Proper orthogonal decomposition of an aeroelastic piecewise-linear system

The objective of this paper is to investigate the Piecewise-Linear Systems behavior through the Proper Orthogonal Decomposition (POD) analysis. The study is conducted considering the free response of a typical aeroelastic application: an airfoil section with a piecewise-linear control surface (flap) hinge that represents a mechanical freeplay. This system can be modeled as the interaction between two different linear dynamical models: the nominal system where the flap hinge is active and the zero system where there is no flap hinge stiffness. Comparing the POD-basis and the eigenmodes associated to the two different systems some information about the participation of each linear model are achieved. Moreover, a qualitative index of the complexity, i.e., nonlinearity, of the response is derived from the energy distribution over the POD basis represented by the distribution of the Proper Orthogonal Values (POVs) among Proper Orthogonal Modes (POMs).