low frequency absorption enhancement by modification of

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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, [email protected]

J Stuart Bolton Purdue University, [email protected]

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

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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/

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



(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]


3


(45 gsm)

foam

hard-backing


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]


3


(45 gsm)

foam

hard-backing


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


• 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)


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]



-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)


12 cm, 3600 gsm single layer of foam is

needed to achieve similar absorption

4

Effect of Flexible Backing


5

►


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]



5

►





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]



5

►





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


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•


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


~ Airspace

Limp membrane (ms)

Foam (8mm, 30kg/m3, 130000Rayls/m)






• 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]


---------- :.


Limp membrane (ms) Airspace





• 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


Limp membrane (ms1) Airspace


Limp membrane (ms2)

Airspace (9 mm)

Airspace Aluminum panel backing (1 mm)


• 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]


Limp membrane (ms1) Airspace


Limp membrane (ms2)

Airspace (9 mm)

Airspace Aluminum panel backing (1 mm)


• 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

https://doi.org/10.1038/ncomms1758

https://doi.org/10.1146/annurev-matsci-070616-124032

https://doi.org/10.1063/1.5108635

https://doi.org/10.4271/2011-01-1623

http://docs.lib.purdue.edu/herrick/

low frequency absorption enhancement by modification of

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