r.patrquim Et Al. - Influence of the Presence of Lining Materials in the Acoustic Behaviour of Perforated Panel Systems

8/4/2019 r.patrquim Et Al. - Influence of the Presence of Lining Materials in the Acoustic Behaviour of Perforated Panel Systems

1/8

ICSV18, Rio de Janeiro, Brazil, 10-14 July 2011 1

INFLUENCE OF THE PRESENCE OF LINING MATERI-ALS IN THE ACOUSTIC BEHAVIOUR OF PERFORATEDPANEL SYSTEMS

Ricardo Patraquim

Castelhano & Ferreira S.A., Av. Colgio Militar, n 24A Benfica, Lisboa, Portugal.

e-mail: [email protected]

Lus Godinho, Antnio Tadeu, Paulo Amado-MendesCICC Centro de Investigao em Cincias da Construo, Dep. Eng. Civil da FCTUC da

Universidade de Coimbra, Rua Lus Reis Santos, Plo 2 da FCTUC, 3030-788 Coimbra,Portugal.

e-mail: [email protected]; [email protected]; [email protected]

Perforated panels are a common technical solution for the acoustical conditioning of closed

spaces. The most usual solutions of this type make use of a perforated surface, made of plas-

terboard or wood, separated from a rigid structure (wall or slab) by an air cavity with a given

thickness. Within this cavity, porous materials may be included to improve the absorbing ef-

fect of the system. The behaviour of these systems is, thus, complex, combining the effect of

the porous absorber (embedded in the cavity) and of an acoustic resonator (originated by thecombined effect of the panels perforation and of the cavity). In many applications, the back

of the panels is lined with fabric, whose characteristics can strongly influence the acoustic

behaviour of the system. In this work, the authors analyze the influence of this lining in the

absorbing properties of the system, performing experimental tests with different types of fab-

ric and evaluating the acoustic absorption in the presence of different system configurations.

To better understand the obtained results, the tested fabrics are also characterized in what

concerns their density and air-flow resistivity, which are known to be relevant to their acous-

tic behaviour. The results obtained in the experimental tests are also compared with theoreti-

cal predictions, attempting to understand the accuracy of those models for the prediction of

the acoustic absorption of such complex systems.

1. Introduction

In order to enhance the sound absorption area of the room surfaces, ceilings and walls are

usually coated using perforates (perforated panels), with an air cavity defined by the gap between

their surface and the rigid wall. In these systems, the process of sound absorption is caused by the

resonance of the air mass contained in the holes (bottlenecks) in a resonant cavity - as a Helmholtz

resonator.

According to Ingard and Bolt [1], the effect of perforated panels corresponds to an addition of

mass reactance of air in each hole to the normal surface impedance under the perforated facing,whereas its acoustic resistance is negligible (for perforated panels with holes of large diameter or

extra wide slots, above the viscous boundary layer). So, the back cavity under the perforated panels


2/8

18th International Congress on Sound and Vibration, Rio de Janeiro, Brazil, 10-14 July 2011

2

should be filled with porous absorbent materials in order to increase the sound absorption of the

system.

In many applications, the back of the perforated panels is lined with fabric (thin acoustic

nonwoven), whose characteristics can strongly influence the acoustic behaviour of the system. In

fact, there are few works studying the influence of this thin acoustic nonwoven on the back of per-

forated panels with a relatively high thickness (12mm) and a low fraction of open area (commonly

between 3% and 15%).

The main reason that triggered this work was the fact that perforated panels were tested in

three different laboratories, and none showed a characteristic behaviour of a resonator Figure 1.

Those panels (designated here as type A, and described in further detail in section 3), included a

nonwoven textile glued on their back. These results indicated that, in the development and imple-

mentation of these systems, it becomes important to assess the factors that can influence their

acoustic performance.

Figure 1. First lab tests no resonance peak, no significant differences

Since the sound absorption of the perforates is strongly dependent on the mounting condi-tions, an experimental parametric study is performed, in order to evaluate, using a reverberation

room and according to the ISO 354:2003 standard, the dependence of the sound absorption in

wooden panels with circular holes on the following parameters: usage of thin acoustic nonwoven as

a resistive layer; use of mineral wool on the back layer of air; small variation of the open area of the

panels. A theoretical analysis is also performed, following the methodology compiled on [2], based

on the works of Morse, Bolt, Ingard and Crandall [3-6].

Following this introduction, the next section presents the definition of perforation impedance

and some existing formulations for computing the sound absorption of the system; Section 3 de-

scribes the experimental setups and procedures; Section 4 gives the results of sound absorption for

the different tests; in Section 5, a comparison between experimental measurements and theoretical

predictions is presented; finally, the concluding remarks are presented in Section 6.

2. Modelling sound absorption of perforated panels

The methods of modelling the sound absorption of perforated panels are based on the conver-

sion of acoustic impedance of a single hole in an average value corresponding to the open area of

the panel. The perforated panel is considered as a set of short tubes of identical length to the thick-

ness of the panel, and the non-perforated material very dense and rigid, and therefore perfectly re-

flective. It is further assumed that the wavelength of the sound that propagates is sufficiently large

compared with the cross-sectional dimension of the tube (i.e., hole). This method includes the termsdue to viscosity of air, radiation (from a hole in a baffle), interactions between holes and the effects

of reactance of the cavity.


3/8


3

These acoustic systems are studied using the concept of the transfer matrix method, which

determines the acoustic impedance along the normal direction of an interface of a material using the

continuity of particle velocity (on both sides of the interface) and knowing the acoustic properties of

the medium (characteristic impedance,ac

Z , and the wavenumber or propagation constant, ak ).

When the nonwoven acoustic textile is placed right behind the perforated panels, then the re-

sistance behaves as though it actually occurs in the openings. According to Ingard and Bolt [1] andto Vr and Beranek [7], acoustic resistance of the absorber is increased to t (where is the

flow resistivity of the nonwoven acoustic textile, t is its thickness and is the fraction of open area

or porosity of the perforated panel).

From the knowledge of the acoustic impedance is possible to determine the sound absorption

coefficient and then estimate its value for diffuse field.

The arrangement of the absorber is shown in Figure 2. We consider the system as locally re-

acting, assuming that the sound in the absorber can propagate only perpendicularly to the plane of

the interface.

x

y

k Zca,

air spacek0 Z0c0 , ,

Z0s

d1

3 1

0

Mineral wool

Perforated

Panel

Rigid

Wall

0

D=2r

aa,

2

t

Thin acoustic

nonwoven

Figure 2. Arrangement of absorber for prediction

At Point 0 the normal surface impedance is infinite ( =0s

Z ), since it is considered a rigid

wall. The normal surface impedance at point 1,

( )1 1

i cotas c a

Z Z k d = (1)

whereac

Z is the characteristic impedance of the mineral wool, and ak is the wavenumber (or

propagation constant). So, to use this model is necessary to have the mineral wool characterized in

respect of these physical quantities by means of measurement, as reported by Cox and DAntonio

[8], or using an empirical predictions from regression analyses of measured data.

As written above, the normal surface impedance at point 2 is:

( )2 1 1

i cotas s c a

t tZ Z Z k d

= + = + (2)

and the surface impedance of the system (point 3) along the normal direction is:

23 sssZZZ

panel+= (3)

where the normal surface impedance of a perforated panel corresponds the idea of the impedance of

one hole (tube) is converted into a single averaged value corresponding to the fraction of perforated

open area and is given by:

tube

panel

s

s

ZZ = (4)


4/8


4

And, according with Crandall [6], the impedance of one hole (tube) is

( )( ) ( )

1 2

1 2

0 0 0 0 0 0

0

2 2i 1 2 2 i

tube

s

s

s s

J k r rZ l c

k r J k r

= + + + (5)

where0

is the air density, is the angular frequency,0l

is the thickness of the perforated panel,

r is the radius of the circular hole, is the coefficient of air viscosity, is the wavelength, nJ is

the nth order of Bessel function and0

isk = is the Stokes wave number.

The second term on the right hand side is the end correction, which also accounts for the in-

teraction between the orifices via the expression (see [7] and [8])

+= 347.047.11

3

16

r(6)

The sound absorption coefficient for a sound incidence angle with respect to the normal of

the surface is given by

( )2

1 ( )R = (7)

where ( )R is the reflection coefficient that can be expressed in terms of the normal surface im-

pedance3s

Z of the system:

3

3

0

0

cos( )

cos

s

s

Z ZR

Z Z

=

+(8)

where0 0 0Z c= is the acoustic impedance of the air.

To estimate the sound absorption coefficient for random incidence, i.e. diffuse field, the au-

thors follow the proposal Vr and Beranek in [7], which state that there is a very close correlation

between the calculation of ( ) from Eq. (7), for incidence of 45= and more complex ap-proaches proposed by other authors for diffuse incidence.

3. Experimental setup and characteristics of the absorbing system

To assess the sound absorption coefficient of the perforated panels under diffuse sound inci-

dence, standardized laboratory tests were performed in a reverberation chamber, following the pro-

cedures specified in the ISO 354:2003 standard. In this section, a brief description of the test condi-

tions is given, together with some details concerning the tested sound absorbing systems.

To perform the sound absorbing tests, a large size reverberant chamber, with a total volume of203.98m3 and a floor area of 5.85m x 5.85m, existing in the laboratory infrastructure of ITeCons, at

the University of Coimbra, was used. This reverberant chamber has previously been prepared in

order to fulfil the requirements of the ISO 354 standard, namely in what concerns the creation of a

diffuse field and the limitation of the reverberation times of the empty chamber. A detailed descrip-

tion of the testing conditions within the chamber can be found in [9], and for the purpose of this

work it is enough to just highlight that 15 sound polycarbonate diffusers, with convex and concave

shapes, totalizing 30 m2, were used to ensure the correct behaviour of the chamber.

Each test sample had an area of approximately 10.8m2, and consisted of perforated wooden

panels over mounted over the floor in a E-50 configuration, incorporating a small resonant cavity

between the panel and the floor. The perforated wooden panels were 12 mm thick, with circular

holes with a diameter of D=8 mm, equally spaced 32 mm along the two orthogonal directions (seeFigure 3). To allow the use of an adequate test area, panels with 600 mm x 600 mm were used,


5/8


5

forming a grid with 6 by 5 individual panels. These panels were supported by a light wooden struc-

ture, mounted over the floor, consisting of an external frame with 4 wooden beams, complemented

by internal beams equally spaced 600 mm, disposed along the smaller dimension.

Two different types of panels were used, designated as A and B, corresponding to different

global perforation areas. In terms of global perforated area, although the hole diameter and spacing

remain constant between all solutions, panel B presents an additional row of holes along each side

of the panel, which originates a slight increase in the perforated area. Thus, in the case of panel A,

this area is approximately 3.57% of the panel area, while in panel type B the perforation corre-

sponds to 4,52% (see Figure 3).

60

32

60 32

D=8

a)

28

32

28 32

D=8

b)Figure 3. Perforation scheme of the different panels (dimensions in mm): a) type A; b) type B.

The support wooden structure is approximately 40 mm thick, which ensures the presence of a

small air-gap with that thickness bellow the panels. Three different solutions were tested, corre-

sponding to: an air-gap, without any absorbing material; a cavity filled with a mineral wool with a

density of 40 kg/m3; a cavity filled with a mineral wool with a density of 70 kg/m3.

On the back of the perforated panels, a nonwoven acoustic textile mat was used, which is a

very usual constructive solution in these type of panels, mostly to avoid the emission of small parti-

cles from the mineral wools. For the purpose of this work, three types of textile mats were used,

which will here be designated as M1, M2 and M3. M1 and M2 correspond to nonwoven textile matsthat are of current use on the back of thin micro perforated metal sheets, in order to improve their

sound absorption; M3 is a standard nonwoven textile mat that is commonly used on the back of

wooden or plasterboard perforated panels. Although no precise data could be obtained for these

mats, it was possible to perform a brief laboratory characterisation, evaluating their air-flow resis-

tivity, an essential parameter to incorporate the effect of these mats in the theoretical models of sec-

tion 2. These values were of 79 MKS rayl, 71 MKS rayl and 27 MKS rayl for the M1, M2 and M3

nonwoven, respectively.

4. Experimental results

An experimental parametric study was performed to evaluate the influence of the differentvariables identified before in the behaviour of the system. Figure 4a illustrates the sound absorption

obtained for the tested system with panels of type A, and with the cavity filled with mineral wool

(with density of 70 kg/m3). Results for the three nonwovens are presented, together with reference

measurements performed without any nonwoven, with and without the mineral wool. For an empty

cavity, and without the nonwoven, the resonant behaviour of the system can, as expected, be ob-

served between 400 Hz and 500 Hz, although with a relatively small absorption coefficient (=0.4).

When mineral wool is used, this resonance lowers to the frequency band of 315 Hz, due to imped-

ance of this material, and the peak becomes notoriously higher (around =1.0). The introduction of

the M3 nonwoven textile produces only a slight variation in this response, with the behaviour of the

system maintaining the same features. In fact, a slight broadening effect occurs, with a small de-

crease in the peak value together with a very slight increase in the absorption observed at low andhigh frequencies. This effect is clearly related to the additional resistivity introduced by M3. How-


6/8


6

ever, when this resistivity is higher (nonwovens M1 and M2), the obtained curves show a very dif-

ferent behaviour, even if the remaining parts of the system are kept constant. For those cases, the

resonant behaviour almost disappears, and the corresponding curves exhibit much smaller absorp-

tion along the mid-frequency range (particularly between 200 Hz and 1000 Hz). This is an impor-

tant observation, which shows that the use of such types of nonwovens can dramatically change the

behaviour of the system, decreasing its expected performance. Between M1 and M2, some differ-

ences can still be noted, with the latter exhibiting an even lower absorption coefficient throughout

the analysed frequency range. In Figure 4b, results for the same mineral wool are presented for the

nonwovens M2 and M3, comparing their effects for the two types of panels analysed in this work. It

is clear, in that figure, that for both types of nonwovens the increase in the open area provides a

perceptible improvement of the absorption. Although this variation is much more evident for M2,

even for M3 it can reach =0.15 above the resonance frequency, which can be considered a signifi-

cant gain.

a) b)

Figure 4. Results for the 70 kg/m3 mineral wool: a) effect of different nonwovens for a given mineral wools

density, using panel type A; b) influence of the nonwoven for panel types A and B.

In Figure 5a, results measured for panel type B using different mineral wool densities anddifferent nonwovens are presented. In this plot, it can be seen that, when using nonwoven M3, the

increase of wool density produces a very small change in the absorption curve in the mid-frequency

range. Indeed, there is even a small absorption decrease at the resonance peak, which the authors

believe is due to the higher contrast between the two materials when higher density wool is used.

a) b)

Figure 5. Influence of the nonwoven for different mineral wool densities: a) results for panel type A; b)

results for panel type B.

This may indicate that a small coupling effect occurs between the thin layer of the nonwoven,

which lowers the peak efficiency of the system. A small increase of absorption in the high fre-quency range is also observed in some of the plots, which was not expected and that the authors


7/8


7

believe is only related to the experimental conditions. Figure 5b presents additional results obtained

for panels of type A. A reference curve, obtained without mineral wool nor nonwoven, is added to

allow comparison. When just the M3 nonwoven is introduced, there is a striking gain in the absorp-

tion coefficients throughout the frequency range; this is performance gain can reach =0.25 at the

peak of resonance. The introduction of mineral wool, within the cavity provides a further step up in

performance, with maximum values of =1.0 being reached at the resonance frequency. As in Fig-

ure 5a, no practical differences are observed between the two mineral wools, with the lower density

solution even exhibiting slightly higher peak absorption.

5. Comparison with theoretical predictions

The theoretical model presented in section 2 was used in order to understand the efficiency of

those models in predicting the behaviour of the tested systems. Although several tests were per-

formed for different cases, we here just illustrate a comparison between the theoretical model re-

sults and the experimental results obtained for a reduced number of cases.

In a first set of results, consider the system composed of type A panels, for which case the

perforated area represents 3.57% of the panel, incorporating the nonwoven mat M3 on its back andwith an air gap filled with 40 kg/m3

mineral wool; an air-flow resistivity of 14152 rayl/m is as-

sumed for this wool, while the nonwoven M3 is characterized by an air-flow resistivity of 27 rayl.

Figure 6a presents a comparison between the theoretical prediction and experimental measurement

for this case. In the plot it becomes apparent that the results match very well, with the peak reso-

nance occurring at the same frequency. In the lower frequency region, the two curves have very

similar trends, and only a small mismatch is visible when the peak absorption is reached at 315 Hz.

At higher frequencies, a larger difference is clear, with an increase in the absorption determined

experimentally that is not predicted by the theoretical model.

A second plot corresponding to the case in which the air-gap is empty and no nonwoven is

used on the back of the panels is presented in Figure 6b. In this case, a much lower absorption coef-

ficient is measured and estimated theoretically, and, again, a reasonable agreement between curvescan be observed up to the resonance frequency. As expected, due to the presence of the mineral

wool, this resonance is now slightly shifted to the right, and occurs at the 400 Hz band. Again, an

unexpected raise in the measured absorption can be observed above 2000 Hz in the experimental

data, which finds no correspondence in the theoretical predictions.

a) b) c)

Figure 6. Comparison between theoretical and experimental results (panel A) for three configurations: a)

nonwoven M3 and mineral wool; b) panels without nonwoven nor wool; c) nonwoven M1 and mineral wool.

A final plot, displayed in Figure 6c, illustrates the behaviour of the system when the non-

woven M1 is used; it is important to note that the flow resistivity is now much higher, with a meas-

ured value of 75 rayl. The theoretical curve now exhibits a much smoother shape, with a pro-

nounced decrease in the peak absorption being registered; the resonant behaviour can still be identi-

fied, although in a less pronounced manner. The effect of the higher resistivity of the nonwoven M1

is thus very visible in the theoretical curve, reducing the peak absorption and broadening the curveso that better performances are observed at higher frequencies. Comparing to the experimental re-


8/8


8

sult, the behaviour is not as similar as in the previous cases. In the experimental curve, the reso-

nance effect of the panel can hardly be identified, and only a small peak is visible at the frequency

of 200 Hz. It can thus be inferred that for higher values of the air-flow resistivity larger discrepan-

cies between the theoretically expected behaviour and the experimental results were observed.

6. Final remarksThis work analysed the behaviour of perforated wooden panels used to provide sound absorp-

tion in closed spaces. Particularly, the work addressed the effect of using different nonwoven tex-

tiles on the back of the panels together with mineral wools of different densities and different perfo-

rated open areas of the panels. The air-flow resistivity of the nonwoven was found to be a determi-

nant variable, influencing the sound absorption of the system. In fact, when used together with a

cavity filled with mineral wool, a nonwoven with high resistivity clearly hinders the development of

the resonant behaviour of the system, dramatically lowering the absorption provided by the panels

at mid-frequencies. If the nonwoven has a small air-flow resistivity, this behaviour is not observed,

and the resonance peak in the absorption curve is still very pronounced. A comparison with theo-

retical results revealed a good agreement when the nonwoven textile exhibits a small resistivity; forhigher values of this parameter, larger discrepancies between the theoretically expected behaviour

and the experimental results were observed.

Acknowledgments

The authors would like to thank Castelhano & Ferreira, S.A. and ITeCons - Instituto de

Investigao e Desenvolvimento Tecnolgico em Cincias da Construo for the support provided

during the preparation of this work.

REFERENCES

1. K.U. Ingard and R.H. Bolt, Absorption characteristics of acoustic material with perforated

facings,Journal of the Acoustical Society of America23, 533-540 (1951).2. R. Patraquim, Perforated wooden panels: design and experimental evaluation of solutions,

Masters Thesis submitted to Instituto Superior Tcnico, Portugal, in partial fulfilment of the

requirements for the Degree of Master of Science in Mechanical Engineering (2008).3. P.M. Morse, R.H. Bolt and R.L. Brown, Acoustic Impedance and sound absorption, Jour-

nal of the Acoustical Society of America12-2, 217-227 (1940).4. R.H. Bolt, On the design of perforated facings for acoustic materials, Journal of the Acous-

tical Society of America19, 917-921 (1947).5.

K.U. Ingard, On the theory and design of acoustic resonators, Journal of the Acoustical So-ciety of America25, 1037-1062 (1953).

6. I.B. Crandall, Theory of vibrating systems and sound, Van Nostrand, New York (1926).

7. I.L. Vr and L.L. Beranek,oise and Vibration Control Engineering, John Wiley & Sons, 2

nd

ed., New York (2005).8. T.J. Cox and P. DAntonio,Acoustic absorbers and diffusers: theory, design and application,

Spoon Press, 1st ed. (2004).9. I. Castro, A. Tadeu, J. Antnio, A. Moreira, P. Amado Mendes and L. Godinho, Cmaras

mveis ITeCons para a realizao de ensaios acsticos: parte II preparao e caracterizao

das cmaras horizontais, Proceedings of Acstica 2008, Coimbra, Portugal, October 20-22

(2008).

Documents

r.patrquim Et Al. - Influence of the Presence of Lining Materials in the Acoustic Behaviour of Perforated Panel Systems