Reduced order models using generalized eigenanalysis

This article discusses the use of generalized eigenanalysis to extract reduced order models from the linearization of structural and aeroelastic problems written in differential-algebraic form. These problems may arise from multi-body analysis and in general from mixed approaches, where a high degree of generality and modelling flexibility are sought. A method based on a shift technique is proposed, that allows to exploit the regularity of the matrix pencil resulting from the linearization of differential-algebraic problems. Alternatively, the generalized Schur decomposition, or QZ decomposition, is directly used to select a cluster of eigenvalues related to the dynamic states. The two approaches are used to reduce the model to ordinary differential in state-space form. The two methods are applied to simple numerical problems, highlighting their robustness and versatility compared to other techniques. They are also applied to numerical models of a high-altitude long endurance aircraft obtained using a free general-purpose multi-body solver and a dedicated mixed variational solver.