Direct computation of nonlinear mapping via normal form for reduced-order models of finite element nonlinear structures
TLDR
The direct computation of the third-order normal form for a geometrically nonlinear structure discretised with the finite element (FE) method, is detailed, allowing to define a nonlinear mapping in order to derive accurate reduced-order models (ROM) relying on invariant manifold theory.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2021-10-01 and is currently open access. It has received 48 citations till now. The article focuses on the topics: Finite element method & Nonlinear system.read more
Citations
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Journal ArticleDOI
Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques
TL;DR: In this article, a review of nonlinear methods for model order reduction in structures with geometric nonlinearity is presented, with a special emphasis on the techniques based on invariant manifold theory.
Journal ArticleDOI
Model order reduction based on direct normal form: application to large finite element MEMS structures featuring internal resonance
TL;DR: A reduction method based on direct normal form computation for large finite element (FE) models is detailed, avoiding the computation of the complete eigenfunctions spectrum and making a direct link with the parametrisation of invariant manifolds.
Journal ArticleDOI
How to compute invariant manifolds and their reduced dynamics in high-dimensional finite element models
Shobhit Jain,George Haller +1 more
TL;DR: In this paper, the authors developed methods for computing invariant manifolds and their reduced dynamics in very high-dimensional nonlinear systems arising from spatial discretization of the governing partial differential equations.
Journal ArticleDOI
Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures
Yichang Shen,Alessandra Vizzaccaro,Nassim Kesmia,Ting Yu,Loic Salles,Olivier Thomas,Cyril Touzé +6 more
TL;DR: In this paper, numerical comparisons of model-order reduction methods for geometrically nonlinear structures in the general framework of finite element (FE) procedures are presented, and a simple analytical example is used to analyze how different treatments of quadratic nonlinearities by the three methods can affect the predictions.
Journal ArticleDOI
High order direct parametrisation of invariant manifolds for model order reduction of finite element structures: application to large amplitude vibrations and uncovering of a folding point
TL;DR: In this article , the parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems in oscillatory form expressed in the physical basis, so that the technique is directly applicable to mechanical problems discretised by the finite element method.
References
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Journal ArticleDOI
Problème général de la stabilité du mouvement
TL;DR: In this article, Sabatier implique l'accord avec les conditions générales d'utilisation (http://www.up-tlse.numdam.org/conditions).
Book
Problème général de la stabilité du mouvement
TL;DR: The Probleme General de la Stabilite du Mouvement (AM-17) as discussed by the authors is the most recent work in this line of work, and is based on the work of as discussed by the authors.
Journal ArticleDOI
Nonlinear normal modes, Part I: A useful framework for the structural dynamicist
TL;DR: The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part II as mentioned in this paper, and numerical methods for the continuation of periodic solutions pave the way for an effective and practical computation of NNMs, and timefrequency analysis is particularly suitable for the analysis of the resulting dynamics.
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A Short Review on Model Order Reduction Based on Proper Generalized Decomposition
TL;DR: This paper revisits a new model reduction methodology based on the use of separated representations, the so called Proper Generalized Decomposition—PGD, which allows to treat efficiently models defined in degenerated domains as well as the multidimensional models arising from multiddimensional physics or from the standard ones when some sources of variability are introduced in the model as extra-coordinates.
Journal ArticleDOI
Normal Modes for Non-Linear Vibratory Systems
Steven W. Shaw,Christophe Pierre +1 more
TL;DR: In this paper, a methodology is presented which extends to non-linear systems the concept of normal modes of motion which is well developed for linear systems and demonstrates how an approximate nonlinear version of superposition can be employed to reconstruct the overall motion from the individual nonlinear modal dynamics.
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