Nonlinear aeroelastic analysis of a two-dimensional panel based on inertial manifolds with delay

Von Karman's large deformation plate theory was used to describe the panel deformation, and the aerodynamic loads were obtained by using the first order piston theory. The nonlinear partial differential equation of the system was derived. Then, the nonlinear Galerkin method based upon inertial manifolds with delay (IMD) was applied to the approaching of the governing equations. By this method, the higher-order modes were expressed by the lower-order modes and a time delay was introduced. Thus the same precision is kept and long computation time is saved. The numerical examples were given, and the dimensionless dynamic pressure and the dimensionless compressive internal force were considered as bifurcation parameters, respectively, to study the stability and bifurcation of the response. In particular, the route to chaos by intermittent transition was studied, and the periodic windows and self-similarity phenomena were captured in the chaos region. Through the phase portraits, FFT analysis and Lyapunov exponent, it demonstrates that there exist four distinct regions, representing stable, buckling, synchronous and non-synchronous motions of the system. In the non-synchronous region, a rich variety of nonlinear responses, such as double-period motion, quasi-period motion and chaotic motion, are found. The results can gain a fundamental understanding and developing of the nonlinear phenomena.