Proper Orthogonal Decomposition for Model Reduction of a Vibroimpact System

The application that inspires this work is the percussion drilling. This problem has impacts and presents uncertainties. In this first analysis the focus is on the construction of an efficient reduced-order model to deal with the nonlinear dynamics due to the impacts. It is important to have an efficient reduced-order model to perform the stochastic analysis. The simplified full model is constructed using the finite element method, and three different bases are used to construct the reduced-order models: LIN-basis (composed by the normal modes of the associated linear problems), PODdir-basis (obtained through proper orthogonal decomposition - direct method) and PODsnap-basis (obtained through proper orthogonal decomposition - snapshot method). The shapes of the elements of LIN-basis, PODdir-basis, and PODsnap-basis are compared. One important conclusion is that the information necessary to represent the details of a vibroimpact dynamics, measured by the proper orthogonal values, is more than the usual 99% recommended.