Periodic and chaotic motions of a square prism in cross-flow

Periodic and chaotic responses of a square prism in cross-flow modelled as a Duffing oscillator and subjected to harmonic excitation are investigated, with the flow velocity as the bifurcation parameter, by the fast Galerkin method and numerical integration. The stability of the periodic solutions is investigated by examining the movement of the eigenvalues of the monodromy matrix. It is observed that the system executes symmetric oscillations for small flow velocities and increases in flow velocity result in symmetry-breaking bifurcation followed by a cascade of period-doubling bifurcations, eventually leading to chaos. Consequently period 1, 2, 4, etc., motions are accompanied by the corresponding dual motions. Bifurcation diagrams, Lyapunov exponents, time histories, initial condition maps and the nature of the motion in the parametric space are presented. © 1994 Academic Press Limited.