Model Reduction Methods Applied to A Nonlinear Mechanical System

Abstract

Modern structures of high flexibility are subject to physical or geometricnonlinearities, and reliable numerical modeling to predict their behavior is essential.The modeling of these systems can be given by the discretization of the problem usingthe Finite Element Method (FEM), however by using this methodology, it is a veryrobust model from the computational point of view, making the simulation processdifficult. Using reduced models has been an excellent alternative to minimizing thisproblem. Most model reduction methods are restricted to linear problems, whichmotivated us to maximize the efficiency of these methods considering nonlinearproblems. For better accuracy, in this study, adaptations and improvements aresuggested in reduction methods such as the Enriched Modal Base (EMB), the SystemEquivalent Reduction Expansion Process (SEREP), QUASI-SEREP and the IteratedImproved Reduced System (IIRS). The stability of a system is discussed according tothe calculation of the Lyapunov exponents and phase space. Numerical simulationsshowed that the reduced models presented a good performance, according to thecommitment of quality and speed of responses (or time saving).

Modelagem numérico-computacional de vigas sanduiches viscoelásticas sujeitas a grandes deslocamentos na presença de Incertezas paramétricas

“…A suposição de que os modos do sistema conservativo associado seriam capazes de representar também os modos do sistema amortecido produz bons resultados para sistemas lineares suavemente amortecidos (BORGES et al, 2019;CUNHA-FILHO et al, 2018;LIMA et al, 2010;JOHNSON e KIENHOLZ, 1980). Entretanto, para sistemas com materiais viscoelásticos, a construção da base de redução, [T], é mais complicada, devido à dependência do viscoelastico em relação à frequência da excitação e a temperatura.…”