Model reduction methods applied to a nonlinear mechanical system

Abstract

Modern structures of high flexibility are subject to physical or geometric nonlinearities, and reliable numerical modeling to predict their behavior is essential. The modeling of these systems can be given by the discretization of the problem using the Finite Element Method (FEM), however by using this methodology, it is a very robust model from the computational point of view, making the simulation process difficult. Using reduced models has been an excellent alternative to minimizing this problem. Most model reduction methods are restricted to linear problems, which
motivated us to maximize the efficiency of these methods considering nonlinear problems. For better accuracy, in this study, adaptations and improvements are suggested in reduction methods such as the Enriched Modal Base (EMB), the System Equivalent Reduction Expansion Process (SEREP), QUASI-SEREP and the Iterated Improved Reduced System (IIRS). The stability of a system is discussed according to the calculation of the Lyapunov exponents and phase space. Numerical simulations showed that the reduced models presented a good performance, according to the commitment of quality and speed of responses (or time saving).