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A mode matching approach for modeling two dimensional porous grating with infinitely rigid or soft inclusions
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10.1121/1.3693655
/content/asa/journal/jasa/131/5/10.1121/1.3693655
http://aip.metastore.ingenta.com/content/asa/journal/jasa/131/5/10.1121/1.3693655

Figures

Image of FIG. 1.
FIG. 1.

Geometry of the periodic cell.

Image of FIG. 2.
FIG. 2.

Details of two rigid-soft interfaces. With one periodic inclusion (a), with two periodic inclusions (b).

Image of FIG. 3.
FIG. 3.

Convergence of the proposed method for a small (a/d = 0.25, – –) and larger inclusion size. The black lines stand for the normal incidence and the gray ones for θ = π/3. The black ▪-markers stand for the rigid inclusion (see on the right) and the gray -markers for the RGW2 porous inclusion (see on the left).

Image of FIG. 4.
FIG. 4.

(Color online) Pressure modulus with the layered rigid circular inclusions at 2674 Hz (first absorption peak of Fig. 5). The horizontal lines stand for the layer interfaces.

Image of FIG. 5.
FIG. 5.

Comparison and illustration of the proposed method with circular inclusions (a = 1.5 cm) on a 2 × 2 cm cell with 11 Layers. — homogeneous Fireflex material, homogeneous RGW2 material, • circular rigid inclusion, –·– circular rigid inclusion from Ref. 10, circular RGW2 inclusion.

Image of FIG. 6.
FIG. 6.

Schematic description of the experimental setup with the square section.

Image of FIG. 7.
FIG. 7.

(Color online) Picture of the experimental setup before total beads and inclusions filling.

Image of FIG. 8.
FIG. 8.

Comparison between simulations (solid line) and measurements (dotted line) for square shape inclusion ( + ) and homogeneous beads .

Image of FIG. 9.
FIG. 9.

Effect of the size a of a square inclusion on the absorption coefficient. The inclusion size ranges from 1 to 18 mm in 1 mm step. (——) stands for the upper bound (18 mm) of the variation interval. The reference homogeneous metal foam absorption is denoted by (––) and the RGW2 wool by (–⋅–). (a) Rigid inclusion, (b) Air inclusion, and (c) RGW2 porous inclusion.

Image of FIG. 10.
FIG. 10.

(a) Influence of the elementary cell period d and(b) of the inclusions height t 2 on the absorption coefficient with rigid square inclusions (with a = 15 mm) grating. The homogeneous metal foam absorption is denoted by (––) in normal incidence. In all cases, (——) stands for the upper bound of the variation interval.

Image of FIG. 11.
FIG. 11.

Effect of the angle of incidence (θ from 0 by 10 to 80°) on the absorption coefficient of a proous layer with rigid square inclusions (with a = 15 mm). The homogeneous metal foam material is denoted by (——) in normal incidence and by (–⋅–) for θ = 80°. The upper bound of the variation interval (80°) is denoted by (––).

Image of FIG. 12.
FIG. 12.

Effect on the absorption coefficient of the orientation of a rigid inclusion embedded in the metal foam (a = 10 mm, thickness 1 mm). The stand for the , the (×) for the and the ( + ) for the orientation. The homogeneous metal foam absorption is denoted by (——).

Tables

Generic image for table
TABLE I.

Material properties used in numerical tests. With the porosity φ, flow resistivity σ, the tortuosity α inf, the viscous and thermal characteristic lengths and .

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/content/asa/journal/jasa/131/5/10.1121/1.3693655
2012-05-04
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A mode matching approach for modeling two dimensional porous grating with infinitely rigid or soft inclusions
http://aip.metastore.ingenta.com/content/asa/journal/jasa/131/5/10.1121/1.3693655
10.1121/1.3693655
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