Soundproof structure body
Provided is a soundproof structure body including an opening member that forms an opening tube line having a cross-sectional area S, and at least two resonance structures for sound waves that are installed inside the opening tube line, and in a case where a cross-sectional area of the resonance structure is defined as Si, a width thereof is defined as di, an interval between the two resonance structures is defined as L, an impedance of the two resonance structures is defined as Zi, and a synthetic acoustic impedance is defined as Zc, a condition of Expression (1) is satisfied at a resonance frequency f0 at which a theoretical absorption value At is a maximum value. This soundproof structure body can realize high absorption using a plurality of resonance structures. At ( f 0, L, S, Si, di, Zi )>0.75 (1), Here, L>0, S>0, Si (i=1, 2)>0, di (i=1, 2)>0
1. A soundproof structure body comprising:
an opening member that forms an opening tube line having a cross-sectional area S; and
at least two resonance structures for sound waves that are installed inside the opening tube line,
wherein a cross-sectional area Si (i=1, 2, . . . , where the resonance structure having a smaller i number is located on an upstream side) in the opening tube line and a width di (i=1, 2, . . . ) of the resonance structure in a waveguide forward direction are more than 0,
at least two resonance structures among the resonance structures are installed to be spaced apart at an interval L (L>0) from each other, and
in a case where an impedance of each of the two resonance structures installed to be spaced apart at the interval L from each other is defined as Zi (i=1, 2), and
a synthetic acoustic impedance, in which the two resonance structures and the interval thereof, a change in the cross-sectional area in the waveguide forward direction, and the two resonance structures are considered, is defined as Zc,
a condition of Expression (1) is satisfied at a resonance frequency f0 at which a theoretical absorption value At given by Expression (2) is a maximum value,
At ( f 0, L, S, Si, di, Zi )>0.75 (1),
where, in a case where L>0, S>0, Si(i=1, 2)>0, di(i=1, 2)>0,
and, f, L, S, Si, di, Zi (i=1, 2) is represented by x,
At ( x )=1−|( Zc ( x )− Z 0)/( Zc ( x )+ Z 0)| 2 −|2/( Ac ( x )+ Bc ( x )/ Z 0+ Z 0 Cc ( x )+ Dc ( x ))| 2 (2),
where, the synthetic acoustic impedance Zc(x) is defined by Expression (3)
Zc
(
x
)
=
Z
0
A
C
(
x
)
+
B
C
(
x
)
Z
0
C
C
(
x
)
+
D
C
(
x
)
,
(
3
)
in Expression (3), Z0 is an acoustic impedance of an opening tube line represented by Zair/S(=Z0) (S is a tube line cross-sectional area),
Zair denotes an acoustic impedance of air and is given by Zair=ρc, ρ denotes a density of air, and c denotes a speed of sound,
Ac(x), Bc(x), Cc(x), and Dc(x) are elements of a synthetic transfer matrix, and are defined by Expression (4), and
in Expression (4), Tc is a synthetic transfer matrix of the two resonance structures
T
C
=
T
d
1
/
2
T
1
T
d
1
/
2
T
L
-
d
1
/
2
-
d
2
/
2
T
d
2
/
2
T
2
T
d
2
/
2
=
(
A
C
(
x
)
B
C
(
x
)
C
C
(
x
)
D
C
(
x
)
)
,
(
4
)
T i (i=1, 2) is a transfer matrix corresponding to a resonance structure in each of the two resonance structures, and is defined by Expression (5)
T
i
=
(
1
0
1
Z
1
1
)
,
(
5
)
T di/2 is a transfer matrix corresponding to a distance of a resonance structure in each of the two resonance structures, and is defined by Expression (6)
T
d
i
/
2
=
(
cos
k
d
2
i
Z
air
s
-
s
i
sin
k
d
2
i
s
-
s
i
Z
air
sin
k
d
2
cos
k
d
2
)
(
i
=
1
,
2
)
,
(
6
)
and
T L-d1/2-d2/2 is a transfer matrix corresponding to a distance between the two resonance structures and is defined by Expression (7)
T
L
-
d
1
/
2
-
d
2
/
2
=
(
cos
k
(
L
-
d
1
2
-
d
2
2
)
i
Z
air
s
sin
k
(
L
-
d
1
2
-
d
2
2
)
i
s
Z
air
sin
k
(
L
-
d
1
2
-
d
2
2
)
cos
k
(
L
-
d
1
2
-
d
2
2
)
)
.
(
7
)
2. The soundproof structure body according to claim 1 , wherein a resonance frequency of the resonance structure located on the upstream side in the waveguide forward direction is set to be different from a resonance frequency of the resonance structure located on a downstream side, out of the two resonance structures.
3. The soundproof structure body according to claim 1 , wherein a resonance frequency of the resonance structure located on the upstream side in the waveguide forward direction is higher than a resonance frequency of the resonance structure located on a downstream side, out of the two resonance structures.
4. The soundproof structure body according to claim 1 , wherein in a case where a wavelength of the resonance frequency f0 is denoted by λ(f0), the interval L satisfies L<λ(f0)/4.
5. The soundproof structure body according to claim 1 , wherein the two resonance structures are integrated.
6. The soundproof structure body according to claim 1 , wherein the at least two resonance structures are three or more resonance structures.
7. The soundproof structure body according to claim 1 , wherein at least one resonance structure of the at least two resonance structures is a Helmholtz resonance structure.
8. The soundproof structure body according to claim 1 , wherein at least one resonance structure of the at least two resonance structures is a film resonance structure.
9. The soundproof structure body according to claim 1 , wherein at least one resonance structure of the at least two resonance structures is an air column resonance structure.
10. The soundproof structure body according to claim 1 , wherein with respect to a wavelength λ(f0) of a frequency satisfying Expression (1),
the cross-sectional area S of the opening tube line satisfies S<π(λ/2) 2 .