Structural Engineering and Mechanics

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Vibrations of long repetitive structures by a double scale asymptotic method

  • Daya, E.M. (Laboratoire de Physique et Mecanique des Materiaux UMR CNRS 7554, Institut Superieur de Genie Mecanique et Productique Universite de Metz) ;
  • Potier-Ferry, M. (Laboratoire de Physique et Mecanique des Materiaux UMR CNRS 7554, Institut Superieur de Genie Mecanique et Productique Universite de Metz)
  • Published : 2001.08.25
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Abstract

In this paper, an asymptotic two-scale method is developed for solving vibration problem of long periodic structures. Such eigenmodes appear as a slow modulations of a periodic one. For those, the present method splits the vibration problem into two small problems at each order. The first one is a periodic problem and is posed on a few basic cells. The second is an amplitude equation to be satisfied by the envelope of the eigenmode. In this way, one can avoid the discretisation of the whole structure. Applying the Floquet method, the boundary conditions of the global problem are determined for any order of the asymptotic expansions.

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