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Reduced-order modeling of geometrically nonlinear rotating structures using the direct parametrisation of invariant manifolds

Article dans une revue avec comité de lecture
Author
MARTIN, Adrien
421305 Institut des Sciences de la Mécanique et Applications Industrielles [IMSIA]
OPRENI, Andrea
125443 Politecnico di Milano [Milan] [POLIMI]
ccVIZZACCARO, Alessandra
220393 University of Bristol [Bristol]
ccDEBEURRE, Marielle
543315 Laboratoire d’Ingénierie des Systèmes Physiques et Numériques [LISPEN]
SALLES, Loic
69530 Imperial College London
93075 Université de Liège = University of Liège = Universiteit van Luik = Universität Lüttich [ULiège]
475999 Département d’Aérospatiale et de Mécanique [Liège]
FRANGI, Attilio
125443 Politecnico di Milano [Milan] [POLIMI]
ccTHOMAS, Olivier
543315 Laboratoire d’Ingénierie des Systèmes Physiques et Numériques [LISPEN]
TOUZÉ, Cyril
421305 Institut des Sciences de la Mécanique et Applications Industrielles [IMSIA]

URI
http://hdl.handle.net/10985/25350
DOI
10.46298/jtcam.10430
Research data linked to this publication
https://zenodo.org/records/7924472
Date
2023-06
Journal
Journal of Theoretical, Computational and Applied Mechanics

Abstract

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.

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