Chaotic Dynamics in Rotating Structures and Fluid-Structure Problems.

The goal of this investigation was to demonstrate the existence of chaotic dynamic behavior in mechanical systems that contain rotating structures andor fluid structure interactions. Progress was made in the study of the non-linear dynamics of rotating beams simple models of helicopter rotor blades and fluid flow induced experimental as well as analytical and numerical simulation. The research resulted in the award of one doctoral degree and offered support to visiting Professor M. Paidoussis, who built a test facility to study flow induced vibrations. In the study of rotating beams, we discovered that quasi-periodic vibrations were often a precursor to chaotic motions. Prof. Paidoussis introduced some strong non-linearities in the form of amplitude limiting constraints in his tube flow experiments. These constraints led to the transition of the original periodic flutter vibrations into chaotic flutter oscillations. The route to this chaos took place via period doubling bifurcations. One of the principal results of this study was the use of fractal mathematics in the experiments to prove that the dynamics of a continuous system could be modeled with a small number of ordinary differential equations. The techniques employed used ideas of fractal dimensions, Lyapunov exponents, auto-correlation, probability density functions, and bifurcation diagrams. AN