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International Journal for Multiscale Computational Engineering
Facteur d'impact: 1.016 Facteur d'impact sur 5 ans: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Imprimer: 1543-1649
ISSN En ligne: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2011002351
pages 515-528


Celine Chesnais
École Nationale des Travaux Publics de l'État, Université de Lyon, DGCB, FRE CNRS 3237, Lyon, France
S. Hans
École Nationale des Travaux Publics de l'État, Université de Lyon, DGCB, FRE CNRS 3237, Lyon, France
Claude Boutin
École Nationale des Travaux Publics de l'État, Université de Lyon, DGCB, FRE CNRS 3237, Lyon, France


This paper deals with the dynamic behavior of periodic reticulated beams made of symmetric unbraced framed cells. Such archetypical cells can present a high contrast between shear and compression deformabilities that opens the possibility of enriched local kinematics. Through the homogenization method of periodic discrete media associated with a systematic use of scaling, the existence of atypical gyration modes is established theoretically. These latter modes appear when the elastic moment is balanced by the rotation inertia, conversely to "natural" modes where the elastic force is balanced by the translation inertia. A generalized beam modeling including both "natural" and gyration modes is proposed and discussed through a dimensional analysis. The results are confirmed on numerical examples.


  1. Boutin, C. and Hans, S., Homogenisation of periodic discrete medium: Application to Dynamics of framed structures. DOI: 10.1016/S0266-352X(03)00005-3

  2. Boutin, C., Hans, S., Ibraim, E., and Roussillon, P., In situ experiments and seismic analysis of existing buildings. Part II. DOI: 10.1002/eqe.503

  3. Boutin, C., Hans, S., and Chesnais, C., Generalized beams and continua. Dynamics of reticulated structures. DOI: 10.1007/978-1-4419-5695-8_14

  4. Caillerie, D., Trompette, P., and Verna, P., Homogenisation of periodic trusses.

  5. Chesnais, C., Dynamique de milieux réticulés non contreventés.

  6. Chesnais, C., Hans, S., and Boutin, C., Wave propagation and diffraction in discrete structures: Effect of anisotropy and internal resonance. DOI: 10.1002/pamm.200700875

  7. Cioranescu, D. and Saint Jean Paulin, J., Homogenization of Reticulated Structures, Applied Mathematical Sciences.

  8. Eringen, A. C., Mechanics of micromorphic continua.

  9. Hans, S. and Boutin, C., Dynamics of discrete framed structures: A unified homogenized description. DOI: 10.2140/jomms.2008.3.1709

  10. Kerr, A. D. and Accorsi, M. L., Generalization of the equations for frame-type structures–a variational approach. DOI: 10.1007/BF01306024

  11. Moreau, G. and Caillerie, D., Continuum modeling of lattice structures in large displacement applications to buckling analysis. DOI: 10.1016/S0045-7949(98)00041-8

  12. Noor, A. K., Continuum modeling for repetitive lattice structures. DOI: 10.1115/1.3151907

  13. Sanchez-Palencia, E., Non-Homogeneous Media and Vibration Theory, Lecture Note in Physics. DOI: 10.1007/3-540-10000-8

  14. Skattum, K. S., Dynamic analysis of coupled shear walls and sandwich beams.

  15. Tollenaere, H. and Caillerie, D., Continuous modeling of lattice structures by homogenization. DOI: 10.1016/S0965-9978(98)00034-9