Civil Engineering Reference
In-Depth Information
4.10.2 Impedance
The quantities
K
and
ρ
having been evaluated, the impedance
Z(M
2
)
at normal incidence
can be calculated in the same way as in the case where the pores are perpendicular to
the surface. This impedance is given by
j
Z
c
Z(M
2
)
=−
φ
cot g
kd
(4.160)
Z
c
and
k
being respectively
Z
c
=
(Kρ)
1
/
2
(4.161)
k
=
ω(ρ/K)
1
/
2
(4.162)
Appendix 4.A Important Expressions
Description on the microscopic scale
Relations between, pressure, velocity, temperature, Eqs. (4.1) -(4.4)
ρ
0
∂
∂t
=−∇
p
+
η
υ
, with the boundary condition at the air-frame interface
υ
=
0
ρ
0
c
p
∂τ
∂p
∂t
, with the boundary condition at the air-frame interface
τ
2
τ
∂t
=
κ
∇
+
=
0.
State equation, Eq. (4.29)
P
o
ρ
o
T
o
[
ρ
o
τ
p
=
+
T
o
ξ
]
Effective density and bulk modulus
Effective density,
∂p
∂x
3
1
jωυ
3
,
Equation
(
4
.
38
)
ρ
=−
Bulk modulus
p/
¯
K
=−
∇
u
,
Equation
(
4
.
39
)
Connection between the bulk modulus and the effective density
ρ
=
ρ
o
/F(ω),
Equation
(
4
.
45
)
1
)F(B
2
ω)
]
,
Equation
(
4
.
46
)
K
=
γP
o
/
[
γ
−
(γ
−
Low-frequency limit:
φσ
jω
+
ρ
=
cte,
Equation
(
4
.
85
),(
4
.
97
)
γP
0
γ
−
j(γ
−
1
)ωB
2
ρ
0
/(φσ)
,
Equation
(
4
.
102
)
K
=
