The author investigates the nonlinear evolution of two different types of instability waves in the problem of fluid-loaded elastic plate in a uniform mean flow. He considers an infinitely long thin elastic plate, restricting his attention to purely two-dimensional motion. Both in the plate equations and in the boundary conditions are included nonlinear effects. The nonlinear plate equation considered here includes elastic restoring force, inertia, nonlinear tension due to bending, and the effect of dampers (or dashpots) attached to the lowside of the plate. Nonlinear effect are also included in boundary conditions.
The author examines various hypotheses which allow to solve the equation by using simple asymptotic methods. So, in the analysis of negative-energy waves he considers the solutions to a linearized equation and to appropriate equations with small parameter, derived from asymptotic solutions of the main equation obtained by taking into account plate tension and oscillations. The nonlinear Schrödinger equations for the amplitude is studied by using multiple scale techniques. The author shows how the nonlinearities act to increase the plate stiffness and thus to destabilize the fluid. He concludes that the amplitude of divergence instability will grow in time, but the nonlinear effects decrease its frequency down to zero, so that this type of instability evolves into a static plate deflection of constant amplitude. The author also analyzes the nonlinear behavior of convective instability.