Comparison of model reduction techniques for large mechanical systems

Abstract

Model reduction is a necessary procedure for simulating large elastic systems, which are mostly modeled by the Finite Element Method (FEM). In order to reduce the system's large dimension, various techniques have been developed during the last decades, many of which share some common characteristics (Guyan, Dynamic, CMS, IRS, SEREP). A fact remains that many reduction approaches do not succeed in reducing the system's dimension without damaging the dynamical properties of the model. The mathematical field of control theory offers alternative reduction methods, which can be applied to sec- ond order Ordinary Differential Equations (ODEs), derived by the FE-discretization of large elastic Multi Body Systems (MBS), e.g., Krylov subspace method or balanced truncation. In this paper, some of these methods are applied to the elastic piston rod. The validity of the reduced models is checked by applying Modal Correlation Criteria (MCC), since only the eigenfrequency comparison is not sufficient. Diagonal Perturbation is proposed as an efficient method for iteratively solving ill-conditioned large sparse linear systems (Ax = b, A: ill-conditioned) when direct methods fail due to memory capacity problems. This is the case of FE-discretized systems, when tolerance failure occurs during the dis- cretization procedure.