Connections between resonance and nonlinearity in swimming performance of a flexible heaving plate

The use of flexibility in underwater vehicles is of interest as a means to augment propulsive performance. As an intermediate step to this aim, the effect of flexibility on performance is often considered for flow past a heaving flexible flat plate. In this setting, previous work has found flexibility to improve performance for certain parameters. While these benefits have been found for a range of flow regimes, the physical role of flexibility remains unclear. Often, resonance is cited as the source of performance peaks, though in certain settings heaving at non-resonant frequencies has been found to be optimal. Other studies have found relationships between flow structures and performance, though the connection of these observations to resonance is still unclear. We use high-fidelity nonlinear simulations and a global linear analysis of the fully-coupled fluid-structure interaction system to study two-dimensional viscous flow past a heaving geometrically nonlinear Euler-Bernoulli beam. The linear analysis is used to unambiguously define resonant behavior in the presence of a viscous fluid. Comparisons between these linear results and nonlinear, finite-amplitude-heaving simulations are made to determine the role of nonlinearity in optimal performance.