  In this paper, we numerically investigate the propulsive performance of
three-dimensional pitching flexible plates with varying flexibility and
trailing edge shapes. To eliminate the effect of other geometric parameters,
only the trailing edge angle is varied from 45{\deg} (concave), 90{\deg}
(rectangular) to 135{\deg} (convex) while maintaining the constant area of the
flexible plate. We examine the impact of the frequency ratio f* defined as the
ratio of the natural frequency of the flexible plate to the actuated pitching
frequency. Through our numerical simulations, we find that the global maximum
mean thrust occurs near f*=1 corresponding to the resonance condition. However,
the optimal propulsive efficiency is achieved around f*=1.54 instead of the
resonance condition. While the convex plate with low and high bending stiffness
values shows the best performance, the rectangular plate with moderate bending
stiffness is the most efficient propulsion configuration. Through dynamic mode
decomposition, we find that the passive deformation can help in redistributing
the pressure gradient thus improving the efficiency and thrust production. A
momentum-based thrust evaluation approach is adopted to link the instantaneous
vortical structures with the time-dependent thrust. When the vortices detach
from the trailing edge, the instantaneous thrust shows the largest values due
to the strong momentum change and convection process. Moderate flexibility and
convex shape help transfer momentum to the fluid, thereby improving thrust
generation and promoting the transition from drag to thrust. The increase of
the trailing edge angle can broaden the range of flexibility that produces
positive mean thrust.
