07 sound absorbing materials · 2021. 2. 4. · dunder hood applications for engine noise dvehicle...
TRANSCRIPT
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D. W. Herrin, Ph.D., P.E. University of Kentucky
Department of Mechanical Engineering
Sound Absorbing Materials
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
2 Dept. of Mech. Engineering University of Kentucky
Overview
The Basics Impedance and Absorption
Transfer Matrix Approach Flow Resistivity
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
3 Dept. of Mech. Engineering University of Kentucky
Relatively massive, stiff barrier having high damping
Most sound is reflected
Some sound is transmitted
Less sound is reflected
Less sound is transmitted
( These two objectives can be combined)
Sound Blocking Versus Sound Absorption
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
4 Dept. of Mech. Engineering University of Kentucky
Bedroom Noisy family or playroom
Ways to reduce noise level in the bedroom:
Which use sound blocking and which use sound absorption?
Example
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
5 Dept. of Mech. Engineering University of Kentucky
Sound Absorbing Materials
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
6 Dept. of Mech. Engineering University of Kentucky
NVH Applications Driven by Auto Industry
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
7 Dept. of Mech. Engineering University of Kentucky
Sound Absorbing Materials in Car
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
8 Dept. of Mech. Engineering University of Kentucky
a: fully reticulated plastic foam (x14)
b: partially reticulated
plastic foam (x14) c: glass fiber (x14) d: mineral (rock) wool (x14)
Examples of Sound Absorbing Materials
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
9 Dept. of Mech. Engineering University of Kentucky
Foams are made of various materials including polyurethane, polyethylene, and polypropylene. Foams are created by pouring premixed liquid products onto a conveyor and allowing the chemical process to create cells (voids) of various size as the foam cures and hardens. Similar to bread rising. If the cell walls are fractured, the foam is called “open cell” If the cell walls remain intact, the foam is called “closed cell” Coverings such vinyl, aluminum, urethane, or aluminized mylar protect the surface, improve appearance, and reduce absorption of liquids, dirt, etc. Coverings may also act as a barrier, e.g., loaded vinyl
Foam Manufacture and Foam Types
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
10 Dept. of Mech. Engineering University of Kentucky
Suspended baffles in gymnasiums or factories Under hood applications for engine noise Vehicle interiors Inside building walls – improves transmission loss Inside office and computer equipment – reduces reverberant buildup of sound Ceiling tiles and carpeting HVAC applications – duct liner
Applications of Sound Absorbing Materials
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
11 Dept. of Mech. Engineering University of Kentucky
Sound is “absorbed” by converting sound energy to heat within the material, resulting in a reduction of the sound pressure. Two primary mechanisms:
vibration of the material skeleton - damping friction of the fluid on the skeleton - viscosity
Mechanisms of Sound Absorption
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
12 Dept. of Mech. Engineering University of Kentucky
Vibration of the material matrix is caused by sound pressure and velocity fluctuations within the material. Damping of the material converts sound to heat. Important for light materials at low frequencies. Difficult to model and measure (ignored here)
Vibration of Material Skeleton
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
13 Dept. of Mech. Engineering University of Kentucky
The oscillating fluid particles within the material rub against the matrix and create heat by friction (viscosity). Primary material parameters affecting absorption: porosity (fraction of air volume in the material) structure factor (orientation of fibers, tortuosity) flow resistance
Friction of the Fluid on the Skeleton
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
14 Dept. of Mech. Engineering University of Kentucky
Overview
The Basics Impedance and Absorption
Transfer Matrix Approach Flow Resistivity
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
15 Dept. of Mech. Engineering University of Kentucky
The wave component within the material parallel to the surface is attenuated rapidly
The material is similar to a set of rigid-wall, parallel capillaries
The particle velocity un in the material is normal to the surface and only a function of the local sound pressure ps at the surface (un is independent of the form of the incident wave)
The Local Reaction Model
un
φ
φ ps
pi
pr
n
s
upz = (independent of pi)
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
16 Dept. of Mech. Engineering University of Kentucky
Specific Boundary Impedance
resistance reactance
(named in honor of Lord Rayleigh)
Absorption coefficient:
jxrupzn
+==surface
raylsmkgmsPa 12
1 ≡=−−
−Units:
( )IncidentEnergySoundAbsorbedEnergySound
=φα
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
17 Dept. of Mech. Engineering University of Kentucky
un jkxAe−
jkxBe+
R is called the pressure reflection coefficient
Specific Boundary Impedance
p, un
x = 0 ( )( )ABABc
cBABA
upz o
o
xnn −
+=
⎟⎟⎠
⎞⎜⎜⎝
⎛ −
+==
=11
0
ρ
ρ
RR
cz
o
n
−
+=11
ρ
ABR =
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
18 Dept. of Mech. Engineering University of Kentucky
While the specific boundary impedance is independent of angle of incidence, the absorption coefficient is not:
An angle of maximum absorption exists:
The maximum absorption here is:
Absorption Coefficient and Impedance
( )( ) ( ) c
xxcrr
xrr
o
nn
o
nn
nn
n
ρρφφφ
φα =ʹ′=ʹ′ʹ′+ʹ′+
ʹ′= where
coscos1cos4
22
( ) ( ) ⎟⎠⎞⎜
⎝⎛ ʹ′+ʹ′= − 221max cos nn xrφ
( )nnn
rzrʹ′+ʹ′
ʹ′=
2maxα
( ) 10 →°α 1→ʹ′nr 0→ʹ′nxif and
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
19 Dept. of Mech. Engineering University of Kentucky
Example Impedance of Foam
-6
-4
-2
0
2
4
6
8
0 1000 2000 3000 4000
Frequency (Hz)
Dim
ensi
onle
ss B
ound
ary
Impe
danc
e
Resistance r'Reactance x'
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
20 Dept. of Mech. Engineering University of Kentucky
Example Sound Absorption Coefficient
0
0.2
0.4
0.6
0.8
1
0 1000 2000 3000 4000Frequency (Hz)
Abso
rptio
n C
oeffi
cien
t
phi = 0 degreesphi = 30 degreesphi = 60 degrees
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
21 Dept. of Mech. Engineering University of Kentucky
0
0.2
0.4
0.6
0.8
1
0 1000 2000 3000 4000Frequency (Hz)
Abs
orpt
ion
Coe
ffici
ent
Glass Fiber
Common Glass Fiber
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
22 Dept. of Mech. Engineering University of Kentucky
Closed Cell vs. Open Cell Foam
0
0.2
0.4
0.6
0.8
1
0 1000 2000 3000 4000 5000Frequency (Hz)
Abs
orpt
ion
Coe
ffici
ent
Closed Cell FoamOpen Cell Foam
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
23 Dept. of Mech. Engineering University of Kentucky
Closed-cell Open-cell
Foam Absorbers must be Open Cell
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
24 Dept. of Mech. Engineering University of Kentucky
0
0.2
0.4
0.6
0.8
1
0 1000 2000 3000 4000 5000
Frequency (Hz)
Abs
orpt
ion
Coe
ffici
ent
2 in. thick
1 in. thick
glass fiber
Effect of Thickness
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
25 Dept. of Mech. Engineering University of Kentucky
cover
Effect of Covering an Absorber
0
0.2
0.4
0.6
0.8
1
0 500 1000 1500 2000
Frequency (Hz)
Abs
orpt
ion
Coe
ffici
ent
Foam without Cover
Foam with Cover
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
26 Dept. of Mech. Engineering University of Kentucky
0
0.2
0.4
0.6
0.8
1
0 500 1000 1500 2000
Frequency (Hz)
Abso
rptio
n C
oeffi
cien
t
2” 1.4”
2”
air gap
Layering of Materials
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
27 Dept. of Mech. Engineering University of Kentucky
vibrating surface
Lining of Partial Enclosures
40
50
60
70
80
90
100
0 1000 2000 3000 4000 5000
Frequency (Hz)
Soun
d Po
wer
Lev
el (d
B)
No Absorption (108.2 dBA)
With Absorption (97.6 dBA)
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
28 Dept. of Mech. Engineering University of Kentucky
Placement of material is often flexible
Plexiglass enclosure
loudspeaker
Full Enclosure
50
55
60
65
70
75
80
85
90
95
100
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000Frequency (Hz)
SP
L (d
B)
Top and BottomFront and RearSidesEmpty
-
Sound Absorption by Porous Materials
Noise and Vibration Short Course
29 Dept. of Mech. Engineering University of Kentucky
Overview
The Basics Impedance and Absorption
Transfer Matrix Approach Flow Resistivity
-
Sound Absorption by Porous Materials
Noise and Vibration Short Course
Plane waves in a porous material: amplitude decreases with distance p and u are not in phase characteristic impedance z’c is a complex number wave number k’ is a complex number
x
xkjoePxp
ʹ′−=)(
czxuxp
ʹ′=)()(
complex
γβ jk −='
Attenuation constant (responsible for wave attenuation)
Sound Propagation – Porous Material
30 Dept. of Mech. Engineering University of Kentucky
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
The sound pressure p and the particle velocity v are the acoustic state variables
any acoustic component
1
2
p1, u1
p2, u2
For any passive, linear component:
Transfer, transmission, or four-pole matrix (A, B, C, and D depend on the component)
The Basic Idea
p1 = Ap2 +BS2u2S1u1 =Cp2 +DS2u2
p1S1u1
!"#
$#
%&#
'#= A B
C D
(
)*
+
,-
p2S2u2
!"#
$#
%&#
'#
or
31 Dept. of Mech. Engineering University of Kentucky
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
p1, u1 p2 ,u2
S
L
A B
(x = 0) (x = L)
Solve for A, B in terms of p1, u1 then put into equations for p2, u2.
(note that the determinant A1D1-B1C1 = 1)
must have plane waves
The Straight Tube
p x( ) = Ae− jkx +Be+ jkx u x( ) = −1jkρoc
dpdx
p 0( ) = p1 = A+B
u 0( ) = u1 =A−Bρoc
p L( ) = p2 = Ae− jkL +Be+ jkL
u L( ) = u2 =Ae− jkL −Be+ jkL
ρocp1 = p2 cos kL( )+u2 jρoc( )sin kL( )u1 = p2 j ρoc( )sin kL( )+u2 cos kL( )
p1S1u1
"#$
%$
&'$
($=
cos kL( ) jρocS2
sin kL( )
jS1ρoc
sin kL( ) S1S2cos kL( )
)
*
+++++
,
-
.
.
.
.
.
p2S2u2
"#$
%$
&'$
($
32 Dept. of Mech. Engineering University of Kentucky
-
Sound Absorption by Porous Materials
Noise and Vibration Short Course
L
k’,zc
(complex wave number and complex characteristic impedance)
Straight Tube with Absorptive Material
p1S1u1
!"#
$#
%&#
'#=
cos k 'L( ) jzcS2sin k 'L( )
jS1zcsin k 'L( ) S1
S2cos k 'L( )
(
)
*****
+
,
-----
p2S2u2
!"#
$#
%&#
'#
33 Dept. of Mech. Engineering University of Kentucky
-
Sound Absorption by Porous Materials
Noise and Vibration Short Course
Transfer Matrix Approach
piSui
!
"##
$
%&&=
Ai BiCi Di
!
"##
$
%&&
pi+1Sui+1
!
"##
$
%&&
[ ] [ ][ ][ ] [ ] ⎥⎦
⎤⎢⎣
⎡==
TT
TTntotal DC
BAT...TTTT 321
Layer 1 Layer 2 Perforate Layer n Z = p1u1=SATCT
For each layer:
air air
Plane Wave Assumption
Overall:
34 Dept. of Mech. Engineering University of Kentucky
-
Sound Absorption by Porous Materials
Noise and Vibration Short Course
35 Dept. of Mech. Engineering University of Kentucky
0
0.2
0.4
0.6
0.8
1
0 500 1000 1500
Frequency (Hz)
Abs
orpt
ion
Coe
ffici
ent
Predicted
Measured
Example - Layered Materials
51 36 51
Units: mm
-
Sound Absorption by Porous Materials
Noise and Vibration Short Course
36 Dept. of Mech. Engineering University of Kentucky
Overview
The Basics Impedance and Absorption
Transfer Matrix Approach Flow Resistivity
-
Sound Absorption by Porous Materials
Noise and Vibration Short Course
37 Dept. of Mech. Engineering University of Kentucky
Bulk k’ and z’c
Surface z and α
Layered z and α
Designing the Absorber from Scratch
????
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
38 Dept. of Mech. Engineering University of Kentucky
Absorption Coefficient vs. Frequency
(Mechel, 1988)
Different densities and thicknesses
Frequency (Hz)
αo
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
39 Dept. of Mech. Engineering University of Kentucky
Flow Resistivity and Absorption
αo
ρof/σ
-
Sound Absorption by Porous Materials
Noise and Vibration Short Course
40 Dept. of Mech. Engineering University of Kentucky
Flow Resistance and Flow Resistivity σ
Vacuum source
u (velocity)
ΔP Sample (thickness t )
Flow resistance:
uPrs
Δ=
Flow resistivity:
trs=σ
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
41 Dept. of Mech. Engineering University of Kentucky
Vacuum pump Flow Meter
Valve Specimen
Pipe Manometer
Specimen Holder
Specimen
Valve Flow Meters
Manometers Pump
ASTM C522-03
Flow Resistance Measurement
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Sound Absorption by Porous Materials
Noise and Vibration Short Course
42 Dept. of Mech. Engineering University of Kentucky
φ
φ
pi
pr
Absorption Coefficient
α φ( ) =sound energy absorbedsound energy incident
-
Sound Absorption by Porous Materials
Noise and Vibration Short Course
43 Dept. of Mech. Engineering University of Kentucky
Flow Resistivity
Abs
orpt
ion
Coe
ffici
ent
solid fluid
Absorption Coefficient and Flow Resistivity
σ tρc
≈ 2
-
Sound Absorption by Porous Materials
Noise and Vibration Short Course
44 Dept. of Mech. Engineering University of Kentucky
Three Empirical Models
732.0754.0
595.0700.0
087.0)0571.01(189.0)0978.01(
−−
−−
−+=ʹ′
−+=ʹ′
XjXzzXjXkk
oc
Delaney and Bazly, 1970 – fibrous materials; f = 250-4000 Hz; σ = ?; 0.012 < X < 1.21
607.0548.0
592.0554.0
105.0)209.01(163.0)188.01(
−−
−−
−+=ʹ′
−+=ʹ′
XjXzzXjXkk
oc
Wu, 1988 – 17 plastic foam materials;
f = 200-2000 Hz; 2900 ≤ σ ≤ 24300 rayls; 0.01 < X < 0.83
655.0725.0
663.0716.0
556.0699.0
502.0641.0
127.0)0563.01(179.0)103.01(
:025.0for 191.0)081.01(
322.0)136.01(:025.0for
−−
−−
−−
−−
−+=ʹ′
−+=ʹ′
>
−+=ʹ′
−+=ʹ′
<
XjXzzXjXkk
XXjXzzXjXkk
X
oc
oc Mechel (after Fahy) – fibrous materials; f = ?; σ = ?; 0.002 < X < 0.5
σρ fX o=
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