Unsteady 3-D lifting surface theory with the free surface effect

This theory concerns unsteady fluid/structure interactions with the gravity effect. Usual assumptions of the linear theories are made and the 3-D lifting surface method of the unsteady aerodynamics is used. Starting from the potential of the Havelock source, we are led to an integral equation, the kernel of which is expressed as a Fourier series with respect to the azimuthal angle. The coefficients of the Fourier expansion are simple integrals approximated by an asymptotic method for large indices. The integral equation is solved by the collocation technics. Problems such as flutter of subcavitating foil-systems for control dynamics in flight near the surface wave provide relevant applications of this theory.