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In the present paper, the initial theoretical results on wave-like aquaticpropulsion of marine craft by propagating flexural waves are reported. Recentexperimental investigations of small model boats propelled by propagatingflexural waves carried out by the present author and his co-workersdemonstrated viability of this type of propulsion as an alternative to awell-known screw propeller. In the attempts of theoretical explanation of theobtained experimental results using the theory of Lighthill for fishlocomotion, it was found that this theory predicts zero thrust for such modelboats, which is in contradiction with the results of the experiments. Oneshould note in this connection that the theory developed by Lighthill assumesthat the amplitudes of propulsive waves created by fish body motion grow fromzero on the front (at fish heads) to their maximum values at the tails. This isconsistent with fish body motion in nature, but is not compatible with thebehaviour of localised flexural waves used for propulsion in the experimentalmodel vessels. To overcome the problem of predicting zero thrust for the abovevessels, it is suggested in the present work that nonlinear distortion oflocalised flexural waves may be responsible for generation of thrust. Thishypothesis is explored in the present work by adding nonlinear harmonics ofpropulsive flexural waves to the formula derived by Lighthill for generatedthrust. For simplicity, only the lowest (third) harmonic growing linearly withthe distance of propagation was used. The resulting formula for the averagedthrust shows that, due to the effect of the third harmonic, the thrust is nolonger zero, thereby demonstrating that nonlinear distortion of the propulsiveflexural waves may be paramount for the existence of wave-like aquaticpropulsion of small marine craft using freely propagating flexural waves.

On the effect of elastic nonlinearity on aquatic propulsion caused by propagating flexural waves