Enhancing the Performance of Microperforated Panel

Absorbers by Designing Custom Backings

Authors:

X. Hua, and D. W. HerrinDepartment of Mechanical EngineeringUniversity of Kentucky

P. JacksonAmerican Acoustical Products Inc.

ABSTRACT

Micro-perforated (MPP) panels are acoustic absorbers that are non-combustible,

acoustically tunable, lightweight, and environmentally friendly. They are normally

spaced from a wall, and the spacing determines the frequency range where the

absorber performs well. The absorption is maximized when the particle velocity

in the perforations is high. Accordingly, the absorber performs best when

positioned approximately a quarter acoustic wavelength from the wall. At

multiples of a half acoustic wavelength, the absorption is minimal. Additionally,

the absorption is minimal at low frequencies due to the limited cavity depth

behind the MPP. By partitioning the backing cavity, the cavity depth can be

strategically increased and varied. This will improve the absorption at low

frequencies and can provide absorption over a wide frequency range. In this

paper, backing substrates have been developed to enhance the absorption

performance. Maa’s model is first reviewed. Then, different MPP and backing

substrate combinations are analyzed using Maa’s theory and the boundary

element method. The broadband absorptive behavior is validated via

measurement in a square impedance tube. Measured results agree reasonably

well with analysis.

1. INTRODUCTION

Micro-perforated panel (MPP) absorbers are a promising replacement for

traditional sound absorbing materials like fibers and foams since they are light

weight, nonflammable, cleanable, durable, and fiber free. Because of these

advantages, MPP absorbers have been utilized in mufflers [Allam, 2009; Masson,

2008], HVAC ducts [Wu, 1997], building interiors [Kang, 2005], engine enclosures

[Corin, 2005], noise barriers [Pan, 2004; Asdrubali, 2007], and in space crafts

[Omrani, 2010].

MPP absorbers are normally manufactured from steel, aluminum or plastic and

have uniformly distributed sub-millimeter sized holes. Porosity typically ranges

from between 0.5% to 2%. The first generation MPP absorbers were metal

panels with circular perforations. In order to reduce the manufacturing cost, slit-

shaped perforations have become prevalent recently. Slits are pressed or

sheared into the metal.

The absorbers are most often spaced from a rigid wall. In fact, it is best to think

of the absorber as a system consisting of both the panel and backing cavity. Air

oscillates back and forth in the perforations. Since the perforations are small, the

acoustic resistance is high. Accordingly, frictional losses are greatest when the

particle velocity in the pores is maximized. This roughly corresponds to spacing

the panels a quarter acoustic wavelength from the wall. Hence, large cavity

depths are required to extend absorption to lower frequencies.

Whereas foams and fibers provide excellent broadband absorption above a

certain frequency, the frequency range that MPP absorbers perform acceptably in

is much narrower due to the sound absorbing mechanism. Absorption is

minimal, when the particle velocity in the perforations is low. Consequently, the

absorption is low in frequency ranges corresponding roughly to multiples of a half

acoustic wavelength.

However, MPP absorbers generally do not perform as well as a fiber or foam

even at the frequencies they are designed for. Yairi et al. [10], Toyoda and

Takahashi [11], and Liu et al. (first SAE Paper) demonstrated that performance is

comparable to traditional absorbing materials only when the backing cavity is

partitioned. The most common partitioning has been a honeycomb.

Liu and Herrin investigated the mechanism for the improved performance with

partitioning using boundary element simulation. The study confirmed the earlier

findings, and provided an explanation for the improvement in performance. The

study indicated that partitioning improves the performance of the absorber by

disrupting wave propagation behind the MPP. It was shown that acoustic waves

that propagated normal to the panel were attenuated equally well with or without

a partitioned substrate. However, the sound pressure due to grazing waves

(propagating parallel to the MSP absorber) was essentially unaffected if

partitioning was not used.

Efforts have been aimed at improving the broadband absorption of MPP

absorbers. For example, double layer [Tao, 2005; Sakagami, 2006 & 2009] or

multi-layer [Ruiz, 2011] MPP absorbers have been suggested. Though the

absorptive performance is improved, multi-layer MPP absorbers effectively

double the materials cost and are more difficult to install. Additionally, partitioning

must also be installed between the layers to improve their effectiveness.

Others have considered varying the cavity depth. For example, Jiang [16] and

Liu et al. [first SAE Paper] investigated using a triangular prism backed cavity.

Sum [17] recommended a parallel stepped configuration. However, these

approaches do not lend themselves to typical box-shaped enclosures. Moreover,

large cavity depths are still required to enhance low frequency absorption.

The work in this paper focuses on improving single-layer MPP absorbers by

developing a partitioned backing. The backing is designed so that the cavity

depth is increased which provides lower frequency absorption without adding

additional volume. Moreover, the cavity depth is varied so that broadband

frequency absorption is achieved. The newly designed backings are

demonstrated using a square impedance tube and using simulation.

2. REVIEW OF MAA’S MODEL AND EQUIVALENT PARAMETERS

2.1 Maa’s Models for Micro-perforated Panel

For a single layer MPP, the particle velocity can be assumed to be continuous

due to the small thickness. Accordingly, Maa [Maa, 1975 and 1998] modeled the

MPP as a transfer impedance and expressed the impedance as:

Z tr=32ηtσρ0 cd 2 (√1+β2/32+ √2

32β d

t )+ j ωtσc ((1+1 /√9+β2 /2 )+0 .85 d

t )

where η is the dynamic viscosity of air, t is the thickness of the MPP, σ is the

porosity, ρ0 is the density of the air, c is the sound speed, d is the single hole di-

ameter, ω is the angular frequency, and is the perforate constant.

For MPP absorbers with rectangular perforations, Maa [Maa, 2000] proposed a

modified model which is similar to the circular perforation MPP model,

Z tr=12ηtσρ0 cd 2 (√1+β2/18+ √2

12β d

t )+ j ωtσc ((1+1/√25+2 β2)+ 1

2F (e ) d

t )

where is the eccentricity of the ellipse and F is the incomplete elliptic

integral of the first kind which is expressed as

The impedance at the surface of a conventional MPP absorber is expressed as

4/0d

2

2

41

lde

20 22 sin1

e

deF

where D is the air cavity depth behind the MPP. It can be observed that the

porosity, thickness, hole diameter, and the cavity depth govern the performance

of the MPP absorber. The effect of varying the cavity depth is shown in Figure 1.

Notice that an extremely low absorption band cannot be avoided when the cavity

depth is approximately half of an acoustic wavelength. Moreover, increasing the

cavity depth lowers the frequency of the high absorption band.

0.0

0.2

0.4

0.6

0.8

1.0

0 1000 2000 3000 4000 5000

Frequency (Hz)

Abs

orpt

ion

Coe

ffici

ent

1 inch cavity depth

2 inch cavity depth

Figure 1 Typical absorption coefficients for a same MPP with different cavity depth.

2.2 Equivalent Parameters Based on Maa’s Model

At first glance, Maa’s model seems difficult to apply to second-generation MPP

absorbers where slits are pressed or cut into metal to reduce the cost. Although

the sound absorbing mechanism is the same, Maa’s equations cannot be applied

directly due to the slit not being irregular in shape (i.e., not circular or elliptical).

Moreover, the slit is often pressed through the material at an angle and the di-

mensions of the slit are not consistent through the thickness.

However, Liu (2013) used a nonlinear least-square data-fitting algorithm to esti-

mate equivalent parameters (usually porosity and hole size) from the measured

absorption. The absorption of a sample with a given cavity depth is first mea-

sured and then a least-square data fitting algorithm is used to select a porosity

cDjZZ tr

cot

and hole diameter that minimize the error. The algorithm has been used to in-

vestigate the effect of manufacturing variability and dust contamination. In the

current effort, the method was used to determine the porosity and hole size of a

MPP with slit perforations so that Maa’s theory could be used for the simulation

models.

Hence, the sound absorption of an MPP sample was measured using ASTM

E1050 [Ref.] with a four-inch cavity behind it. Maa’s model was fitted to the mea-

sured data from 200 to 1500 Hz. The fitted equivalent hole size and porosity

were 0.26 mm and 8% respectively. The fitted and measured absorption are

compared in Figure 16.

0.0

0.2

0.4

0.6

0.8

1.0

0 500 1000 1500 2000

Frequency (Hz)

Abso

rptio

n C

oeffi

cien

t

Data-fitted

Measured

Figure 16 The Data-fitted and measured absorption of a selected MSP with 102 mm

empty backing cavity.

3. SIMULATION OF BACKING MPP PLUS BACKING SUBSTRATES

3.1 Plane Wave Model for Parallel Cavities

Using the electrical analogy, the MPP and the backing air cavity can both be

modeled as impedances in series. The MPP is both resistive and reactive

whereas the backing air cavity is purely reactive. Figure 3a illustrates the analo-

gous electrical circuit. Next, consider the case where the cavity is partitioned into

a series of channels with varying depths as shown in Figure 3b. It can be as-

sumed that the sound pressure is constant on the front surface of the MPP. In

that case, the combined transfer impedance and reactance for each cavity may

be considered in parallel with its neighbor as shown in Figure 3b.

Ztr

ZcavityPlane Wave Cavity

(a)

Zi

Ztr

Plane Wave

1

2

…

n

(b)

Figure 3 Electrical analogy of traditional MPP absorber (a) and multi-channel MSP ab-

sorber (b).

The total volume velocity at the surface of the MPP is equal to the sum of the vol-

ume velocities in the individual channels. Thus,

where u is the particle velocity at the surface of the MPP and ui are particle veloc-

ities directly behind the MPP in each channel. By assuming sound pressure is

constant across the surface of the MPP, the velocities can be written in terms of

specific acoustic impedances and sound pressure. Thus,

where Zi and Si are the acoustic impedance (Equation X) and cross-sectional

area of the ith air channel respectively. Therefore, the combined impedance of

the series of air cavities can be expressed as

n

iii SuuS

n

i i

i

cavity

cavity

ZPS

ZPS

1

where si is the cross-sectional area ratio between the ith channel and the whole

cavity. The normal incident absorption coefficient of the multi-channel MPP ab-

sorber can be calculated using the equation

Where R and X are real and imaginary part of Z respectively.

The simplest case is a two-channel cavity. In that case, the impedance can be

expressed as

In a similar manner, a three-channel cavity can be expressed as

where the impedances for each channel are governed by the lengths of the chan-

nels.

n

i i

icavity

Zs

Z

1

1

2200

004XcR

cR

2

2

1

1

1

Zs

ZsZcavity

323121

3213ZZZZZZ

ZZZZcavity

3.2 Modeling a Three-Channel Cavity

In order to better evaluate the folded three-channel MSP absorber, a modified

model, J-shape three-channel model, is investigated. In this model, the three

channel share the same cross-sectional area as in the three-channel model. The

maximal thickness D of the absorber is pre-determined. The first and second

channels behavior maintains the same as the three-channel model. The third

channel, which is folded, is not modeled simply as a straight duct but as a simple

expansion chamber as shown in Figure 10.

D1

D2

D

Figure 10 Simple expansion approximation for the third channel.

The cross-sectional area of each channel is assumed as a square with the di-

mension a. And then, the length lu and area su of the upstream duct of the third

channel is (D+D2)/2 and a2 respectively. The length lc and area sc of the chamber

is 2a and a(D-D2) respectively. The length ld and area sd of the downstream duct is

(D+D2)/2-D1 and a2. According to the transfer matrix theory, the surface imped-

ance at the outlet of the third channel can be expressed as

where

21

113 Ts

TZ

u

3.3. BEM SIMULATION OF BACKING SUBSTRATES

In order to validate the plane wave models described before, the two-channel

and three-channel MSP absorbers are simulated numerically using boundary ele-

ment models, as shown in Figure 13. A 95 mm by 95 mm square duct is created

with an MSP placed 100 mm away from the top. The MSP is modeled as a trans-

fer relationship that relates the respective particle velocities (vn1 and vn2) and

sound pressures (P1 and P2) on either side of the MSP, which can be written as

where Ztr is the transfer impedance of the MSP. The cavity behind the MSP is

partitioned ideally by rigid elements without any thickness. A unit velocity bound-

ary condition is applied on the Red surfaces. Couple field points are randomly

picked to calculate the impedance and further acquire the absorption coefficient.

(a) (b)

Figure 13 Boundary element models of two-channel (a) and three-channel (b) MSP ab-

sorbers. Unit velocity boundary condition on red and MSP transfer relation on green.

)sin()cos()sin()sin()sin()cos(

)cos()sin()sin()cos()cos()cos(11

dcuu

ddcu

c

d

dcuu

cdcu

klklklss

klklklss

klklklssklklklT

)sin()cos()cos()sin()sin()sin(

)cos()sin()cos()cos()cos()sin(21

dcuddcuc

du

dcucdcuu

klklklsklklklsss

klklklsklklklsT

2

1

2

1

11

11

PP

ZZ

ZZvv

trtr

trtr

n

n

Besides boundary element method, the plane wave model for MSP absorbers is

also validated experimentally in a square impedance tube. The tube is made of

aluminum with the cross-sectional area 95 mm by 95 mm; and the cutoff fre-

quency is approximately 1800 Hz. A two-microphone method with random noise

excitation is applied to measure the absorption coefficient based on ASTM 1050.

Two different backing cavities are built and tested, a two-channel cavity and a

three-channel cavity that are shown in Figure 15. The partition sheets is made of

steel with 0.12 mm thick that can be ignored compared with the acoustic wave

length. All potential gaps are sealed with plumber’s putty.

(a) (b)

Figure 15 Photos of two-channel (a) and three-channel (b) cavity design inside square

impedance tube.

Figure 17 shows the absorption comparison of the two-channel MSP absorber.

The plane wave model agrees well with the boundary element model and the

measured result below 1200 Hz. The absorption behavior at low frequency is im-

proved to a great extent compared with the traditional MSP absorber; however

the low absorption at around 800 Hz occurs, which cannot be avoided with two-

channel design as analyzed in the section 3.2. The absorption comparison of the

three-channel MSP absorber is shown in Figure 18. The plane wave model com-

pares well with the other two results. It is also shown that the low frequency ab-

sorption is further improved; and the behavior at around 800 Hz is enhanced sig-

nificantly.

0.0

0.2

0.4

0.6

0.8

1.0

0 500 1000 1500 2000

Frequency (Hz)

Abs

orpt

ion

Coe

ffici

ent

BEMPlane WaveMeasurementEmpty Backing

Figure 17 The absorption comparison of the two-channel MSP absorber among plane

wave model, boundary element model measurement and measurement with empty cavity.

0.0

0.2

0.4

0.6

0.8

1.0

0 500 1000 1500 2000

Frequency (Hz)

Abs

orpt

ion

Coe

ffici

ent

BEM

Plane Wave

Empty Backcing

Measurement

Figure 18 The absorption comparison of the three-channel MSP absorber among plane

wave model, boundary element model measurement and measurement with empty cavity.

5. CONCLUSION

By partitioning the backing cavity to create parallel multi-channels, the traditional

MSP absorber can be improved without increasing the cavity volume. Maa’s

model is utilized to characterize irregular-shaped MPP or MSP by nonlinear data

fitting. According to the fitted hole diameter and porosity, plane wave theory is

effective to help design the backing channels below cutoff frequency.

The two-channel design improves the absorption at low frequency. For a 102 mm

material space, the absorption reaches 0.7 at around 340 Hz. However, a low

absorption in higher frequency range is inevitable. A three-channel design is able

to achieve the both targets, high absorption at low frequency and a broadband

absorption thereafter. By folding the longest channel, the material space can be

utilized much more efficiently. A two-channel and a three-channel MSP absorber

are investigated numerically and experimentally. Both of the results compares

well with the plane wave model.

ACKNOWLEDGMENTS

This work was supported

REFERENCES

[1] M. Q. Wu, Micro-perforated panels for duct silencing, Noise Control Eng. J.

45(2) (1997) 69-77.

[2] J. Kang, M. W. Brocklesby. Feasibility of applying micro-perforated absorbers

in acoustic window systems. Appl. Acoust. 66(6) (2005) 669–689.

[3] J. Pan, R. Ming and J. Guo, Wave Trapping Barriers, Proceedings of

ACOUSTICS 2004, Gold Coast, Australia, November, 2004.

[4] R. Corin, L. Weste, Sound of silence, iVT International, 105-107, 2005.

[5] F. Masson, P. Kogan, and G. Herrera, Optimization of muffler transmission

loss by using microperforated panels, FIA2008, Buenos Aires, November,

2008.

[6] S. Allam, Y. Guo and M. Abom, Acoustical Study of Micro- Perforated Plates

for Vehicle Applications, 2009 SAE Noise and Vibration Conference Proceed-

ings 2009-01-2037, St. Charles, IL, 2009.

[7] Abderrazak Omrani, Imad Tawfiq, Vibro-acoustic analysis of micro-perforated

sandwich structure used in space craft industry, Mechanical Systems and

Signal Processing. 25(2) (2010) 657-666.

[8] F. Asdrubali, G. Pispola, Properties of transparent sound absorbing panels for

use in noise barriers, J. Acoust. Soc. Am. 121 (2007), pp. 214–221.

[9] Z. Tao, B. Zhang, D. Herrin, and A. Seybert, Prediction of Sound-Absorbing

Performance of Micro-Perforated Panels Using the Transfer Matrix Method,

2005 SAE Noise and Vibration Conference Proceedings, Traverse City, MI,

2005.

[10] K. Sakagami, M. Morimoto and W. Koike. A numerical study of double-leaf

micro-perforated panel absorbers. Appl. Acoust. 67 (2006) 609-619.

[11] K. Sakagami, T. Nakamori, M. Morimoto and M. Yairi. Double-leaf microp-

erferated panel space absorbers: A revised theory and detailed analysis.

Appl. Acoust. 70 (2009) 703–709.

[12] H. Ruiz, P. Cobo, and F. Jacobsen. Optimization of multi-layer microperfo-

rated panels by simulated annealing. Appl. Acoust. 72(10) (2011) 772-776.

[13] J. Liu, D. W. Herrin. Enhancing Micro-perforated Panel Attenuation by

Partitioning the Adjoining Cavity, Applied Acoustics, Vol. 71 (2010), pp. 120-

127.

[14] C. Wang, L. Cheng, J. Pan and G. Yu, Sound absorption of a micro-perfo-

rated panel backed by an irregular-shaped cavity, J. Acoust. Soc. Am.

127 (2010), pp. 214–221.

[15] W. Jiang, X. Liu, and C. Wang, Some Numerical and Experimental Study

of Micro-Perforated Panel Acoustic Absorbers with Heterogeneous Cavities,

ICSV13, July 2-6, 2006, Vienna, Austria.

[16] D. Y. Maa, Theory and design of Microperforated-panel sound-absorbing

construction, ScientiaSinica XVIII 55-71, 1975.

[17] D. Y. Maa, Theory of microslitabsorbers, ActaAcustica, 2000-06(2000)

[18] J. Liu, X. Hua and D. W. Herrin. Effective parameters estimation for microp-

erforated panel absorbers and applications, Applied Acoustics,

[19]