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ences, riable for a

specific purpose. For instance concert use refers to different types of music, like folk music and rock music which requires different acoustical characteristics.

When a multipurpose hall switches from conference use to concert use, reflective surfaces should be replaced with sound absorptive materials. Panels with acoustically differing faces configured to serve different functions can be developed and proposed as a variable acoustic solution [4]. In this case, sound absorption characteristics of selected materials are determined according to the specific volume of interest and defined uses.

If the volume of the space is assumed to be constant, changing sound absorption properties of materials may supply proper reverberation time [5]. Porous or fibrous materials, panel absorbers, or volume absorbers can be preferred as sound absorbent materials. The properties of porous materials (such as fibre length, density or material thickness), the air gap width behind panels and the lining separating porous material from the auditorium may be decisive in the characteristics of a variable acoustic system. If this lining is a multiple perforated panel, sound absorption performance of the system depends also on the properties of each perforated panel such as perforation type, diameter, central distance and perforation ratio

Therefore, by modifying some or all these parameters, a range of sound absorption coefficients provided by one such variable system is possible. Within this range, perforation can be arranged according to the hall needs from functional differences.

In this paper a preliminary study is carried out to assess sound absorption of perforated shapes that may be suitable for achieving a variable acoustic solution, for room acoustic design, making use of combinations of macro-perforated panels with different perforation rates and micro-perforated panels, porous materials and airgaps of varying thicknesses. With this propose an analytical model making use of the transfer matrix method to obtain sound absorption coefficient for normal incidence is used to evaluate different configurations using circular shaped perforated panels. 2. ANALYTICAL MODEL DESCRIPTION

The approach used in this paper to model the sound absorption of perforated panels is based on the conversion of the 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 similar length to the thickness of the panel, and the non-perforated material is assumed to be rigid. It is also 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 terms due to viscosity of air, radiation (from a hole in a baffle), interactions between holes and the effects of reactance of the cavity.

The perforated panel is studied using the concept of the transfer matrix method [6], where the acoustic impedance along the normal direction of an interface of a material is determined using the continuity of particle velocity (on both sides of the interface) and knowing the acoustic properties of the medium (characteristic impedance,

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

Knowing the acoustic impedance it 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 1. The system is considered as locally reacting, assuming the normal incidence of sound to the plane of the interface.

consi

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nce is infin

mpedance at

1

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eral wool,

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corresponda single

s given by:

ube) is

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ir

), since

and ak i

it is necessaities by meairical predic

ds the idea oaveraged

0

it is

(1)

s the

ary to ans of ctions

(2)

of the value

(3)

(4)

where 0 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 and

0isk is the Stokes wave number.

The second term on the right hand side is the end correction, which also accounts for the interaction between the orifices via the expression (see [7] and [8])

347.047.11

3

16

r

(5)

The sound absorption coefficient for a sound incidence angle with respect to the normal of the surface is given by

21 ( )R

(6)

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

surface impedance 3sZ of the system:

3

3

0

0

cos( )

coss

s

Z ZR

Z Z

(7)

where 0 0 0Z c is the acoustic impedance of the air.

3. PROPERTIES OF THE LAYERS COMPOSING ABSORBING SYSTEMS The panel systems analysed consist of one or two layers of perforated panels with circular holes with thickness, diameter of the hole and perforation rates defined in Table 1, which are mounted over a resonating cavity whose thicknesses may vary between 0 and 150 mm. The resonating cavity may be partially filled with a porous material, with the properties of the mineral wool which are also defined in Table 1.

Table 1 – Properties of perforated panels and porous materials ID Perforated

panels Thickness

(mm) Diameter of the hole

(mm)

Perforation rate (%)

MPA Macro-Perforated 12 8 6.4 MPB Macro-Perforated 12 6 3.6 MPC Macro-Perforated 12 6 64 mP Micro-Perforated 0.8 0.5 6.4 ID Porous material Thickness

(mm) Density (kg/m3)

Flow resistivity Pa.s.m-2

MW Mineral Wool 40mm 40 28377

4. PA In thwith systeconfi 4.1 P

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Figure 2 – Ganalyz

Table 2 –

Configu1C - A

1C - B

1C - C

1C - D

1C - E

1C - F

Sound are 3. In thediately behe when this

RIC STUDY

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uration LM

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MPA

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MPB

MPB

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carried assuution of diffons, the inf

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RESULTS

uming diffeferent layersfluence of

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configuratiod position of

of each sysns

Layer 3 Airgap d1=150mAirgap d1=110mMW

Airgap d1=150mAirgap d1=110mMW

the differenhat when tabsorption ly after the r

erent sets ofs in sound adifferent c

aluate the e the airgael (MPA orable 2.

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nt systems he mineral displays higrigid surface

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gure 3 – Soufigurations

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gure 4 – Geo

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econd set of ence of the

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ickness, a sperforated pa mineral

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f configuratiairgap thic

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second set opanel (MPAwool layer

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guration #2)

rst set of b) Macro-

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4.3 D

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re 5 displaymineral wooce that the pknesses incrn the minerrption also

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ure 5 – Sounconfiguratio

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his subsectirting a secofiguration wrovide a refe

perforated

Definition of

guration C - A

C - B

C - C

C - D

C - E

C - F

ys the soundol is positiopeak of sounreases, whilral wool is pmoves to t

5 to 0.40 wh

nd absorptions (configu

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was assignederence resulpanels hav

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d absorptionned on the

nd absorptiole its ampliplaced immhe lower fr

hen moving

ion coefficieuration #2):aneral wool p

rates

parison betwated panel

d as Configult Configurae similar pe

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or each systns

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MW

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Airgd1=11

Airgd1=6

Airgd1=1

nts regardine perforatedo the lower fayed a smoofter the rigidbut its ampfrom 110mm

d by the geowool placedinst the rigi

ing perforatehind the sB and is dis

A and 3C-B properties (s

tem of the se

r 3 LayW A

d1=W A

d1=W A

d1=gap 10mm

M

gap 0mm

M

gap 0mm

M

ng Configurd panel (Figfrequenciesoth decreasd surface, thlitude signim thickness

ometries used against thed surface.

tion rates iurface pan

splayed in Fwere define

see configu

econd set of

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110mm Airgap =60mm

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MW

MW

rations #2. Wgure 5a), wes when the ase of about he peak in sificantly chs to 10mm.

ed in the sece perforated

is performenel (PMA). Figure 6. In ed assuming

uration 3C-A

f

When e may airgap 10%.

sound anges

b)

cond set d panel;

ed by This

order g that A and

3C-C#3.

Fi

The ppreseperfoFromthan one,

C). Table 4

igure 6 – Ge

Table 4 –

Config3C - A

3C - B

3C - C

plot displayence of a seorated panelm the analys

that obtainbut with thi

Figu

displays the

eometries uanalyze th

Definition

guration A

yed in Figurecond perforl (MPA) wisis of this pned for a siickness of 2

re 7 – Sounused in the

e properties

used in the the influence

of the differco

Layer 1 MPA

MPA

MPB

re 7 exhibitsrated panel ith a mineralot it can beingle perfor24mm.

nd absorptioe third set of

s of the diffe

hird set of cof the differ

rent layers fonfiguration

Layer -

MPB

-

s the sound(MPB) posal wool linee seen that rated panel

on coefficienof configura

erent layers

configuratiorent perfora

for each sysns

2 LayeMW

MW

MW

d absorptionitioned immed against ithis panel dwith ident

nt provided tions (confi

of the set o

ons (configuation rates

stem of the t

r 3 LayAirgd1=Airgd1=Airgd1=

coefficientmediately bet and an airdisplays a sical propert

by the geomguration #3

of configura

uration #3)

third set of

yer 4 gap 110mm gap 110mm gap 110mm

t provided behind the surgap of 110similar beharties to the

metries 3)

ations

to

by the urface 0 mm. aviour MPB

4.4 A

In tha mic8), fitwo a4C-Gto 4Crefer

Fig

Assembling

is sub-secticro-perforatirst to analyairgap thic

G to 4C-H) C-J). The

rence. Table

gure 8 – Geanaly

Table 5 – D

Configu4C - A

4C - B 4C - C

4C - D MW MW/AG

4C - E 4C - F

4C - G 4C - H

4C - I

a micro-pe

on we analyted panel. Wyse the souncknesses (t=and then weresult for

e 5 provides

eometries usyze the influ

Definition o

uration LM

Mm mM

G M

mm

MM

m

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s the relevan

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of the differeco

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MPA mP

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mP mP

MPC MPC

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anel with a

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nt propertie

fourth set of acro-perfora

ent layers foonfiguration

Layer -

-

- - -

MPA MPA

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macro-perf

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d by each th(see ConfigConfigurat

N and MN/s of the laye

f configuratiation and m

for each systns

2 LayeMW

MWMW

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forated linin

macro-perfoons was defhese panels urations 4Cions 4C-E tAG) is alsers.

ions (configmicro-perfor

tem of the fo

er 3 La Air

d1= - Air

d1= -

- Aird1=

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d1=

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ng panel

orated panelfined (see Findividuall

C-A to 4C-Dto 4C-F andso displaye

guration #4)ration

fourth set of

ayer 4 rgap =110mm

rgap =110mm

rgap =110mm

rgap =110mm

rgap =110mm rgap =110mm

l with Figure y, for

D and d 4C-I d for

) to

f

Figuranalywithimicroabsorpaneld) app

Figurconfigur

4.5 Iposit

One woolprope

re 9 displaysysis of these n the mediumo-perforated rption providl. However wproaches tha

re 9 – Soundrations (con

Interior mactions inside

last case wal is placed ierties of the

s the sound aplots it can bm and high fis assemble

ded by this when we incrat provided b

d absorptionfiguration

and d) as

cro-perforae the airgap

as also analin varying pe layers in T

absorption prbe seen that frequencies aed to the masystem is qurease perfora

by the micro-

n coefficien#5): a )and ssuming an

ated panel liof a macro

lysed, wherepositions in

Table 6).

roperties of the micro-p

approaching acro-perforauite similar ation rate (M-perforated so

a)

c) nt provided d c) assumin

airgap with

lined with mo-perforated

e the perfornside the ai

the fourth seerforated pathe behavior

ated MPA (Fto that obtai

MPC), sound aolution.

by the geomng an airgaph thickness d

mineral wood system

rated panel Mrgap (see F

et of configunel providesr of a mineraFigures 9a ained for the absorption (s

metries usedp with thicknd1=0mm.

ol placed in

MPB lined Figure 10 an

urations. Fros sound absoal wool. Whand b), the

macro-perfosee Figures 9

d in the fifthkness d1=11

varying

with the mind details o

om the rption en the sound

forated 9c and

b)

d)

h set of 10mm; b)

ineral on the

Figanaly

Figurthat winsidelayereobtain

Figu

gure 10 – Glyze the influ

Table 6 –

Configur5C - A

5C - B

5C - C

re 11 displaywhen the pere the airgap,ed system isned with this

ure 11 – Sou

Geometries uuence of an

– Definition

ration LaMP

MP

MP

ys the resultsrforated pan, the presencs now obsers solution.

und absorptof

used in the fn interior pe

position

of the differco

yer 1 LayPA MPB

PA Airgd1=5

PA Airgd1=

s provided bel MPB withce of two peved. Conseq

ion coefficieof configura

fourth set oferforated pans inside the

rent layers fonfiguration

yer 2 LB M

gap 50.5mm

M

gap 110mm

-

by set of conh the mineraeaks, relatedquently, a br

ent provideations (confi

f configuratanel lined we airgap

for each sysns

ayer 3 LaMW -

MPB MwoM

nfiguration #al wool movd to the resonroader range

ed by the geofiguration #5

tions (configwith mineral

stem of the f

ayer 4 LaAid1

Mineral ool

Aid1

MPB Mwo

#5. In this ples to an intenating behavof absorptio

ometries use5)

guration #5l wool in var

fifth set of

ayer 5 irgap 1=110mm irgap 1=50.5mm

Mineral ool lot we may ermediate povior of this mon is succes

sed in the fif

5) to rying

notice osition multi-ssfully

fth set

4. CONCLUSIONS

In this paper a parametric study was carried out to analyse sound absorption of perforated shapes that may be suitable for achieving a variable acoustic solution, for room acoustic design, making use of combinations of macro-perforated panels with different perforation rates and micro-perforated panels, porous materials and airgaps of varying thicknesses. From the performed analysis we may identify the following conclusions for definition of guidelines for future design:

- Placing the porous material on the back of the perforated panel allows to increase sound absorption amplitudes;

- When increasing the airgap thicknesses from 0mm to 150mm it is possible to move the peak of sound absorption to lower frequencies;

- When assembling two macro-perforated panels of different perforations with the perforated panel with smaller diameter on the back, the behaviour of the system is similar to the macro-perforated panel with smaller diameter of the hole, placed on the back, but with thinness similar to the total width of the panel;

- Micro-perforated panel lining a macro-perforated panel with low perforation rates displays similar behaviour to that obtained for the macro-perforated panel.

- Inserting inside a perforated panel a second movable perforated panel lined with a porous material may increase the frequency range of sound absorption.

ACKNOWLEDGEMENTS

This work is financed by FEDER funds through the Competitivity Factors Operational Programme - COMPETE within the scope of the project ADJUST - Development of acoustic panels progressively adjustable with smart acting – SII & DT Project CENTRO-01-0247-FEDER-033884 This work was also partly financed by FEDER funds through the Competitivity Factors Operational Programme - COMPETE and by national funds through FCT – Foundation for Science and Technology within the scope of the project POCI-01-0145-FEDER-007633 and through the Regional Operational Programme CENTRO2020 within the scope of the project CENTRO-01-0145-FEDER-000006.

6. REFERENCES [1] G. Thün, K. Velikov, L. Sauvé, W. McGee, “Design Ecologies for Responsive Environments: Resonant Chamber, an Acoustically Performative System”. ACADIA 12 Synthetic Digital Ecologies, Proceedings of the 32nd Annual Conference of the Association for Computer Aided Design in Architecture (2012).

[2] M. Barron, Acoustics for multi-purpose use, “Auditorium Acoustics and Architectural Design”, Second., London and New York: Spon Press, (2010).

[3] F. A. Everest and K. C. Pohlmann, “Adjustable Acoustics”, in Master Handbook of Acoustics, 5th ed., McGraw-Hills, (2009).

[4] MD.Egan “Architectural Acoustics”, New York, USA: McGraw-Hill (1988).

[5] LL Beranek. “Concert Halls and Opera Houses Music, Acoustics, and Architecture”, New York, USA: Springer-Verlag; 2004.

[6] R. Patraquim, L. Godinho, A. Tadeu, P. Amado-Mendes, “Influence of the presence of lining materials in the acoustic behaviour of perforated panel Systems”, ICSV 18, Rio de Janeiro, Brazil (2018).

[7] T.J. Cox and P. D’Antonio, “Acoustic absorbers and diffusers: theory, design and application”, Spoon Press, 1st ed. (2004).

[8] I.B. Crandall, “Theory of vibrating systems and sound,” Van Nostrand, New York (1926).