  We investigate the role of resonance in finite-amplitude swimming of a
flexible flat plate in a viscous fluid. The role of resonance in performance
remains unclear for two reasons: i) a lack of definition of resonance for the
fully-coupled fluid-structure interaction system in a viscous flow, and ii) the
presence of nonlinear effects, which makes it difficult to disentangle resonant
and non-resonant mechanisms in finite-amplitude swimming. We address point i)
and provide an unambiguous definition for system resonance by computing global
linear stability modes of the fully-coupled fluid-structure interaction system
that account for the viscous fluid, the plate, and the coupling between them.
We then resolve point ii) by considering high-fidelity nonlinear simulations of
systematically increased amplitude. By comparing the results for different
amplitudes with one another and with the linear stability modes, we separate
linear and/or resonant effects from nonlinear and/or non-resonant effects.
Resonant behavior is observed over a wide range of plate stiffnesses, with
peaks in trailing-edge motion and thrust occurring near the resonant frequency
defined by the global linear analysis. The peaks broaden and weaken with
increasing heave amplitude, consistent with an increased damping effect from
the fluid. At the same time, non-resonant mechanisms are present at large heave
amplitudes. The input power exhibits qualitatively different dynamics at large
heave amplitudes compared to smaller heave amplitudes, where resonance
dominates. Moreover, leading-edge separation is present for stiff plates at
large heave amplitudes, which can drastically alter the performance
characteristics from what one would expect through linear predictions.
