  We use small-amplitude inviscid theory to study the swimming performance of a
flexible flapping plate with time-varying flexibility. The stiffness of the
plate oscillates at twice the frequency of the kinematics in order to maintain
a symmetric motion. Plates with constant and time-periodic stiffness are
compared over a range of mean plate stiffness, oscillating stiffness amplitude,
and oscillating stiffness phase for isolated heaving, isolated pitching, and
combined leading edge kinematics. We find that there is a profound impact of
oscillating stiffness on the thrust, with a lesser impact on propulsive
efficiency. Thrust improvements of up to 35% relative to a constant-stiffness
plate are observed. For large enough frequencies and amplitudes of the
stiffness oscillation, instabilities emerge. The unstable regions may confer
enhanced propulsive performance; this hypothesis must be verified via
experiments or nonlinear simulations.
