Exact nonlinear model reduction for a von Kármán beam: Slow-fast decomposition and spectral submanifolds
TLDR
This work applies two recently formulated mathematical techniques, Slow-Fast Decomposition (SFD) and Spectral Submanifold (SSM) reduction, to a von Karman beam with geometric nonlinearities and viscoelastic damping to results in a drastic reduction of the finite-element beam model to a one-degree-of freedom nonlinear oscillator.About:
This article is published in Journal of Sound and Vibration.The article was published on 2018-06-09 and is currently open access. It has received 53 citations till now. The article focuses on the topics: Slow manifold & 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
Explicit backbone curves from spectral submanifolds of forced-damped nonlinear mechanical systems
Thomas Breunung,George Haller +1 more
TL;DR: In this article, the authors extend these results to periodically or intermittently or not at all, and propose a reduced-order model for nonlinear unforced mechanical vibrations in spectral submanifolds.
Journal ArticleDOI
Exact model reduction by a slow–fast decomposition of nonlinear mechanical systems
George Haller,Sten Ponsioen +1 more
TL;DR: In this article, the authors derive conditions under which a general nonlinear mechanical system can be exactly reduced to a lower-dimensional model that involves only the softer degrees of freedom, called slow-fast decomposition (SFD).
Journal ArticleDOI
Model reduction to spectral submanifolds and forced-response calculation in high-dimensional mechanical systems.
TL;DR: In this paper, spectral submanifold (SSM) theory is used to extract forced response curves without any numerical simulation in high-degree-of-freedom, periodically forced mechanical systems.
Journal ArticleDOI
Data-driven modeling and prediction of non-linearizable dynamics via spectral submanifolds
TL;DR: In this article , the authors developed a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic linear part that are subject to external forcing with finitely many frequencies.
References
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M. C. C. Bampton,Roy R. Craig +1 more
TL;DR: In this article, a method for treating a complex structure as an assemblage of distinct regions, or substructures, is presented using basic mass and stiffness matrices, together with conditions of geometrical compatibility along substructure boundaries.
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Book
Nonlinear Dimensionality Reduction
John Aldo Lee,Michel Verleysen +1 more
TL;DR: The purpose of the book is to summarize clear facts and ideas about well-known methods as well as recent developments in the topic of nonlinear dimensionality reduction, which encompasses many of the recently developed methods.
MonographDOI
An introduction to nonlinear finite element analysis
TL;DR: The Finite Element Method: A Review 3. Heat Transfer and other Field Problems in One Dimension 4. Nonlinear Bending of Straight Beams 5. Bending Elastic Plates 7. Flows of Viscous Incompressible Fluids 8. Non-linear Analysis of Time-Dependent Problems 9. Finite Elements Formulations of Solids and Structures 10. Material Nonlinearities and Coupled Problems as mentioned in this paper
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