Dynamic stability of elastic plate at jet flow

The mathematical model of the dynamic system containing an elastic plate at a one-sided flow of ideal incompressible gas stream with a separation of jet according to Kirchhoff's scheme is offered. The behavior of elastic material is described by the nonlinear model considering both longitudinal and transversal deformations of an elastic plate. The solution of an aerohydrodynamic part of a problem is based on methods of the theory of functions of complex variable. The related system of the integro-differential equations with partial derivatives containing only unknown plate deformations functions is obtained. Basing on the building of the functional corresponding to this system of the equations the sufficient conditions for stability of system solutions are established. Definition of elastic body stability corresponds to the Lyapunov's concept of stability of dynamic systems.