Reduction Model Methods Applied of Mechanical Nonlinear System

Gonçalves, Daniel Ferreira; Júnior, Lázaro Antônio da Fonseca; Rezende, Stéfany Mayara Ferreira de; Borges, Romes Antonio; Lima, Antônio Marcos Gonçalves de

doi:10.20906/cps/cilamce2015-0732

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“…Static methods are typically based on Guyan reduction and variations of it. Dynamic methods are based on real and complex modal analysis and modal methods [12], [13], [14] and [15].…”

Section: Introductionmentioning

confidence: 99%

“…Some methods use modal matrices including eigenvectors arranged in a specific column format such as the System Equivalent Reduction Expansion Process (SEREP), suggested in [29] and [30]. This allows extensive use of this method in elastic multibody problems [13], [14], [15], [31], [32] and [33]. A similar approach was suggested to reduce mechanical mass-spring systems with nonlinear models using the Quasi-Guyan method [34], [35] and [36].…”

Section: Introductionmentioning

confidence: 99%

“…In some studies, model reduction is based on a set of Ritz vectors. The transformation matrix or set of base vectors is obtained from the truncation of some normal modes followed by residual enrichment vectors [1], [2], [11] and [15]. Recent research, such as [37], emphasizes the importance of the correct choice of modes to be retained for the reliability and efficiency of the reduced model.…”

Section: Introductionmentioning

confidence: 99%

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Model Reduction Methods Applied to A Nonlinear Mechanical System

Borges

Gonçalves

Lima

et al. 2019

Int J Innov Educ Res

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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).

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“…Static methods are typically based on Guyan reduction and variations of it. Dynamic methods are based on real and complex modal analysis and modal methods [12], [13], [14] and [15].…”

Section: Introductionmentioning

confidence: 99%