Proper Orthogonal Decomposition Reduced-Order Model for Nonlinear Aeroelastic Oscillations

In this study, the proper orthogonal decomposition method in conjunction with a Galerkin projection scheme is employed to solve the title problem of a fluttering plate in both two and three dimensions undergoing supersonic flow using von Karman's large deflection plate theory and quasi-steady supersonic aerodynamic theory. Proper-orthogonal-decomposition-based reduced-order models are constructed by using the responses as snapshots from the conventional Galerkin method, which also plays a role as a reference method in this paper. Results for the buckled, limit cycle oscillation, and chaotic responses of the simply supported plate are presented and compared with the Galerkin solutions. Numerical examples demonstrate that the proper orthogonal decomposition reduced-order model permits a much lower-dimensional model as compared to that obtainable via the Galerkin approach. For example, for a plate length-to-width ratio equal to 4, only two proper orthogonal decomposition modes are required to describe the panel oscillation with good accuracy. This produces a reduction in the computational time to less than 3 s in comparison with almost 900 s when using the 16 modes required to obtain the same accuracy with the Galerkin approach.