Direct computation of nonlinear mapping via normal form for reduced-order models of finite element nonlinear structures
File(s)
Accepted version
Author(s)
Vizzaccaro, Alessandra
Shen, Yichang
Salles, Loic
Blahos, Jiri
Touze, Cyril
Type
Journal Article
Abstract
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 nonlinear mapping in order to derive accurate reduced-order models (ROM) relying on invariant manifold theory. The proposed reduction strategy is direct and simulation free, in the sense that it allows to pass from physical coordinates (FE nodes) to normal coordinates, describing the dynamics in an invariant-based span of the phase space. The number of master modes for the ROM is not a priori limited since a complete change of coordinate is proposed. The underlying theory ensures the quality of the predictions thanks to the invariance property of the reduced subspace, together with their curvatures in phase space that accounts for the non-resonant nonlinear couplings. The method is applied to a beam discretised with 3D elements and shows its ability in recovering internal resonance at high energy. Then a fan blade model is investigated and the correct prediction given by the ROMs are assessed and discussed. A method is proposed to approximate an aggregate value for the damping, that takes into account the damping coefficients of all the slave modes, and also using the Rayleigh damping model as input. Frequency–response curves for the beam and the blades are then exhibited, showing the accuracy of the proposed method.
Date Issued
2021-10-01
Date Acceptance
2021-05-21
Citation
Computer Methods in Applied Mechanics and Engineering, 2021, 384
ISSN
0045-7825
Publisher
Elsevier
Journal / Book Title
Computer Methods in Applied Mechanics and Engineering
Volume
384
Copyright Statement
© 2021 Elsevier B.V. All rights reserved
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000677395100006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Technology
Physical Sciences
Engineering, Multidisciplinary
Mathematics, Interdisciplinary Applications
Mechanics
Engineering
Mathematics
Reduced order modelling
Normal form
Geometric nonlinearities
Nonlinear mapping
LARGE-AMPLITUDE VIBRATIONS
NUMERICAL COMPUTATION
SPECTRAL SUBMANIFOLDS
PERIODIC VIBRATION
CYLINDRICAL-SHELLS
MODAL DERIVATIVES
REDUCTION
SYSTEMS
DYNAMICS
DECOMPOSITION
Publication Status
Published
Article Number
ARTN 113957
Date Publish Online
2021-06-12