Chaotic Motions of Self‐Excited Forced and Autonomous Square Prisms

Abstract

The motion of oscillators governed by the standard equations for the aerodynamic galloping of square prisms is studied for two cases: a harmonically forced, single elastically mounted bar immersed in a uniform flow, and an autonomous, elastically coupled pair of such bars. It is shown that the behavior of the forced oscillator has similarities to the behavior of the standard circle map. Thus it is possible to describe how locked‐in oscillatory forms are organized within the forcing amplitude/frequency parameter space and to identify transitions from quasiperiodicity to chaos and turbulent intermittencies. For the coupled pair of oscillators, two stable attractors were identified on which the orbits are topologically similar, respectively, to the two normal modes of the associated linear system. Depending upon the system parameters, one of the attractors contains orbits that may be periodic, quasiperiodic, or chaotic. Beyond a critical flow velocity this attractor vanishes. For the other attractor, only periodic orbits were identified. This work is the first stage of a numerical and experimental investigation aimed at assessing the potential role of chaotic dynamics in bluff body fluid elasticity, with a view to application in ocean engineering.