Post on 25-Nov-2021
Purdue University Purdue University
Purdue e-Pubs Purdue e-Pubs
Publications of the Ray W. Herrick Laboratories School of Mechanical Engineering
11-2020
Low Frequency Absorption Enhancement by Modification of Poro-Low Frequency Absorption Enhancement by Modification of Poro-
Elastic Layered Sound Package Elastic Layered Sound Package
Yutong Xue Purdue University, xyt@alumni.purdue.edu
J Stuart Bolton Purdue University, bolton@purdue.edu
Follow this and additional works at: https://docs.lib.purdue.edu/herrick
Xue, Yutong and Bolton, J Stuart, "Low Frequency Absorption Enhancement by Modification of Poro-Elastic Layered Sound Package" (2020). Publications of the Ray W. Herrick Laboratories. Paper 233. https://docs.lib.purdue.edu/herrick/233
This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information.
Low Frequency Absorption Enhancement by Modification of Poro-Elastic Layered Sound Package
Yutong (Tony) Xue* and J. Stuart Bolton
Ray W. Herrick Laboratories, Purdue University, West Lafayette, IN 47907
*now at Seagate Technology, MN
This presentation will be posted at Herrick E-Pubs: http://docs.lib.purdue.edu/herrick/
I 1,--~-7"~~~;:::::::::::::~;;:::2:::~:s~~~ g 0.8 .0 <( a> 0.6 () C Q)
:'Q 0.4 () C
«i 0.2 E ...
--2cm layer
--4cm layer
--8cm layer
~ o t;;;;..-.;;;;;;ec=:::::::~~~~~.c_J_--~-~~~~~_,____c_J 102 103 104
Frequency [Hz]
Motivation
• Low Frequency Noise Control
• “The attenuation of low-frequency sound has been a challenging task because the intrinsic dissipation of materials is inherently weak in this regime.” [1]
• “The acoustic response of any structure or material must obey the causality principle, which relates the absorption spectrum of a sample to its required minimum thickness.” [2]
• Existing Solutions and their Limitations
• Metamaterials – weight, volume, manufacturability, cost
• Active Noise Control (ANC) – robustness, multiple sources, latency, cost
• Current Study Optimization of poro-elastic sound package using layered structure modeling tool
1
Modeling of Layered Sound Packages
• Transfer Matrix Method (TMM) [3] • Poro-elastic layer modeling example [4]
• Efficient modeling tool to predict absorption coefficient and transmission loss for complex multi-layer acoustical systems
• Enabling design and optimization based on parametric study of sound packages
air gap [2x2]
stiff panels [2x2] limp porous layer [2x2]
elastic solid layer [4x4] → [2x2]
poro-elastic layer [6x6] → [2x2]
• Big idea: [2x2] matrices multiplied in a series
2
~ ---..
foam (properties below)
bonded (glued)
hard-backing
- Foam-Backing
0.9
0.1
o ~--~--~~~~~~~---~-~-~~~~~
102 103
Frequency [Hz]
104
𝜌b = 30kgΤm3 , 𝑑 = 25 mm, 𝜎 = 130 × 103 MKS RaylsΤm 𝜙 = 0.9, 𝛼∞ = 6.025, 𝐸0 = 4 × 105Pa, 𝜂 = 0.265, 𝜈 = 0.39
Effect of Surface & Back Treatments
3
Bonded/Bonded (BB) membrane
(45 gsm)
foam
hard-backing
1 ,----------,-----,--------,------r-----r----,-----.-----.-----------,-----,-----,--------,------r-----r----,-----,-----,
- Foam-Backing
C
2 0.8 a. ,._ 0 en .0 <( 0.6 (l) 0 C (l) "'O ·o 0.4 C
cu E 0 0.2 z
- BB
o b ~~~~::::::::::::::=L____L______j____________l___ __ _____j____ _ ____L________j_________j____------'--------_____[__~
102 103
Frequency [Hz]
3
Effect of Surface & Back Treatments
Bonded/Bonded (BB) membrane
(45 gsm)
foam
hard-backing
Unbonded/Bonded (UB)
airspace
(1 mm)
hard-backing
1
C
2 0.8 a. ,._ 0 en .0 <( 0.6 (l) 0 C (l) "'O o 0.4 C
cu E 0 0.2 z
- Foam-Backing - BB ········ UB
o b ~~~~::::::::::::::=L____L______j____________l___ __ _____j____ _ ____L________j_________j____------'--------_____[__~
102 103
Frequency [Hz]
Effect of Surface & Back Treatments
3
Bonded/Bonded (BB) membrane
(45 gsm)
foam
hard-backing
Unbonded/Bonded (UB)
airspace
(1 mm)
hard-backing
Bonded/Unbonded (BU)
airspace
(1 mm)
hard-backing
,
.
"'·
1 - Foam-Backing - BB
C
2 0.8 ········ UB - - BU a. ,___ ______ ____, ._
0 en 0
<( 0.6 (l) 0 C (l) O o 0.4 C
cu E 0 0.2 z
I I
I I
I
I
I
\
0 ~ ~~~:::::;::========-----'---------------'-------1_ __ _______j__ _ ____.l____________l____________L________j________________L__~
102 103
Frequency [Hz]
1
C
2 0.8 a. ,._ 0 en .0 <( 0.6 (l) 0 C (l) "'O ·o 0.4 C
cu E 0 0.2 z
- Foam-Backing - BB ········ UB - - BU ---- uu
I
I I
I
I I
I
0 ~~~~:::::;::========-----'---------------'-------1_ __ _______j__ _ ____.l____________l____________L________j________________L__~
102 103
Frequency [Hz]
Effect of Surface & Back Treatments
3
Bonded/Bonded (BB) membrane
(45 gsm)
foam
hard-backing
Unbonded/Bonded (UB)
airspace
(1 mm)
hard-backing
Bonded/Unbonded (BU)
airspace
(1 mm)
hard-backing
Unbonded/Unbonded (UU)
airspace
(1 mm)
airspace
(1 mm) hard-backing
1
0.9 -
§ 0.8 -
a 0 0.7 -C/) .0 <( 0.6 -Q) (.)
ffi 0.5 -"C g 0.4 -
~ 0.3 -i....
0 Z 0.2 -
I
-
1---- "BU" configuration (25 mm, 795 gsm) - hard-backing
0 ------~--~'----' --' ~ '-~'-'~'-l------~'----'----' --' - '--' ~'-'-102 103
Frequency [Hz]
Effect of Additional Top Absorbent
4
Airspace
Membrane (45gsm)
• BU configuration Poro-elastic (foam) layer (25mm, 30kg/m3, 130000Rayls/m)
Airspace (1mm)hard-backing
280 Hz
Effect of Additional Top Absorbent
• BU configuration
Airspace Adding a limp porous layer (3.2cm, 40kg/m3, 80000Rayls/m) on
top to improve high frequency absorption
Membra
-ne (45gsm)
Poro-elastic (foam) layer (8mm, 30kg/m3, 130000Rayls/m)
Airspace (1mm)hard-backing
0.9
§ 0.8
a 0 0.7 Cl) .0 <( 0.6 Q) (.)
ffi 0.5 "C g 0.4
~ 0.3 i....
0 Z 0.2
0.1
o~---~-- ----~-~~---~------~-~~ 102 103
Frequency [Hz]
A typical automobile dash panel sound
treatment weighs around 5000 gsm [5]
BU + limp layer provides absorption
above 0.5 from 280 Hz to 10 kHz
4
0.9
§ 0.8
a 0 0.7 Cl) .0 <( 0.6 Q) (.)
ffi 0.5 "C g 0.4
~ 0.3 i....
0 Z 0.2
0.1
---- "BU" configuration (25 mm, 795 gsm) - hard-backing - "BU"+ limp layer (40 mm, 1565 gsm)- hard-backing
,--, --- --Foam-Backing (120 mm, 3600 gsm) \
\ \ ' \ ' ' ,- .. ' I ,., ', I ,., 1•
' ,I ' , .. I \ , .. , _,,, "'---,; '\ .. , -~ ,_, -....... ___ ......... -o~---~------~-~~---~------~-~~ 102 103
Frequency [Hz]
Effect of Additional Top Absorbent
• BU configuration
-Airspace Adding a limp porous layer (3.2cm, 40kg/m3, 80000Rayls/m) on
top to improve high frequency absorption
Membrane (45gsm)
Poro-elastic (foam) layer (8mm, 30kg/m3, 130000Rayls/m)
Airspace (1mm)hard-backing
12 cm, 3600 gsm single layer of foam is
needed to achieve similar absorption
4
Effect of Flexible Backing
• BU configuration
5
►
Airspace Adding a limp porous layer (3.2cm, 40kg/m3, 80000Rayls/m) on
top to improve high frequency absorption Membrane (45gsm)
Poro-elastic (foam) layer (8mm, 30kg/m3, 130000Rayls/m) Airspace (1mm)
Airspace Aluminum panel
0.9
§ 0.8
a 0 0.7 Cl) .0 <( 0.6 Q) (.)
ffi 0.5 "C g 0.4
~ 0.3 i....
0 Z 0.2
0.1
- "BU"+ limp layer (40 mm, 1565 gsm) - hard-backing --Change to 10 mm aluminum panel backing
o~---~------~-~~---~------~-~~ 102 103
Frequency [Hz]
Effect of Flexible Backing
• BU configuration
5
►
Airspace Adding a limp porous layer (3.2cm, 40kg/m3, 80000Rayls/m) on
top to improve high frequency absorption Membrane (45gsm)
Poro-elastic (foam) layer (8mm, 30kg/m3, 130000Rayls/m) Airspace (1mm)
Airspace Aluminum panel
0.9
§ 0.8
a 0 0.7 Cl) .0 <( 0.6 Q) (.)
ffi 0.5 "C g 0.4
~ 0.3 i....
0 Z 0.2
0.1
- "BU"+ limp layer (40 mm, 1565 gsm) - hard-backing --Change to 10 mm aluminum panel backing --Change to 3 mm aluminum panel backing
o~---~------~-~~---~------~-~~ 102 103
Frequency [Hz]
Effect of Flexible Backing
• BU configuration
5
►
Airspace Adding a limp porous layer (3.2cm, 40kg/m3, 80000Rayls/m) on
top to improve high frequency absorption Membrane (45gsm)
Poro-elastic (foam) layer (8mm, 30kg/m3, 130000Rayls/m) Airspace (1mm)
Airspace Aluminum panel
0.9
§ 0.8
a 0 0.7 Cl) .0 <( 0.6 Q) (.)
ffi 0.5 "C g 0.4
~ 0.3 i....
0 Z 0.2 ~
0.1
- "BU"+ limp layer (40 mm, 1565 gsm) - hard-backing --Change to 10 mm aluminum panel backing --Change to 3 mm aluminum panel backing --Change to 1 mm aluminum panel backing
o~---~------~-~~---~------~-~~ 102 103
Frequency [Hz]
Shifts due
to reduced
impedance
of backing
C
2 "O 0.6 a. Q) .... C)
g ~ .0 Q)
<( ~ 0.4 Q) I
o,::r CI ~o -0 o 0.2 c~
I
«JO
E g o 0 Z 10-4
Mass per Unit Area
[kg/m2]
------
103
105
104 Airflow Resistivity [MKS Rayls/m]
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
o = 1000 Rayls/m a = 1585 Rayls/m
~ 0.5
10' 10' 104 1o' 103 104
Fraquency(Hz) Fraquency(Hz)
~ 0.5
10' 10' 104 1o' 10' 104
Fraquency(Hz) a = 39811 Rayts/m
~ 0.5
102 10' 104 10' 10' 104
Fraquency(Hz) Fraquency(Hz) a = 251189 Rayls/m o = 398107 Rayls/m
10' 10' 104 10' 10' 104
Fraquency(Hz) Fraquency(Hz)
a = 2512 Rayls/m a = 3981 Rayls/m 11 m -0.001
-- m1-0.0015849
~ 0.5 --m,-0.0025119 __ m,-0.0039811
-- m1-0.0063096 0
104 -- m1-0.01 1o' 10' 10• 10 ' 10' 103
Fraquency(Hz) Fraquency(Hz) -- m1-0.01S849
o s 25119 Rayts/m --m,-0.025119
--m,-0.009811
m1-0.063096
~ 0.5 --m1a0.1
--m,-0.15849
0 --m,-0.25119
102 10' 104 10 ' 1o' 103 10, --m,.o.391111
Fraquency(Hz) --m,~.63096
a = 158489 Rayls/m --m, .. 1
m1• 1.5849
~ 0.5
--m1a2.5119
--m,=3.9811 m ··-
I --m,. ,o 102 10' 104 ,o' 103 10 Fraquency(Hz) Fraquency(Hz)
a = 630957 Rayls/m o = 1000000 Rayls/m
~ 0.5
10' 10' 10• 1o' 10' 10•
Fraquency(Hz) Fraquency(Hz)
Low Frequency Absorption Optimization
,..___________,~
Airspace Limp membrane (ms)
Foam (8mm, 30kg/m3, 130000Rayls/m)
Limp porous layer (32mm, 40kg/m3, σ)
Airspace (1 mm) Airspace Aluminum panel backing (1 mm)
Optimizing averaged-absorption in 100-1000Hz
• Two optimal solutions were acquired, in both of which the performance was
dominated by the airflow resistivity
6
------
C
2 "O 0.6 a. Q) ... C) o ro (/) .... .0 Q) <( > 0.4 Q) <J' o,::r CI Q) 0 ~ o 0.2 co _ ....
I -o ro o E .- 0 106 ... ~ 0
10-4 z 105
Mass per Unit Area 104
Airflow Resistivity [kg/m2] 102 103 [MKS Rayls/m]
1
0.9
5 0.8 :.:; a. 0 0.7 en .0 <( 0.6
0.55 Q) u ~ 0.5
"O
0.5 ·g 0.4
~ 0.3 ... 0.45 0 z 0.2
0.1 0.4
0 102
0.35
0.3
0.25
0.2
...
-- -
--Solution 1: a-=105 Rayls/m, m =103 gsm s
Solution 2: a-=6.31x104 Rayls/m, m5=1 gsm
103
Frequency [Hz]
104
Low Frequency Absorption Optimization
~ Airspace
Limp membrane (ms)
Foam (8mm, 30kg/m3, 130000Rayls/m)
Limp porous layer (32mm, 40kg/m3, σ)
Airspace (1 mm) Airspace Aluminum panel backing (1 mm)
Optimizing averaged-absorption in 100-1000Hz
• Two optimal solutions were acquired, in both of which the performance was
dominated by the airflow resistivity
• The optimal absorption can be achieved by either an extreme light or heavy
membrane, which indicates that the performance was controlled by B.C.s
6
C
2 "O 0.6 a. Q) .... C) o ro (/) .... ~ ~ 0.4 Q) <J' o,::r CI Q) 0 ~ o 0.2 co _ ....
I -o ro o E =. o 0 Z 10-4
Mass per Unit Area
[kg/m2]
------
102 103
105
104
Airflow Resistivity [MKS Rayls/m]
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
1 ~-----,,-----------.---------.---.--------.-----,--------,-------.---,------r-------.--------,----,-------,-----,-------,----=:::J
0.9
§ 0.8 ::; a. 0 0.7 en .0 <( 0.6 Q) 0 w o.s
"O ·g 0.4
~ 0.3 .... 0 z 0.2
0.1
:..--------- ,I -- - -
--Solution 1: a-=105 Rayls/m, m5 =103 gsm
- - Solution 2: a-=6.31x104 Rayls/m, m5=1 gsm
---- Solution 2 & Turning off the foam layer 0 t:::::::::::::::::::::=-__j__ _ __j_ _ __j____L____J___L__[_~ ~-:..:.:.:----=----------'1 04 102 103
Frequency [Hz]
Low Frequency Absorption Optimization
---------- :.
Limp porous layer (32mm, 40kg/m3, σ)
Limp membrane (ms) Airspace
Airspace (9 mm) Airspace Aluminum panel backing (1 mm)
Optimizing averaged-absorption in 100-1000Hz
• Two optimal solutions were acquired, in both of which the performance was
dominated by the airflow resistivity
• The optimal absorption can be achieved by either an extreme light or heavy
membrane, which indicates that the performance was controlled by B.C.s
• Switching off the foam would not affect much of the optimal absorption
6
C 0 :g_ "C .... Q)
0 g> .2 ffi <( ~ Q) I
u'N' CI ~o ·- 0 g~
I -o ~o ........ 0 z
0 .7
0 .6
0 .5
0 .4
0.3
0.2
0.1
102
Mass per Unit Area
[kg/m2]
------
105 106 Airflow Resistivity [MKS Rayls/m]
0.65
0.6
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
103 0.15
~ 0.5
~ 0.5
o = 10CNlRayts/m
102 103
Frequency{Hz) o = 6310 Rayts/m
102 103
10•
10•
OL_ _______ .,,,.._
101 102 103 104
Frequency(Hz)
·~ili 101 102 103 104
Frequency(Hz)
o = 1585 Rayts/m
102 103 10'
Frequency(Hz) a = 10000 Rayls/m
102 103 10'
Frequency(Hz)
,.:t\]i 0 ~-------~--101 102 103 104
Frequency(Hz)
-~~ 101 102 103 10'
Frequency(Hz)
o = 2512 Rayts/m
~ 0,5
102 103 10'
Frequency(Hz) a = 15849 Rayls/m
~ 0.5
0 L_ ______ _;:,,.. ...
101 102 103 104
Frequency(Hz)
-~Kfi 0 101 102 103 104
F requency(Hz)
-~~ 101 102 103 10'
Frequency(Hz)
~ 0.5
o = 3981 Rayts/m
102 103
Frequency(Hz)
1 ~o• 25119Rayls/m ,.,
~ o.
0
s --m.1-0.0019602m11-0.19802
--m11c0.0031203 m92-0.19688
m11-0.0049007 m11-0.1951
--m,1-0.0076573 m11-0.19234
101 102 103 10' --m,,-o.01187m92•0.18813 Frequency(Hz) __ m.1-o 018182 m12• 0 18182
1 " .. 158489 Rayls/m --m,1-0027361m12-01726-4
--m11-0 040152 m12•0 15985
--m11-0 056949 m12■0 1'305
~ 05 --m11-007737Jm12-01~
o~--------~- • --: .. ::·:";:"°"737: 101 102 103 104 m•1-o 15985 m 12 ■O 040152
Frequency(Hz) = m::-0:17264 m:■0:027361
"
1~a:i: 1000000Rayts/m --m,1-0.18182m12•0.018182 __ m.,-0.18813 m.z•0.01187
--m,1-0.19234 m12■0.0076573
< o.s --m,1-0.1951 m12•0.0049007 __ m11•0.19688 m12■0.003 1203
o~--------~-101 102 103 10'
Frequency(Hz)
--m,1-0.19802 m111■0 .0019802
Low Frequency Absorption Optimization
Limp membrane (ms1) Airspace
Limp porous layer (32mm, 40kg/m3, σ)
Limp membrane (ms2)
Airspace (9 mm)
Airspace Aluminum panel backing (1 mm)
Optimizing averaged-absorption in 100-1000Hz
• One optimal solutions were captured with top membrane~120 gsm, bottom
membrane~80 gsm, and limp porous layer σ=~4x105 Rayls/m, in which the
airflow resistivity of the limp porous layer still dominates the performance
7
C 0
0.7
:g_ -c 0.6 .... Q)
0 g> _2 ffi 0.5 <( ~ ~ ~ 0.4 CI ~o •u g o.3 E: ....
I
«i g 0.2 E .-.... ~ 0 z 0.1
102
Mass per Unit Area
[kg/m2]
------0.65
0.6
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
103 0.15
105 106 Airflow Resistivity [MKS Rayls/m]
1 ~----~--~--~~-~~~~~,-----~--~-~-~-~~~~ ... •······• ... . /' -......
0.9 ~
5 0.8 f
a 0 0.7 f-
"' .0 <( 0.6 f-
a> ()
~ 0.5 f-
-o ·g 0.4 f- •
~ 0.3 f- :
~ . ~ 0.2 ~ /
,/ ~. . . ;/ •·· ....
/ \ ._\
♦
·~. ",,.
-
••,,.. ..,,," "• ....... . .. 0.1 >- ••·•••• •••• • ' •• ·· ·· ······· · · -
......... I········ Solution: c,=3.98x104 Rayls/m, m51 =123 gsm, m52=77 gsm I ·····• ....... ........... . 0 '--------'--'------------------------LJ.._-L.._--'----'----'---'-_J
102 103 104
Frequency [Hz]
Low Frequency Absorption Optimization
Limp membrane (ms1) Airspace
Limp porous layer (32mm, 40kg/m3, σ)
Limp membrane (ms2)
Airspace (9 mm)
Airspace Aluminum panel backing (1 mm)
Optimizing averaged-absorption in 100-1000Hz
• One optimal solutions were captured with top membrane~120 gsm, bottom
membrane~80 gsm, and limp porous layer σ=~4x105 Rayls/m, in which the
airflow resistivity of the limp porous layer still dominates the performance
• Averaging among a continuous band of frequencies does not help the
whole picture and does not guarantee good performance at all frequencies
• This configuration provides +0.1 absorption than previous one, but would
trade off high frequency performance 7
Summary
• Low frequency sound absorption can be optimized for conventional sound package involving porous layers (fibers, foam) to provide industry-acceptable performance while maintaining cost-effective features including lightweight and thinness
• TMM model serves as an efficient multi-layer sound package modeling tool to enable optimization of complex layered structures
• Boundary conditions (unbonding vs. bonding) plays an significant role for low frequency absorption
• Finite impedance backing (panel) is more practical when optimizing absorption
• An optimized sound package (40mm, 1520 gsm) with a highly-resistive absorbent (32mm, at front) and a surface-bonded foam (8mm, at back) can achieve an averaged sound absorption > 0.55 among 100-1000Hz
• An alternative optimized sound package (40mm, 1435 gsm) with a highly-resistive absorbent (32mm) plus two limp membranes without the foam layer can achieve an averaged sound absorption > 0.65 among 100-1000Hz, but would trade off high frequency performance
8
References
[1] J. Mei et al., “Dark acoustic metamaterials as super absorbers for low-frequency sound,” Nature Communications Vol.3: Article
756 (2012). https://doi.org/10.1038/ncomms1758.
[2] M. Yang and P. Sheng, “Sound absorption structures: from porous media to acoustic metamaterials,” Annu. Rev. Mater. Res. Vol.47: pp. 83–114 (2017). https://doi.org/10.1146/annurev-matsci-070616-124032.
[3] Y. Xue, J. S. Bolton and Y. Liu, “Modeling and coupling of acoustical layered systems that consist of elements having different
transfer matrix dimensions”, J. Appl. Phys. Vol.126: 165012 (2019). https://doi.org/10.1063/1.5108635.
[4] J. S. Bolton, “Poro-elastic materials and the control of low frequency sound,” Plenary speech at Noise-Con 2019, San Diego, CA.
[5] A. Parrett et al., “Application of micro-perforated composite acoustic material to a vehicle dash mat,” SAE Technical Paper
2011-01-1623, 2011, https://doi.org/10.4271/2011-01-1623.
Thanks for your attention!
And a special THANKS to the Organization Committee
Please follow Herrick E-Pubs: http://docs.lib.purdue.edu/herrick/ for presentations and more
9