On the frequency response computation of geometrically nonlinear flat structures using reduced-order finite element models - Archive ouverte HAL
Article Dans Une Revue Nonlinear Dynamics Année : 2019

On the frequency response computation of geometrically nonlinear flat structures using reduced-order finite element models

Résumé

This paper presents a general methodology to compute nonlinear frequency responses of flat structures subjected to large amplitude transverse vibrations, within a finite element context. A reduced-order model (ROM)is obtained by an expansion onto the eigenmode basis of the associated linearized problem, including transverse and in-plane modes. The coefficients of the nonlinear terms of the ROM are computed thanks to a non-intrusive method, using any existing nonlinear finite element code. The direct comparison to analytical models of beams and plates proves that a lot of coefficients can be neglected and that the in-plane motion can be condensed to the transverse motion, thus giving generic rules to simplify theROM. Then, a continuation technique, based on an asymptotic numerical method and the harmonic balance method, is used to compute the frequency response in free (nonlinear mode computation) or harmonically forced vibrations. The whole procedure is tested on a straight beam, a clamped circular plate and a free perforated plate for which some nonlinear modes are computed, including internal resonances. The convergence with harmonic numbers and oscillators is investigated. It shows that keeping a few of them is sufficient in a range of displacements corresponding to the order of the structure’s thickness, with a complexity of the simulated nonlinear phenomena that increase very fast with the number of harmonics and oscillators.
Fichier principal
Vignette du fichier
LISPEN_NDYN_2019_THOMAS.pdf (4.13 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02289755 , version 1 (17-09-2019)

Licence

Identifiants

Citer

Arthur Givois, Aurelien Grolet, Olivier Thomas, Jean-François Deü. On the frequency response computation of geometrically nonlinear flat structures using reduced-order finite element models. Nonlinear Dynamics, 2019, 97 (2), pp.1747-1781. ⟨10.1007/s11071-019-05021-6⟩. ⟨hal-02289755⟩
172 Consultations
212 Téléchargements

Altmetric

Partager

More