Normal form analysis of a forced aeroelastic plate

A nonlinear elastic plate in a supersonic unsteady flow forced by a dynamic excitation and a biaxial compressive load is studied. The physical behavior of the plate is modelized by the Von Kármán equations and the aerodynamic loads are modeled by using the piston theory including nonlinearities up to the third order. The space-continuum model is space-discretized by a Galerkin projection and then studied by a perturbation approach based on the Normal Form method in order to reduce the system to a simpler and essential form defined by its resonance conditions. A physical interpretation of the involved small divisors is given by analyzing how different equation parameters influence the reduced normal form model in the neighborhood of both static and dynamic bifurcation points.