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

2nd International Conference on Mathematical Modeling in Physical Sciences 2013

物理学;数学

Dupont, S.^1,2,3 ; Gazalet, J.^1,2,3 ; Kastelik, J.C.^1,2,3

Univ Lille Nord de France, F-59000 Lille, France^1

UVHC, IEMN-DOAE, F-59313 Valenciennes, France^2

CNRS, UMR 8520, F-59650 Villeneuve D'Ascq, France^3

关键词: Digital signal processing tools;    Mathematical expressions;    Periodic modulation;    Phononic band gaps;    Physical interpretation;    Physical meanings;    Second-order partial differential equation;    Waves in periodic media;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/490/1/012120/pdf
DOI  :  10.1088/1742-6596/490/1/012120

来源: IOP

【 摘 要 】

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.