Aeroelastic system development using proper orthogonal decomposition and Volterra theory

Volterra theory and proper orthogonal decomposition are combined into a hybrid methodology for reduced-order modeling of aeroelastic systems. The outcome of the method is a set of linear ordinary differential equations describing the modal amplitudes associated with both the structural modes and the proper orthogonal decomposition basis functions for the fluid. The structural modes are sine waves of varying frequency, and the new approach is applied to the fluid dynamics equations. The structural modes are treated as forcing terms that are impulsed as part of the fluid model realization. By the use of this approach, structural and fluid operators are coupled into a single aeroelastic operator while the parameter (or parameters) of interest for sensitivity analysis are preserved. The approach is applied to an elastic panel in supersonic crossflow. The resulting aeroelastic model provides correct limit-cycle oscillation prediction over a wide range of panel dynamic pressure values. Time integration of the reduced-order aeroelastic model is four orders of magnitude faster than the high-order solution procedure developed by the use of traditional fluid and structural solvers.