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Article Dans Une Revue Journal of Physics: Conference Series Année : 2014

Waves in periodic media : Fourier analysis shortcuts and physical insights, case of 2D phononic crystals

Résumé

Phononic crystal is a structured media with periodic modulation of its physical properties that influences the propagation of elastic waves and leads to a peculiar behaviour, for instance the phononic band gap effect by which elastic waves cannot propagate in certain frequency ranges. The formulation of the problem leads to a second order partial differential equation with periodic coefficients; different methods exist to determine the structure of the eigenmodes propagating in the material, both in the real or Fourier domain. Brillouin explains the periodicity of the band structure as a direct result of the discretization of the crystal in the real domain. Extending the Brillouin vision, we introduce digital signal processing tools developed in the frame of distribution functions theory. These tools associate physical meaning to mathematical expressions and reveal the correspondence between real and Fourier domains whatever is the physical domain under consideration. We present an illustrative practical example concerning two dimensions phononic crystals and highlight the appreciable shortcuts brought by the method and the benefits for physical interpretation. ©2014 IOP Publishing
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Origine : Publication financée par une institution
Licence : CC BY - Paternité

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hal-00961500 , version 1 (13-07-2022)

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Samuel Dupont, Joseph Gazalet, Jean-Claude Kastelik. Waves in periodic media : Fourier analysis shortcuts and physical insights, case of 2D phononic crystals. Journal of Physics: Conference Series, 2014, 2nd International Conference on Mathematical Modeling in Physical Sciences 2013 (IC-MSQUARE 2013) 1–5 September 2013, Prague, Czech Republic, 490 (1), pp.012120. ⟨10.1088/1742-6596/490/1/012120⟩. ⟨hal-00961500⟩
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