Adrien Martin ; Andrea Opreni ; Alessandra Vizzaccaro ; Marielle Debeurre ; Loic Salles et al. - Reduced-order modeling of geometrically nonlinear rotating structures using the direct parametrisation of invariant manifolds

jtcam:10430 - Journal of Theoretical, Computational and Applied Mechanics, June 1, 2023 - https://doi.org/10.46298/jtcam.10430
Reduced-order modeling of geometrically nonlinear rotating structures using the direct parametrisation of invariant manifoldsArticle

Authors: Adrien Martin 1,2,3; Andrea Opreni ORCID4; Alessandra Vizzaccaro ORCID5; Marielle Debeurre 6,7; Loic Salles ORCID8,9; Attilio Frangi ORCID4; Olivier Thomas ORCID6,7; Cyril Touzé ORCID1,2,3

The direct parametrisation method for invariant manifolds is a nonlinear reduction technique which derives nonlinear mappings and reduced-order dynamics that describe the evolution of dynamical systems along a low-dimensional invariant-based span of the phase space. It can be directly applied to finite element problems. When the development is performed using an arbitrary order asymptotic expansion, it provides an efficient reduced-order modeling strategy for geometrically nonlinear structures. It is here applied to the case of rotating structures featuring centrifugal effect. A rotating cantilever beam with large amplitude vibrations is first selected in order to highlight the main features of the method. Numerical results show that the method provides accurate reduced-order models (ROMs) for any rotation speed and vibration amplitude of interest with a single master mode, thus offering remarkable reduction in the computational burden. The hardening/softening transition of the fundamental flexural mode with increasing rotation speed is then investigated in detail and a ROM parametrised with respect to rotation speed and forcing frequencies is detailed. The method is then applied to a twisted plate model representative of a fan blade, showing how the technique can handle more complex structures. Hardening/softening transition is also investigated as well as interpolation of ROMs, highlighting the efficacy of the method.


Published on: June 1, 2023
Accepted on: April 11, 2023
Submitted on: December 6, 2022
Keywords: rotating structure,invariant manifold,geometric nonlinearity,nonlinear normal modes,[PHYS.MECA.VIBR]Physics [physics]/Mechanics [physics]/Vibrations [physics.class-ph],[PHYS.MECA.STRU]Physics [physics]/Mechanics [physics]/Structural mechanics [physics.class-ph]

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Archived | swh:1:dir:97292192b4790c2af01e25f4694d024561c5638c;origin=https://github.com/MORFEproject/MORFEInvariantManifold.jl;visit=swh:1:snp:cbd3f3eaf0dc99efb1d6bed706c3b4c3b67a1077;anchor=swh:1:rev:f56492ccd78890ee2b82970ae8941d6e39c0c147 1
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Martin, A., Opreni, A., Vizzaccaro, A., Debeurre, M., Salles, L., Frangi, A., Thomas, O., & Touzé, C. (2023). Accompanying data for the paper "Reduced order modeling of geometrically nonlinear rotating structures using the direct parametrisation of invariant manifolds" (1–) [dataset]. Zenodo. 10.5281/ZENODO.7924472

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