Feedback-Induced Flutter Instability of a Flexible Beam in Fluid Flow

A pinned-free beam in axial fluid flow, subjected to feedback-based actuation at the pinned end, is investigated. The actuation may be a moment or a prescribed angle and it is proportional to the state (curvature, slope, or displacement) of the beam at some point along its length. All equations and boundary condition terms are non-dimensionalized and the stability of the system is studied over a range of external flow velocity and sensing location. For each combination of flow velocity and sensing location, the critical gain (positive or negative) for the onset of flutter is determined. This process, which is repeated for each combination of actuation and sensing modes, reveals that the closed-loop system exhibits a rich set of stability transitions, each associated with a traveling waveform in the flexible beam at the onset of flutter. With the intent of exploring the use of flexible fluttering beams for underwater propulsion, the efficiency of these waveforms is computed using slender-body theory. Additional insights into the efficiency of the waveforms are obtained through considerations of the smoothness of the traveling waveforms.