Large scale modulation of high frequency acoustics fields in porous media

Claude Boutin (1) , Antoine Rallu , Stephane Hans (1)

1 DGCB - Département génie civil et batiment

We investigate, through a multi-scale asymptotic approach, high frequency acoustic fields of large correlation length in periodic porous media. High frequencies mean local dynamics at the pores scale, and therefore absence of scale separation in the usual sense of homogenization. However, as suggested by [Craster et al, PRSA, 2010], meanwhile the pressure is fast varying in the pores (according to periodic eigenmodes), the mode amplitude can present large scale modulation, hence introduces another type of scale separation on which the asymptotic procedure applies. The principle of this approach is first presented on a network of inter-connected Helmoltz resonators. The equations governing the modulations carried by a given eigenmode, at frequencies close to the eigenfrequency, are derived. Because of the local dynamic state, the number of cells on which the carrying periodic mode is defined, becomes a parameter. In a second part, this “multicell” procedure is extended to porous media saturated by a perfect gas. One obtains the whole family of large modulation phenomena, with a strict use of the “multi” periodicity condition. To conclude, this approach extracts, from the comprehensive Floquet-Bloch modal space, the particular frequency range enabling large modulations, therefore large correlation, of high frequency acoustic perturbations.

Mots clés: Floquet-Bloch mode; Multicell Homogenization; Porous media; Acoustics

Domaines: Acoustique [physics.class-ph]

Claude Boutin, Antoine Rallu, Stephane Hans. Large scale modulation of high frequency acoustics fields in porous media. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00810989⟩