cross flow under both fluid and impact forces. This research is relevant to two areas: (1) First, fluid-structural problems continue to be important in the power industry, especially in heat exchange systems where up to thousands of pipe-like structures interact with a fluid medium. [Three years ago in Japan for example, there was a shut down of the Monju nuclear power plant due to a failure attributed to flow induced vibrations.] (2) The second area of relevance is to nonlinear systems and complexity phenomena; issues such as spatial temporal dynamics, localization and coherent patterns entropy measures as well as other complexity issues. Early research on flow induced vibrations in tube row and array structures in cross flow goes back to Roberts in 1966 and Connors in 1970. These studies used linear models as have many of the later work in the 1980's. Nonlinear studies of cross flow induced vibrations have been undertaken in the last decade. The research at Cornell sponsored by DOE has explored nonlinear phenomena in fluid-structure problems. In the work at Cornell we have documented a subcritical Hopf bifurcation for flow around a single row of flexible tubes and have developed an analytical model based on nonlinear system identification techniques. (Thothadri, 1998, Thothadri and Moon, 1998, 1999). These techniques have been applied to a wind tunnel experiment with a row of seven cylinders in a cross flow. These system identification methods have been used to calculate fluid force models that have replicated certain quantitative vibration limit cycle behavior of the vibrating cylinders. The methods are based on nonlinear analysis ideas such as harmonic balance and center manifold theory. In a set of new experiments we have looked at the dynamics of 300 and 1000 vibrating rods in cross flow. Classic fluid structure experiments have generally taken a reductionist view of fluid-elastic dynamics, namely one attempts to measure or derive forceflow relations for a single structure and then extend the results to a large number of structures. However in strongly non-linear systems such reductionist analysis does not always capture important phenomena such a chaotic dynamics, localization and coherent structures. In the case of large numbers of closely packed structures in a fluid flow, strong nonlinear effects include impact between structures. Also in large arrays, there is a natural random deviation from an exact periodic pattern that may affect the global spatial and temporal dynamics. Another complexity is the time delay effect of upstream eddies from vibrating structures driving downstream structures

Nonlinear Dynamics and Control of Large Arrays of Coupled Oscillators: Application to Fluid-Elastic Problems