The nonlinear panel flutter problem solved by Dowell in 1966 is used to investigate the new application of the proper orthogonal decomposition model reduction technique to aeroelastic analysis. Emphasis is placed on the nonlinear structural dynamic equations with nonconservative forcing modeled assuming a supersonic, inviscid flow. Here the aeroelastic coupled equation is presented in discrete form using a finite difference approach, and subsequently in state space form, to be integrated as a set of first order differential equations. In this paper, a POD approach is developed for generalized second-order differential equations; however, the application of POD to the governing equations in state space form is also discussed. This study compares the results and effectiveness of the model reduction technique for integration of the full set of degrees of freedom. The solution is compared to Dowell’s classic results which forms the base reference for the model reduction study. The reduced order model is then created from the full simulation model. Accuracy of the solution, reduced computational time, limits of stability, and the strengths and weaknesses of the model reduction are investigated.
Snapshot selection for groundwater model reduction using proper orthogonal decomposition
