Bibliography · Method & applications

Publications.

The DPIM method behind MORFE.jl is the result of a decade of work on nonlinear normal forms, invariant manifolds, and FE-native reduction. The list below covers the theoretical foundations, software releases, and applications across MEMS, civil structures, rotating machinery, and shells.

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20241 entry
Method

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

A. Vizzaccaro, G. Gobat, A. Frangi, C. Touzé.

Nonlinear Dynamics ·112(8), 6255–6290 ·2024

PDF ↗ doi:10.1007/s11071-024-09333-0
20233 entries
Method

High-order direct parametrisation of invariant manifolds for model order reduction of finite element structures: application to generic forcing terms and parametrically excited systems.

A. Opreni, A. Vizzaccaro, C. Touzé, A. Frangi.

Nonlinear Dynamics ·111(6), 5401–5447 ·2023

PDF ↗ doi:10.1007/s11071-022-07978-3
Application

Frequency combs in a MEMS resonator featuring 1:2 internal resonance: ab initio reduced order modelling and experimental validation.

G. Gobat, L. Zega, P. Fedeli, C. Touzé, A. Frangi.

Nonlinear Dynamics ·111(4), 2991–3017 ·2023

PDF ↗ doi:10.1007/s11071-022-08029-7
Application

Nonlinear model order reduction of resonant piezoelectric micro-actuators: an invariant manifold approach.

A. Opreni, G. Gobat, C. Touzé, A. Frangi.

Computers & Structures ·289, 107154 ·2023

PDF ↗ doi:10.1016/j.compstruc.2023.107154
20221 entry
Method

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.

A. Vizzaccaro, A. Opreni, L. Salles, A. Frangi, C. Touzé.

Nonlinear Dynamics ·110(1), 525–571 ·2022

PDF ↗ doi:10.1007/s11071-022-07651-9
20213 entries
Method

Direct computation of nonlinear mapping via normal form for reduced-order models of finite element nonlinear structures.

A. Vizzaccaro, Y. Shen, L. Salles, J. Blahoš, C. Touzé.

Computer Methods in Applied Mechanics and Engineering ·384, 113957 ·2021

PDF ↗ doi:10.1016/j.cma.2021.113957
Application

Model order reduction based on direct normal form: application to large finite element MEMS structures featuring internal resonance.

A. Opreni, A. Vizzaccaro, A. Frangi, C. Touzé.

Nonlinear Dynamics ·105(2), 1237–1272 ·2021

PDF ↗ doi:10.1007/s11071-021-06641-7
Review

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques.

C. Touzé, A. Vizzaccaro, O. Thomas.

Nonlinear Dynamics ·105(2), 1141–1190 ·2021

PDF ↗ doi:10.1007/s11071-021-06693-9
How to cite

If MORFE shows up in your work, please cite the method papers.

The CMAME 2021 paper is the primary reference for the FE-native DPIM algorithm. For high-order and forced extensions, also cite the Nonlinear Dynamics 2022 paper.

Primary method · BibTeX

@article{vizzaccaro_dpim_2021,
  title   = "Direct computation of nonlinear mapping via normal form for reduced-order models of finite element nonlinear structures",
  author  = "Vizzaccaro, A. and Shen, Y. and Salles, L. and Blaho{\v{s}}, J. and Touz{\'e}, C.",
  journal = "Computer Methods in Applied Mechanics and Engineering",
  volume  = "384",
  pages   = "113957",
  year    = "2021",
  doi     = "10.1016/j.cma.2021.113957"
}

High-order extension · BibTeX

@article{vizzaccaro_hodpim_2022,
  title   = "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",
  author  = "Vizzaccaro, A. and Opreni, A. and Salles, L. and Frangi, A. and Touz{\'e}, C.",
  journal = "Nonlinear Dynamics",
  volume  = "110",
  number  = "1",
  pages   = "525--571",
  year    = "2022",
  doi     = "10.1007/s11071-022-07651-9"
}