Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques
This paper aims at reviewing nonlinear methods for model order reduction in structures with
geometric nonlinearity, with a special emphasis on the techniques based on invariant …
geometric nonlinearity, with a special emphasis on the techniques based on invariant …
[HTML][HTML] Network dynamics of coupled oscillators and phase reduction techniques
B Pietras, A Daffertshofer - Physics Reports, 2019 - Elsevier
Investigating the dynamics of a network of oscillatory systems is a timely and urgent topic.
Phase synchronization has proven paradigmatic to study emergent collective behavior …
Phase synchronization has proven paradigmatic to study emergent collective behavior …
How to compute invariant manifolds and their reduced dynamics in high-dimensional finite element models
Invariant manifolds are important constructs for the quantitative and qualitative
understanding of nonlinear phenomena in dynamical systems. In nonlinear damped …
understanding of nonlinear phenomena in dynamical systems. In nonlinear damped …
Nonlinear normal modes and spectral submanifolds: existence, uniqueness and use in model reduction
G Haller, S Ponsioen - Nonlinear dynamics, 2016 - Springer
We propose a unified approach to nonlinear modal analysis in dissipative oscillatory
systems. This approach eliminates conflicting definitions, covers both autonomous and time …
systems. This approach eliminates conflicting definitions, covers both autonomous and time …
Direct computation of nonlinear mapping via normal form for reduced-order models of finite element nonlinear structures
The direct computation of the third-order normal form for a geometrically nonlinear structure
discretised with the finite element (FE) method, is detailed. The procedure allows to define a …
discretised with the finite element (FE) method, is detailed. The procedure allows to define a …
High-order direct parametrisation of invariant manifolds for model order reduction of finite element structures: application to generic forcing terms and parametrically …
The direct parametrisation method for invariant manifolds is used for model order reduction
of forced-damped mechanical structures subjected to geometric nonlinearities. Nonlinear …
of forced-damped mechanical structures subjected to geometric nonlinearities. Nonlinear …
The parameterization method for invariant manifolds I: manifolds associated to non-resonant subspaces
We introduce a method to prove existence of invariant manifolds and, at the same time to
find simple polynomial maps which are conjugated to the dynamics on them. As a first …
find simple polynomial maps which are conjugated to the dynamics on them. As a first …
Model order reduction based on direct normal form: application to large finite element MEMS structures featuring internal resonance
Dimensionality reduction in mechanical vibratory systems poses challenges for distributed
structures including geometric nonlinearities, mainly because of the lack of invariance of the …
structures including geometric nonlinearities, mainly because of the lack of invariance of the …
Phase reduction and phase-based optimal control for biological systems: a tutorial
A powerful technique for the analysis of nonlinear oscillators is the rigorous reduction to
phase models, with a single variable describing the phase of the oscillation with respect to …
phase models, with a single variable describing the phase of the oscillation with respect to …
The parameterization method for invariant manifolds II: regularity with respect to parameters
The Parameterization Method for Invariant Manifolds II: Regularity with Respect to Parameters
Page 1 The Parameterization Method for Invariant Manifolds II: Regularity with Respect to …
Page 1 The Parameterization Method for Invariant Manifolds II: Regularity with Respect to …