Plane unsteady inviscid incompressible hydrodynamics of a thin elastic profile

The problem of motion of a thin flexible profile in a flow of ideal incompressible liquid is solved. The oscillating profile moves translationally in the fluid. It causes generation of a vortex sheet behind the trailing edge of the wing. The wake affects the profile's motion. The flexible profile is modelled as a thin plate of a constant thickness. The problem is described by a system of integrodifferential equations which is solved by means of the Boubnov -Galerkin procedure with the subsequent usage of integral transformations. The analysis of the stability of the steady solution of the problem is presented for the first eigenform of oscillations of a thin plate.