  In this paper I consider the self-excited rotation of an elliptical cylinder
towed in a viscous fluid as a canonical model of nonlinear fluid structure
interactions with possible applications in the design of sensors and energy
extraction devices. First, the self-excited ellipse system is shown to be
analogous to the forced bistable oscillators studied in classic chaos theory. A
single variable, the distance between the pivot and the centroid, governs the
system bifurcation into bi-stability. Next, fully coupled computational fluid
dynamics simulations of the motion of the cylinder demonstrate limit cycle,
period doubling, intermittently chaotic, and fully chaotic dynamics as the
distance is further adjusted. The viscous wake behind the cylinder is presented
for the limit cycle cases and new types of stable wakes are characterized for
each. In contrast, a chaotic case demonstrates an independence of the wake and
structural states. The rotational kinetic energy is quantified and correlated
to the vortex shedding and the trajectory periodicity. Chaotic and high-period
system responses are found to persist when structural damping is applied and
for Reynolds numbers as low as 200.
