The propulsive performance of a flexible foil with prescribed pitching and heaving motions
about any pivot point location and passive chordwise flexural deflection is analysed within
the framework of the linear potential flow theory and the Euler–Bernoulli beam equation
using a quartic approximation for the deflection. The amplitude of the flexural component
of the deflection and its phase, the thrust force, input power and propulsive efficiency are
computed analytically in terms of the stiffness and mass ratio of the plate, frequency, pivot
point location and remaining kinematic parameters. It is found that the maximum flexural
deflection amplitude, thrust and input power are related to the first fluid–structure natural
frequency of the system, corresponding to the deflection approximation considered. The
same relation is observed for the propulsive efficiency when an offset drag is included
in the analytical expressions. These results, which are valid for small amplitude and
sufficiently large stiffness of the foil, are compared favourably with previous related results
when the foil pivots about the leading edge. The configurations generating maximum thrust
and efficiency enhancement by flexibility are analysed in relation to those of an otherwise
identical rigid foil.
