Comptes Rendus
A two scale method for modulated vibration modes of large, nearly repetitive, structures
Comptes Rendus. Mécanique, Volume 331 (2003) no. 6, pp. 443-448.

Nearly repetitive structures can present at least two kinds of vibration modes: localized modes and modulated ones. In this Note, the multiple scale method is applied to characterize a packet of modulated modes. In this respect, only small size problems are to be solved: periodic problems posed on a few basic cells and amplitude equations, which define a sort of homogenized model for this type of modes. It is established that the influence of the non-repetitive part of the structure is accounted by a boundary condition.

Les structures à forme presque répétitive peuvent avoir au moins deux types de modes, localisés ou modulés. Dans cette Note, la méthode des échelles multiples est appliquée pour caractériser un paquet de modes modulés. Pour cela, on n'a à résoudre que des problèmes de petite taille : des problèmes périodiques posés sur quelques cellules de base et des équations d'amplitudes, qui définissent une sorte de modèle homogénéisé pour ce type de modes. On montre que l'influence de la partie non répétitive de la structure est prise en compte par une condition aux limites.

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DOI: 10.1016/S1631-0721(03)00093-7
Keywords: Computational solid mechanics, Solids and structures
Mot clés : Mécanique des solides numérique, Solides et structures

El Mostafa Daya 1; Khalid Jeblaoui 1; Michel Potier-Ferry 1

1 Laboratoire de physique et mécanique des matériaux, UMR CNRS 7554, Université de Metz, ISGMP, Ile du Saulcy, 57045 Metz cedex 01, France
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El Mostafa Daya; Khalid Jeblaoui; Michel Potier-Ferry. A two scale method for modulated vibration modes of large, nearly repetitive, structures. Comptes Rendus. Mécanique, Volume 331 (2003) no. 6, pp. 443-448. doi : 10.1016/S1631-0721(03)00093-7. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00093-7/

[1] K. Jeblaoui, Analyse à deux échelles des vibrations de structures à forme répétitive ou presque répétitive, Thèse, Université de Metz, 1999

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[3] J. Sanchez-Hubert; E. Sanchez-Palencia Vibrating and Coupling Continuous Systems, Asymptotic Methods, Springer-Verlag, Berlin, 1989

[4] E.M. Daya; M. Potier-Ferry Vibrations of long repetitive structures by a double scale asymptotic method, Structural Engrg. Mech., Volume 12 (2001), pp. 215-230

[5] E.M. Daya; B. Braikat; N. Damil; M. Potier-Ferry Continuum modeling for the modulated vibration modes of large repetitive structures, C. R. Mecanique, Volume 330 (2002), pp. 333-338

[6] D.W. Jordan; P. Smith Non-linear Ordinary Differential Equations, Clarendon Press, Oxford, 1987

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