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

  • Arthur GivoisEmail author
  • Aurélien Grolet
  • Olivier Thomas
  • Jean-François Deü
Original paper
  • 24 Downloads

Abstract

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 the ROM. 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.

Keywords

Geometric nonlinearities Non-intrusive stiffness evaluation procedure Reduced-order finite element model Continuation method 

Notes

Acknowledgements

The French Ministry of Research is warmly thanked for the financial support of this study, through the Ph.D. Grant of the first author.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest

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Authors and Affiliations

  1. 1.Laboratoire d’Ingénierie des Systèmes Physiques et Numériques (LISPEN EA 7515)Arts et Métiers ParisTechLilleFrance
  2. 2.Laboratoire de Mécanique des Structures et des Systèmes Couplés (LMSSC EA 3196)Conservatoire National des Arts et MétiersParisFrance

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