[Modèle continu pour les modes de vibrations modulés des longues structures répétitives]
Grâce à la théorie de l'homogénéisation, on peut prédire les basses fréquences de vibrations des structures longues et répétitives. Pour des fréquences moyennes, beaucoup de modes ont une forme modulée. Nous présentons ici un modèle continu qui permet de prendre en compte cette classe de modes, grâce à la méthode des échelles multiples. Ce modèle dépend d'un paramètre réel qu'on peut calculer en résolvant par éléments finis des problèmes définis sur quelques cellules de base. Une application est présentée dans le cas de l'élasticité 2D.
By homogenization theory, one can predict the vibrations of long repetitive structures in the low frequency range. Beyond this range, many modes have a modulated shape. Based on a multiple scale analysis, a continuum model is presented, that is able to account for this class of modes. This model involves a real coefficient that can be computed from the finite element resolution of problems defined on a few basic cells. An application in 2D elasticity is presented.
Accepté le :
Publié le :
Mots-clés : mécanique des solides numérique, solides et structures
El Mostafa Daya 1 ; Bouazza Braikat 2 ; Noureddine Damil 2 ; Michel Potier-Ferry 1
@article{CRMECA_2002__330_5_333_0,
author = {El Mostafa Daya and Bouazza Braikat and Noureddine Damil and Michel Potier-Ferry},
title = {Continuum modeling for the modulated vibration modes of large repetitive structures},
journal = {Comptes Rendus. M\'ecanique},
pages = {333--338},
publisher = {Elsevier},
volume = {330},
number = {5},
year = {2002},
doi = {10.1016/S1631-0721(02)01464-X},
language = {en},
}
TY - JOUR AU - El Mostafa Daya AU - Bouazza Braikat AU - Noureddine Damil AU - Michel Potier-Ferry TI - Continuum modeling for the modulated vibration modes of large repetitive structures JO - Comptes Rendus. Mécanique PY - 2002 SP - 333 EP - 338 VL - 330 IS - 5 PB - Elsevier DO - 10.1016/S1631-0721(02)01464-X LA - en ID - CRMECA_2002__330_5_333_0 ER -
%0 Journal Article %A El Mostafa Daya %A Bouazza Braikat %A Noureddine Damil %A Michel Potier-Ferry %T Continuum modeling for the modulated vibration modes of large repetitive structures %J Comptes Rendus. Mécanique %D 2002 %P 333-338 %V 330 %N 5 %I Elsevier %R 10.1016/S1631-0721(02)01464-X %G en %F CRMECA_2002__330_5_333_0
El Mostafa Daya; Bouazza Braikat; Noureddine Damil; Michel Potier-Ferry. Continuum modeling for the modulated vibration modes of large repetitive structures. Comptes Rendus. Mécanique, Volume 330 (2002) no. 5, pp. 333-338. doi : 10.1016/S1631-0721(02)01464-X. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(02)01464-X/
[1] K. Jeblaoui, Analyse à deux échelles des vibrations de structures à forme répétitive ou presque répétitive. Thèse, Université de Metz, 1999
[2] Vibrating and Coupling Continuous Systems. Asymptotic Methods, Springer-Verlag, Berlin, 1989
[3] Continuum modeling for repetitive lattice structures, Appl. Mech. Rev., Volume 41 (1988), pp. 285-296
[4] Continuum modeling of lattice structures in large displacement. Applications to buckling analysis, Computers and Structures, Volume 68 (1998), pp. 181-189
[5] Composite and Reinforced Elements of Construction, Wiley, Chichester, 1992
[6] Homogenized thermoelastic model for a beam of a periodic structure, Internat. J. Engrg. Sci., Volume 37 (1999), pp. 631-642
[7] Vibrations of long repetitive structures by a double scale asymptotic method, Structural Engrg. Mech., Volume 12 (2001), pp. 215-230
- An efficient method for estimating the structural stiffness of flexible floating structures, Marine Structures, Volume 93 (2024), p. 103527 | DOI:10.1016/j.marstruc.2023.103527
- High frequency homogenization for a one-dimensional acoustic black hole lattice, Wave Motion, Volume 115 (2022), p. 103067 | DOI:10.1016/j.wavemoti.2022.103067
- A hybrid symplectic and high-frequency homogenization analysis for the dispersion property of periodic micro-structured thin plate structures, Applied Mathematical Modelling, Volume 93 (2021), p. 276 | DOI:10.1016/j.apm.2020.12.017
- Effective wave motion in periodic discontinua near spectral singularities at finite frequencies and wavenumbers, Wave Motion, Volume 103 (2021), p. 102729 | DOI:10.1016/j.wavemoti.2021.102729
- Homogenization Methods and Generalized Continua in Linear Elasticity, Encyclopedia of Continuum Mechanics (2020), p. 1231 | DOI:10.1007/978-3-662-55771-6_112
- Vibrations of nonlinear elastic lattices: low- and high-frequency dynamic models, internal resonances and modes coupling, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 476 (2020) no. 2236 | DOI:10.1098/rspa.2019.0532
- Homogenization Methods and Generalized Continua in Linear Elasticity, Encyclopedia of Continuum Mechanics (2019), p. 1 | DOI:10.1007/978-3-662-53605-6_112-1
- A rational framework for dynamic homogenization at finite wavelengths and frequencies, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 475 (2019) no. 2223, p. 20180547 | DOI:10.1098/rspa.2018.0547
- Inner Resonance in Media Governed by Hyperbolic and Parabolic Dynamic Equations. Principle and Examples, Generalized Models and Non-classical Approaches in Complex Materials 1, Volume 89 (2018), p. 83 | DOI:10.1007/978-3-319-72440-9_6
- Asymptotic analysis of high-frequency modulation in periodic systems. Analytical study of discrete and continuous structures, Journal of the Mechanics and Physics of Solids, Volume 117 (2018), p. 123 | DOI:10.1016/j.jmps.2018.04.014
- Influence of geometric and physical nonlinearities on the internal resonances of a finite continuous rod with a microstructure, Journal of Sound and Vibration, Volume 386 (2017), p. 359 | DOI:10.1016/j.jsv.2016.09.025
- A generalized theory of elastodynamic homogenization for periodic media, International Journal of Solids and Structures, Volume 84 (2016), p. 139 | DOI:10.1016/j.ijsolstr.2016.01.022
- On asymptotic elastodynamic homogenization approaches for periodic media, Journal of the Mechanics and Physics of Solids, Volume 88 (2016), p. 274 | DOI:10.1016/j.jmps.2015.12.020
- FEM formulation of homogenization method for effective properties of periodic heterogeneous beam and size effect of basic cell in thickness direction, Computers Structures, Volume 156 (2015), p. 1 | DOI:10.1016/j.compstruc.2015.04.010
- Effects of the local resonance in bending on the longitudinal vibrations of reticulated beams, Wave Motion, Volume 57 (2015), p. 1 | DOI:10.1016/j.wavemoti.2015.03.001
- Large scale modulation of high frequency waves in periodic elastic composites, Journal of the Mechanics and Physics of Solids, Volume 70 (2014), p. 362 | DOI:10.1016/j.jmps.2014.05.015
- Modelisation of modulated vibration modes of repetitive structures, Journal of Computational and Applied Mathematics, Volume 168 (2004) no. 1-2, p. 117 | DOI:10.1016/j.cam.2003.07.001
Cité par 17 documents. Sources : Crossref
Commentaires - Politique