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 …
Data-driven modeling and prediction of non-linearizable dynamics via spectral submanifolds
We develop a methodology to construct low-dimensional predictive models from data sets
representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic …
representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic …
Nonlinear normal modes of vibrating mechanical systems: 10 years of progress
Y Mikhlin, KV Avramov - Applied …, 2023 - asmedigitalcollection.asme.org
This paper contains review of the theory and applications of nonlinear normal modes, which
are developed during last decade. This review has more than 200 references. It is a …
are developed during last decade. This review has more than 200 references. It is a …
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 …
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 …
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 …
Nonlinear model reduction to fractional and mixed-mode spectral submanifolds
ABSTRACT A primary spectral submanifold (SSM) is the unique smoothest nonlinear
continuation of a nonresonant spectral subspace E of a dynamical system linearized at a …
continuation of a nonresonant spectral subspace E of a dynamical system linearized at a …
Model reduction to spectral submanifolds and forced-response calculation in high-dimensional mechanical systems
We show how spectral submanifold (SSM) theory can be used to extract forced-response
curves without any numerical simulation in high-degree-of-freedom, periodically forced …
curves without any numerical simulation in high-degree-of-freedom, periodically forced …
Frequency combs in a MEMS resonator featuring 1: 2 internal resonance: ab initio reduced order modelling and experimental validation
This paper is devoted to a detailed analysis of the appearance of frequency combs in the
dynamics of a micro-electro-mechanical systems (MEMS) resonator featuring 1: 2 internal …
dynamics of a micro-electro-mechanical systems (MEMS) resonator featuring 1: 2 internal …