Porous frame excitation by point sources in air and by stress circular and line sources –modes of air saturated porous frames - Propagation of Sound in Porous Media - page 182

mode related to the shear wave 3 λ/ 4 resonance. The compressional wave λ /4 resonance
will provide a more dominant contribution if the source height is increased, or if the
point source is replaced by a loudspeaker set at one or several meters above the porous
layer.

Appendix 8.A Coefficients r ij and M i,j

The coefficients r ij expressed with E = α 1 α 2 (µ 1 − µ 2 ) , F = α 1 ξ(µ 1 − µ 3 ) ,

G = α 2 ξ(µ 2 − µ 3 ) , L = α 3 E + ξ(F − G) , H ij = exp ( − jl(α i + α j )) are given by:

G) ] H 11
L

r 11 = [ α 3 E + ξ(F +

(8.A.1)

r 12 =− 2 ξF H 12
L

(8.A.2)

r 13 =− 2 ξE H 13
L

(8.A.3)

2 ξG H 21
L

r 21 = (8.A.4)

G) ] H 22
L

r 22 = [ α 3 E − ξ(F + (8.A.5)

r 23 =− 2 ξE H 23
L

(8.A.6)

r 31 =− 2 α 3 G H 31
L

(8.A.7)

r 32 = 2 α 3 F H 32
L

(8.A.8)

G) ] H 33
L

r 33 = [ α 3 E − ξ(F − (8.A.9)

Rµ j )k j ,B j The coefficients M i,j expressed with A j = (j/ω)(Q + = (j/ω) [ (P +

Qµ j )k j − 2 Nξ 2 ] ,C j = (jN/ω)(α 3 − ξ 2 ) are given by: (j/ω) 2 Nα j ξ ,and H =−

M 1 , 1 = C 1 ( 1 − r 11 ) − C 2 r 12 + Hr 13 (8.A.10)

M 1 , 2 =− C 1 r 21 + C 2 ( 1 − r 22 ) + Hr 23 (8.A.11)

M 1 , 3 =− C 1 r 31 − C 2 r 32 + H( 1 + r 33 )

(8.A.12)

M 2 , 1 =− jα 1 ( 1 − r 11 ) + jα 2 r 12 − jξr 13 (8.A.13)

M 2 , 2 =− jα 2 ( 1 − r 22 ) + jα 1 r 21 − jξr 23 (8.A.14)

M 2 , 3 = jα 1 r 31 + jα 2 r 32 − jξ( 1 + r 33 ) (8.A.15)

M 3 , 1 =− jµ 1 α 1 ( 1 − r 11 ) + jµ 2 α 2 r 12 − jµ 3 ξr 13 (8.A.16)

M 3 , 2 =− jµ 2 α 2 ( 1 − r 22 ) + jµ 1 α 1 r 21 − jµ 3 ξr 23 (8.A.17)

M 3 , 3 = jµ 1 α 1 r 31 + jµ 2 α 2 r 32 − jµ 3 ξ( 1 + r 33 ) (8.A.18)