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 …

Nonlinear model reduction for a cantilevered pipe conveying fluid: A system with asymmetric damping and stiffness matrices

M Li, H Yan, L Wang - Mechanical Systems and Signal Processing, 2023 - Elsevier
We construct reduced-order models (ROMs) for a geometrically nonlinear viscoelastic
cantilevered pipe conveying fluid, a dynamical system that includes asymmetric damping …

[HTML][HTML] Nonautonomous spectral submanifolds for model reduction of nonlinear mechanical systems under parametric resonance

T Thurnher, G Haller, S Jain - Chaos: An Interdisciplinary Journal of …, 2024 - pubs.aip.org
We use the recent theory of spectral submanifolds (SSMs) for model reduction of nonlinear
mechanical systems subject to parametric excitations. Specifically, we develop expressions …

Capturing the edge of chaos as a spectral submanifold in pipe flows

B Kaszás, G Haller - Journal of Fluid Mechanics, 2024 - cambridge.org
An extended turbulent state can coexist with the stable laminar state in pipe flows. We focus
here on short pipes with additional discrete symmetries imposed. In this case, the boundary …

Deep learning-based surrogate models for parametrized PDEs: Handling geometric variability through graph neural networks

NR Franco, S Fresca, F Tombari… - … Interdisciplinary Journal of …, 2023 - pubs.aip.org
Mesh-based simulations play a key role when modeling complex physical systems that, in
many disciplines across science and engineering, require the solution to parametrized time …

Reduced Order Modelling of Fully Coupled Electro‐Mechanical Systems Through Invariant Manifolds With Applications to Microstructures

A Frangi, A Colombo, A Vizzaccaro… - International Journal for …, 2023 - Wiley Online Library
This article presents the first application of the direct parametrisation method for invariant
manifolds to a fully coupled multiphysics problem involving the nonlinear vibrations of …

[HTML][HTML] Nonlinear model reduction to random spectral submanifolds in random vibrations

Z Xu, RS Kaundinya, S Jain, G Haller - Journal of Sound and Vibration, 2024 - Elsevier
Dynamical systems in engineering and physics are often subject to irregular excitations that
are best modeled as random. Monte Carlo simulations are routinely performed on such …

Data-free non-intrusive model reduction for nonlinear finite element models via spectral submanifolds

M Li, T Thurnher, Z Xu, S Jain - Computer Methods in Applied Mechanics …, 2025 - Elsevier
The theory of spectral submanifolds (SSMs) has emerged as a powerful tool for constructing
rigorous, low-dimensional reduced-order models (ROMs) of high-dimensional nonlinear …

Direct parametrisation of invariant manifolds for non-autonomous forced systems including superharmonic resonances

A Vizzaccaro, G Gobat, A Frangi, C Touzé - Nonlinear Dynamics, 2024 - Springer
The direct parametrisation method for invariant manifold is a model-order reduction
technique that can be applied to nonlinear systems described by PDEs and discretised, for …

Model reduction for nonlinearizable dynamics via delay-embedded spectral submanifolds

J Axås, G Haller - Nonlinear Dynamics, 2023 - Springer
Delay embedding is a commonly employed technique in a wide range of data-driven model
reduction methods for dynamical systems, including the dynamic mode decomposition, the …