  In the present paper, the initial theoretical results on wave-like aquatic
propulsion of marine craft by propagating flexural waves are reported. Recent
experimental investigations of small model boats propelled by propagating
flexural waves carried out by the present author and his co-workers
demonstrated viability of this type of propulsion as an alternative to a
well-known screw propeller. In the attempts of theoretical explanation of the
obtained experimental results using the theory of Lighthill for fish
locomotion, it was found that this theory predicts zero thrust for such model
boats, which is in contradiction with the results of the experiments. One
should note in this connection that the theory developed by Lighthill assumes
that the amplitudes of propulsive waves created by fish body motion grow from
zero on the front (at fish heads) to their maximum values at the tails. This is
consistent with fish body motion in nature, but is not compatible with the
behaviour of localised flexural waves used for propulsion in the experimental
model vessels. To overcome the problem of predicting zero thrust for the above
vessels, it is suggested in the present work that nonlinear distortion of
localised flexural waves may be responsible for generation of thrust. This
hypothesis is explored in the present work by adding nonlinear harmonics of
propulsive flexural waves to the formula derived by Lighthill for generated
thrust. For simplicity, only the lowest (third) harmonic growing linearly with
the distance of propagation was used. The resulting formula for the averaged
thrust shows that, due to the effect of the third harmonic, the thrust is no
longer zero, thereby demonstrating that nonlinear distortion of the propulsive
flexural waves may be paramount for the existence of wave-like aquatic
propulsion of small marine craft using freely propagating flexural waves.
