  We study a linear inviscid model of a passively flexible swimmer with
distributed flexibility, calculating its propulsive performance and optimal
distributions of flexibility. The frequencies of actuation and mean stiffness
ratios we consider span a large range, while the mass ratio is fixed to a low
value representative of swimmers. We present results showing how the trailing
edge deflection, thrust coefficient, power coefficient, and efficiency vary
with frequency, mean stiffness, and stiffness distribution. Swimmers with
distributed flexibility have the same qualitative features as those with
uniform flexibility. Significant gains in thrust can be made, however, by
tuning the stiffness such that a resonant response is triggered, or by
concentrating stiffness towards the leading edge if resonance cannot be
triggered. To minimize power, the opposite is true. Meaningful gains in
efficiency can be made at low frequencies by concentrating stiffness away from
the leading edge, since doing so induces efficient travelling wave kinematics.
We also speculate on the effects of a finite Reynolds number in the form of
streamwise drag. The drag adds an offset to the net thrust produced by the
swimmer, causing efficiency-maximizing distributions of flexibility to tend
towards thrust-maximizing ones, representative of what is found in nature.
