KNE408 Engineering projects B

Anechoic chamber design

Author: Zongtai LI - 490735

Supervisor: Dr. Damien Holloway

10th October 2020

I

DECLARATIONS

ZongtaiLi

Signed:

Dated:14/10/2020

I

ACKNOWLEDGEMENTS

I would like to thank my supervisor Dr Damien Holloway, who has given me a lot of

important suggestions and support throughout my honour project. He provided a lot of

relevant professional knowledge materials, helped me solve many professional problems that

troubledme,andmademyhonourprojectmoresmoothly.

I want to thank my partner Zi Yi Kam. Due to the epidemic, when I was unable to return to

Australia. It was he who gave me a lot of real data for impedance tube experiments in

Australia, and he helped me to successfully compare the experimental values with the

simulatedvalues.Iamverygratefulforhisguidanceandhelp

II

ABSTRACT

Ananechoicroomreferstoanacousticlaboratorythatminimizesinternalsoundreflectionand

external noise. The main purpose of the anechoic room is to simulate the acoustic conditions

of free space without obstacles.External noise is eliminated by the building itself, the thick

masonry walls and the silencers in the ventilation ducts in the anechoic room (even the

anechoic room must have an outlet for air toflow, otherwise it will endanger the health of the

staff inside. The room the inner surface of the watch is covered with a blanket or made of

horizontalandverticalwedge-shapedsound-absorbingmaterialstoreducethesoundreflection

toonethousandth.

Themainfocusofthisarticleistomodelthethree-dimensionalimpedancetubewiththefinite

element method. In order to study the sound absorption performance of this porous material,

the finite element method (FEM) is used here. By establishing a finite element model, the

relationship between sound absorption coefficient and frequency is studied, and the influence

of mesh size on sound absorption quality is studied. Finally, the finite element results are

compared withthe impedance tube experiment results to establish that the model can run well

sothatthemodelcanbeusedtosimulateothermaterialsthatcannotbeobtained.

Because the most important thing in Anechoic chamber design is to determine the sound-

absorbing materials needed for the anechoic chamber. We evaluated the sound absorption of

polyurethane foam as a wide and versatile porous material. The most important acoustic

parameterofporousmaterialsistheabsorptioncoefficient. Accordingtoit,thesematerialsare

classified as absorbing or reflecting. The absorption coefficient can be defined as the

relationship between the sound energy absorbed by a material and the total incidence that

strikes it. This coefficientis limited between0 for non-absorbent materials and 1for complete

absorption. In order to study the sound absorption coefficient of sound-absorbing materials,

we used impedance tubes to measure the existing materials FM100, FM50 G-G and FM50G-

W.

Finally, according to the results of the finite element analysis, in order to make the sound

absorption coefficient of the sound-absorbing material close to 1, the five coefficients of the

material's JCA model should be respectively: Fluid Resistivity should be greater than 13000

(Nsm^-4), Porosity and Tortuosity should be very Close to 1, it is very suitable when the

Viscous Characteristic Length of the material is 200um when using the model analysis, and

the Thermal Characteristic Lengrh changes according to the thickness of the material. When

the thickness of the material is 0.1m, the recommended Thermal Characteristic Lengrh is

recommendedItis400um.

III

Table of Contents

Anechoicchamberdesign.......................................................................................................................I

DECLARATIONS....................................................................................................................................I

ACKNOWLEDGEMENTS....................................................................................................................II

ABSTRACT............................................................................................................................................III

ListofTables.........................................................................................................................................VI

ListofFigures......................................................................................................................................VII

ListofAbbreviationsandAcronyms....................................................................................................IX

ListofSymbols........................................................................................................................................X

1.INTRODUCTION...............................................................................................................................1

1.1Background.......................................................................................................................................1

1.2ResearchObjectives..........................................................................................................................2

1.3Studyprotocols..................................................................................................................................3

1.4ThesisStructure................................................................................................................................3

2.LITERATUREREVIEW...................................................................................................................4

2.1AStudyofAnechoicchamber..........................................................................................................4

2.2AstudyofPoroussound-absorbingmaterial..................................................................................7

2.3AstudyofFiniteElementMethod...................................................................................................9

2.4Economicanechoicchambermaterial-polyurethaneacousticsponge.......................................12

3.METHOD..........................................................................................................................................19

3.1FiniteElementMethod...................................................................................................................19

3.1.1Introduction..................................................................................................................................19

3.1.2Theory...........................................................................................................................................19

3.1.3AcousticanalysisbasedonANASYS............................................................................................21

3.2Johnson-Champoux-Allard(JCA)Model.....................................................................................26

3.2.1Introduction..................................................................................................................................26

3.2.2EstimationofJCAparameters.....................................................................................................28

3.3ImpedanceTube.............................................................................................................................30

3.3.1Introduction.................................................................................................................................30

3.3.2laboratoryapparatus....................................................................................................................31

3.3.3Experimentalsteps........................................................................................................................32

4.RESULT&DISCUSSION...............................................................................................................33

4.1Chapterintroduction......................................................................................................................33

4.2Therelationshipbetweenfluidresistivityandabsorptioncoefficientofmaterials....................34

4.2TherelationshipbetweenmaterialPorosityandabsorptioncoefficient.....................................35

4.3TherelationshipbetweenmaterialTortuosityandabsorptioncoefficient..................................36

4.4TherelationshipbetweenmaterialViscousCharacteristicLength(um)andabsorption

coefficient..............................................................................................................................................36

4.5TherelationshipbetweenmaterialThermalCharacteristicLength(um)andabsorption

coefficient..............................................................................................................................................37

4.6Thematchingresultofthefiniteelementmodelresultandtheimpedancetubeexperiment

result......................................................................................................................................................38

4.7Theinfluenceofmaterialthicknessonsoundabsorptioncoefficient.........................................40

5.CONCLUSIONANDFURTHERWORK......................................................................................41

IV

5.1Conclusion......................................................................................................................................41

5.2Recommendationforfutureresearch............................................................................................42

REFERENCES.....................................................................................................................................43

APPENDIX...........................................................................................................................................46

AppendixAFiniteelementmodeldata...............................................................................................46

AppendixBImpedancetubeexperimentdata....................................................................................53

V

List of Tables

Table1:Acousticabsorptioncoefficientofpolyurethanefoam

Table2:SummaryofJCAparameters

Table3.JCAModelcoefficientsofsevenmaterialsanalyzedbyfiniteelementmodel

Table4:Materialcharacteristicsmatchedbythefiniteelementanalysismodelaccordingtothe

experimentalresultsoftheimpedancetube

Table5:Dataofmaterial1simulatedbythemodel

Table6:Dataofmaterial2simulatedbythemodel

Table7:Dataofmaterial3simulatedbythemodel

Table8:Dataofmaterial4simulatedbythemodel

Table9:Dataofmaterial5simulatedbythemodel

Table10:Dataofmaterial6simulatedbythemodel

Table11:Dataofmaterial7simulatedbythemodel

Table12:DataofFM100,Thick=0.1msimulatedbythemodel

Table13:DataofFM50G-GThick=0.05msimulatedbythemodel

Table14:DataofFM50G-GThick=0.1msimulatedbythemodel

Table15:DataofFM50G-GThick=0.15msimulatedbythemodel

Table16:DataofFM50G-WThick=0.05msimulatedbythemodel

Table17:ExperimentaldataofimpedancetubeofmaterialFM100

VI

List of Figures

Figure1:Soundprocessingprocessofsound-absorbingmaterials

Figure2:Thereflectionofsoundwavesonthewallsoftheanechoicchamberisminimized

Figure3:Two-dimensionalgridimage

Figure2:Thereflectionofsoundwavesonthewallsoftheanechoicchamberisminimized

Figure3:Two-dimensionalgridimage

Figure4:Megaserver’spatentedsoundabsorptionsystem

Figure5:Thesound-absorbingmaterialsparticipatinginthetest,fromlefttorightareFM100,

FM50G-G,FM50G-W

Figure6:Geometricmodelingofimpedancetube

Figure7:EngineeringDataoftheimpedancetubemodel

Figure8:Modelingprocessdiagramofimpedancetube

Figure9:ElementsizedistributionofModel

Figure10:MaterialFM50,soundpressuredistributiondiagramat2600hz

Figure11:Structureofporousmaterials

Figure12:SketchofB&KLiboinstallation

Figure13Experimentalinstrumentdiagramofimpedancetube

Figure14:Sketchoftheexperimentaldevice

Figure15:Theinfluenceoffluidresistivityonfluid(fluidresistivity=2000,7000,12000)

Figure16:TheinfluenceofPorosityonfluid(Porosity=0.8and0.9)

Figure17:TheinfluenceofTortuosityonfluid(Tortuosity=1.5and2.5)

Figure18:TheinfluenceofViscousCharacteristicLengthonfluid(ViscousCharacteristic

Length=50and200um)

Figure19:TheinfluenceofThermalCharacteristicLengthonfluid(ThermalCharacteristic

Length=200and800um)

Figure20:MatchingresultofimpedancetubeexperimentofmaterialFM100withfiniteelement

model

Figure21:MatchingresultofimpedancetubeexperimentofmaterialFM50G-Gwithfinite

elementmode

Figure22:MatchingresultofimpedancetubeexperimentofmaterialFM50G-Wwithfinite

elementmodel

Figure23:TherelationshipbetweenthesoundabsorptioncoefficientandfrequencyofFM50with

differentthicknesses

Figure24:Therelationshipbetweenthefrequencyofmaterial1andthesoundabsorption

coefficient

Figure25:Therelationshipbetweenthefrequencyofmaterial2andthesoundabsorption

VII

coefficient

Figure26:Therelationshipbetweenthefrequencyofmaterial3andthesoundabsorption

coefficient

Figure27:Therelationshipbetweenthefrequencyofmaterial4andthesoundabsorption

coefficient

Figure28:Therelationshipbetweenthefrequencyofmaterial5andthesoundabsorption

coefficient

Figure29:Therelationshipbetweenthefrequencyofmaterial6andthesoundabsorption

coefficient

Figure30:Therelationshipbetweenthefrequencyofmaterial7andthesoundabsorption

coefficient

Figure 31: The relationship between the frequency of the material FM100 and the sound

absorptioncoefficient

VIII

List of Abbreviations and Acronyms

ISO:InternationalOrganizationforStandardization

FEM:FiniteElementMethod

JCA:Johnson-Champoux-AllardModel

ECM：electromagneticcompliance

IX

List of Symbols

 Hz-hertz

 dB-decibel

 m-Meter

 Kg-kilogram

X

1. INTRODUCTION

1.1 Background

An anechoic chamber is an acoustic laboratory that minimizes the reflection of internal sounds

and noise from the outside. The building itself and the thick masonry walls and mufflers in the

ventilation ducts in the anechoic room can eliminate external noise. (Even the anechoic room

must have an outlet for air to flow, otherwise, it will endanger the health of the staff inside).

“Generally, the surface of the room can be covered with a blanket or made of horizontal and

vertical wedge-shaped sound-absorbing materials, which can reduce the reflection of sound to

one-thousandth [1].” “In this case, the anechoic chamber can be used to study free-space

unobstructed acoustic experiments, and to obtain the true absorption and scattering

characteristicsofsoundwithoutinterferencefromsoundreflection[2].”

“The sound-absorbing material used in the anechoic chamber requires a sound absorption

coefficient greater than 0.99. The gradual absorption layer is generally used, usually with a

wedge or cone structure, and glass wool is used as the sound-absorbing material. The main

point of the sound-absorbing structure is the sound-absorbing material on the wall! It uses a

porous(orfibrous)materialtomakeaconeorspike-shapedsound-absorbingbody[3].”Dueto

the gradual transitional nature of the sound absorption layer, the acoustic impedance of the

material can be well-matched with the air's acoustic impedance. When the sound wave is

incident from the tip, the stream enters the sound absorption body and is efficiently absorbed.

Itsessenceistocreateanapproximatefreefieldspaceforthestudyoftheacoustic.

Because the most important thing in Anechoic chamber design is to determine the sound-

absorbing materials needed for the anechoic chamber. We evaluated the sound absorption of

polyurethane foam as a wide and versatile porous material. The most important acoustic

parameterofporous materialsistheabsorptioncoefficient.Accordingtoit,these materialsare

classified as absorbing or reflecting. The absorption coefficient can be defined as the

relationship between the sound energy absorbed by a material and the total incidence that

strikes it. This coefficient is limited between0 for non-absorbent materials and 1for complete

absorption. In order to study the sound absorption coefficient of sound-absorbing materials,

we used impedance tubes to measure the existing materials FM100, FM50 G-G and FM50G-

W. But in order to be able to study unavailable materials, this article introduces a three-

dimensional finite element analysis method for predicting the sound insulation capability of

polyurethane foam as a passive soundabsorber. The focus of this article is tomodel the three-

dimensional impedance tube with the finite element method. In order to study the sound

1

absorptionperformance of this porousmaterial, the finiteelement method(FEM)isusedhere.

By establishing a finite element model, the relationship between sound absorption coefficient

andfrequencyisstudied,andtheinfluenceofmeshsizeonsoundabsorptionqualityisstudied.

Finally, the finite element results are compared with the impedance tube experiment results to

establish that themodel canrunwell sothat the model canbe usedtosimulate other materials

thatcannotbeobtained.

1.2 Research Objectives

The main purpose of this project is to determine the most suitable indoor wall material for the

anechoicroom

1. According to the sound treatment process of the sound-absorbing material shown in

Figure 1, it can be known that if the reflection of sound to the material is effectively

increased, the sound can be greatly reduced back to the room. According to this

characteristic, determine the most suitable sound-absorbing material in the anechoic

chamber.

Figure1:Soundprocessingprocessofsound-absorbingmaterials

2. The finite element method (FEM) is used to study the sound absorption performance of

the determined sound-absorbing material. By establishing a finite element model, the

relationship between sound absorption coefficient and frequency is studied, and the

influenceofmeshsizeonsoundabsorptionqualityisstudied.

3. Researchtheexperimentaldataofimpedancetubeonexistingmaterialsobtainedfromthe

laboratory.

2

4. Finally, the finite element results are compared with the impedance tube experiment

results to establish that the model can run well so that the model can be used to simulate

othermaterialsthatcannotbeobtained.

1.3 Study protocols

1. Firstly,some ISOstandardsforanechoicchamberdesignshouldbedetermined;inaddition,

some information on anechoic chambers or anechoic chamber designs in recent academic

literatureshouldbeidentified.

2. Find suitable sound-absorbing materials and conduct finite element analysis on the

materials. Suchas porosityresistingtortuositymaterialmodelparametersadjustedtomatch

the published tentative date will need to be. Moreover, it compares with exposed walls and

differentmaterials.Finally,verificationresultsinthebestsound-absorbingcontent.

3. According to the results obtained in the above steps, use ANSYS to complete the anechoic

chamber's modelling. ("ANSYS software is a large-scale general finite element analysis

(FEA)softwaredevelopedbytheAmericanANSYScompany[4].")

4. The finite element analysis results are matched with the experimental results obtained from

the impedance tube experiment, verifyingthat the ANASYS model canbe used tosimulate

sound-absorbingmaterialsandexplorethepropertiesofthematerials.

1.4 Thesis Structure

Thestructureofthisarticleisasfollows:

Chapter 1 is an introduction, introducing the background required for the design of the

anechoicroomandtheoriginalcontentofthispaper.

Chapter 2 is a literature review, which mainly studies the characteristics of the anechoic

chamber andvarious standards requiredfor the constructionof the anechoic hall.And how does

the anechoic room reduce noise? It also introduces professional terms related to an anechoic

chamber. A porous sound-absorbing material was also studied. After comparing the documents,

a cost-effective sound-absorbing cloth, polyurethane sponge, was determined. Also considered,

themethodusedtostudymaterials-finiteelementanalysis.

Chapter 3 is a method, here is the method used to study the characteristics of sound-absorbing

3

materials in this research. Including finite element analysis method, impedance tube experiment

method.Thispartalsogivestheexperimentalstepsandresultsofthetwomethods.

Chapter4istheresultsanddiscussionandcomparestheresultsthathave beenobtainedwiththe

researchofothers.Andevaluatetheresultsobtained.Togetareasonableconclusion.

Chapter 5 is the Conclusion. It summarizes the full text and clearly shows the results. Chapter 7

isreferenced,whichwillintroducethedocumentsusedinthisthesis.

2. LITERATURE REVIEW

2.1 A Study of Anechoic chamber

For those entering the anechoic room for the first time, it is unaccustomed to it. It is entirely

differentfrom the externalauditoryfeelings. There isno echoof high-five speech.The soundof

the friction of the underwear while walking is unprecedentedly clear. Without saying anything,

it seems quiet here to hear his blood flowing. In this tranquil environment, the first contact with

theanechoicroomwillimmediatelyfeellonelinessandslightfear[5]

The sound absorption material used in the anechoic chamber requires a sound absorption

coefficient higher than 0.99. Generally, a continuous absorption layer is used, and the tine or

cone structure is commonly used, andglass wool is used as the sound-absorbing material, and

softfoamplasticisalsoused.

Since the 1940s, the principle of gradual transition has been applied to make porous (or

fibrous) materials into cone-shaped or spike-shaped sound-absorbing bodies, collectively

called sound-absorbing spikes. When the sound wave is incident from the tip, due to the

gradualtransitionof the sound-absorbinglayer,the acoustic impedance ofthe material andthe

air impedance can be matched well, so that the sound wave is introduced into the sound-

absorbing body and is efficiently absorbed. So far, high-quality anechoic chambers at home

andabroadhaveadoptedaspikestructureasasound-absorbingbody.

The sound absorption characteristics of the sound absorption spike are related to the length of

the peak, the filling material, and the depth of the cavity. The longer the period of the split

under the same article, the better the low-frequency sound absorption performance of the

separation. Adjusting the depth of the cavity can also effectively improve the spike structure's

4

low-frequencysoundabsorptioncharacteristics.

The figure below demonstrates the mechanism of minimizing reflectionafter soundwaves are

incident on the surrounding wedge in the anechoic chamber. W in the figure shows that the

incident sound wave I is incident on the wall of the anechoic room. The blue area is a wall

composedofaseriesofwedgesWofheight H.Whenthesoundwave hitsthewall,aseriesof

reflected waves R will be generated, which in turn will be in the gap of the air A (this bounce

may (at least temporarily) produce a standingwave mode inA. The soundenergy of the wave

R will pass through the air.The molecular viscosity (especially near corner C) dissipates [5].

Besides, when using foam to make a wedge, another dissipationmechanism occurs duringthe

wave/wall interaction [6]. Therefore, when the reflected wave R escapes the gap A (and

returns to the sound source) along the I direction, the component R ′ decreases significantly.

Evenif this interpretationis two-dimensional, it is representative andsuitable for practical use

inanechoicchambersThree-dimensionalwedgestructure.[7]

Figure2:Thereflectionofsoundwavesonthewallsoftheanechoicchamberisminimized[8]

Generally, ifthesoundpressure generatedinthepoint soundsource inthe freefieldshouldbe

inversely proportional to the distance from the sound source, it can be determined that the

performance of the anechoic chamber is satisfactory. The main index used to measure the

performanceoftheanechoicroom.Ingeneral,acoustictests,thisdeviationisrequiredtobeno

higher than± 1dB; formicrophone calibration, this deviationisnecessarytobe nohigherthan

±0.1dBaroundthecalibrationdistance[9].

Thecharacteristicsoftheanechoicroomaremainlyreflectedinthefollowingpoints:

1. Freefieldspace

5

The anechoic chamber's primary function is to provide a semi-free-field space or free-field

space for acoustic testing. The open field means that when sound waves propagate in an

infinitelylarge area,there is noreflector or reflectingsurface. The free fieldradiusis anindex

usedtomeasurethesize oftheopenfield.Ina well-designedanechoicchamber,theopenfield

radiusshouldbe1.0mfromthecenterpointtothetip[10,11].

2. Backgroundnoise

Another function of the anechoic chamber is to provide a low background noise environment

to meet the requirements of the test environment. In the test frequency range, the background

noise level is at least 6dB more economical than the sound pressure level of the measured

soundsource,preferably12dBlower[9,10].

3. Cutofffrequency

In the design of an anechoic chamber, the lowest frequency with a spiked sound absorption

coefficientof0.99isusuallycalledthecutofffrequency.Whenthesoundabsorptionsystemof

thewallcanguarantee99%ofthesoundabsorptioncoefficient,itcanensurethat theanechoic

room meets the free field conditions above the cutoff frequency. Measurements below the

cutoff frequency can be corrected according to ISO 3746 and ISO 3747 standards. For

example, in a 10 × 10 × 10m laboratory,a 1m long sound-absorbing slab is laid on each side,

anditslow-frequencycutofffrequencycanreach50Hz[9,10].

Up to 125Hz frequency can be expanded to 50Hz anechoic room identification method

according to the national standard ISO 3746 and national standard GB6882-2008 'Acoustics

--- Determination of noise source sound power': anechoic room and semi-anechoic room

precision method. The free field identification method specified in the anechoic chamber is

tested. That is, under 125Hz and above 4000Hz, 1/3 octave center frequency interval single

frequency signal is used, and between 125Hz and 4000Hz, 1/1 octave center frequency

interval single frequency signal is used. The measured sound pressure level and pure sound

aremeasured—thedifferencebetweenpressurelevels[9,11].

According to this, according to the maximum allowable difference stipulated in ISO3746 and

GB6882-2008,theallowablemeasurementradiusandthefreeareaoftheopensoundfieldthat

meet the standard can be determined. The maximum permissible difference between the

measured sound level and the theoretical sound level specified in ISO3745 and GB6882.

Acoustic room (semi-anechoic room) acoustic performance parameters Semi-anechoic room

design standard ISO3746 and GB6882-2008 cutoff frequency 125Hz (can be extended to

6

50Hzaccordingtorequirements)noise floor16dB(11dB withuniquedesign) 3.The internal

dimensionsaredesignedaccordingtoneedsandstandards[9,11].

2.2 A study of Porous sound-absorbing material

Due to the lack of understanding of noise control methods, the sound absorption properties and

soundinsulationpropertiesofmaterialsareoftenconfusedascompletelydifferentconcepts.The

difference between the sound absorption properties of materials and the sound insulation

propertiesisthatthesoundabsorptionpropertiesrefertotheabilitytoconvertsoundenergyinto

other energy when the sound source contacts the material, with the purpose of reducing the

reflected sound energy. The sound insulation properties of a material refer to the size of the

transmitted sound energy that the material transmits from one side of the material to the other

side of the incident sound source, and the purpose is to make the transmitted sound energy

smaller. There are also big differences between the two materials in terms of equipment. The

sound-absorbing material reflects little incident sound energy, which means that sound energy

can quickly enter and penetrate the material. Acoustic materials with such properties are typical

porous sound-absorbing materials, which are usually foam, particles or fiber materials in the

process of forming a porous structure. Its structural feature is that the content has some

interpenetrating micropores from the front to the inside, which means it has a specific

permeability. For soundinsulationmaterials,itisnecessarytopreventthetransmissionof sound

andreduce thetransmissionof soundenergy, sothis means thatitcannot beas loose,breathable

and porous as sound-absorbing materials. On the contrary, its content should be denser, such as

steel plates, lead plates, brick walls and other types of materials. In engineering, the objectives

andfocus of soundabsorptionprocessingand audioisolation processingare different.Reducing

the repetitive reflection of sound in the room is the purpose of sound absorption processing,

which is to use the sound-absorbing material covered on the indoor surface to reduce room

vibration and shorten the duration of reverberation. In the case of continuous noise, this

reductioninreverberationtimeismanifestedasareductionintheindoornoiselevel.Theunique

role of sound-absorbing materials is further embodied in the ability to shorten and adjust the

roomreverberationtime,andnoothermaterialcanreplaceit.Becausethevolumeoftheroomis

directly proportional to the reverberation time, the larger the volume of the building space, the

longer the reverberation time. Currently, it is usually necessary to adjust the reverberation time

through sound-absorbing materials. Therefore, acoustic materials usually refer to sound-

absorbing elements. Among many methods and methods to control noise pollution, sound-

absorbing materials are the most basic method that can be used to reduce noise, while porous

sound-absorbingmaterialsarethemostwidelyused.

7

Thesoundabsorptionmechanismofporousmaterialsismainly:

Whensoundwavespassthroughthesurfaceoftheporousmaterial,theairinthemicroporesis

excited to vibrate, and the relative motion between the sky and the solid ribs occurs. Due to

theviscosityoftheair,theviscousresistanceisgeneratedinthemicropores,sothatthekinetic

energy of the vibrating air is continuously converted into Thermal energy, thereby attenuating

soundenergy.

When the air is adiabatically compressed, heat exchange occurs between the sky and the

whole wall, and the sound energy is converted into heat energy. The rational absorption

spectrum characteristic curve of porous sound-absorbing materials can be obtained from

practical experience data. The overall trend is that when the frequency becomes larger, the

sound absorption coefficient also increases with the increase, and the sound absorption

coefficient gradually increases from a low rate to a high standard. A resonance absorption

peakanddifferentdegreesofupsanddowns.Belowtheresonancesoundabsorptionfrequency,

the sound absorption frequency characteristics are like the frequency characteristics of the

resonance sound absorption structure. Above the resonance sound absorption frequency, the

sound absorption coefficient fluctuates within the range between the peak and valley, that is,

with the rate, the amplitude of the fluctuation of the sound absorption coefficient gradually

decreases and tends to a value that does not change significantly with frequency. This shows

that the porous sound-absorbing material does not have a sound absorption upper limit

frequency, so it has better high-frequency sound absorption performance than the perforated

plateresonancesoundabsorptionstructure[12].

The porous material contains a lot of ultra-fine micropores and gaps or called capillary

structure,filledwithairbetweenthetwo.Whenthesoundwave isperpendicularlyincidenton

the surface of the porous material, part of it is reflected by the surface of the content, and the

otherpartistransmittedintothematerialthroughthecapillarythatistransparenttotheoutside.

The vibration of the sound wave entering the material causes the violent movement of the air

inthecapillary,causingittorubagainsttheholewall.Undertheactionoffrictionandviscous

force,partof the soundenergy isconvertedintoheatenergy, whichattenuates the soundwave

andweakensthereflectedsoundenergytoachievethesoundabsorptioneffect.Also,theairin

thecapillaryandtheheatexchange betweenthehole wallandthematerial cause heatloss and

also cause attenuation of sound energy. Therefore, the sound absorption effect of porous

materials is the result of the viscous force and friction force of air, and the heat conduction

betweentheskyandthematerialbetweenthecapillaries[13].

8

Poroussound-absorbingmaterialscanbedividedintoorganicsound-absorbingmaterials,such

as cotton fibre, felt, wood fibre board, polyester cotton and other Organic fibre materials;

inorganic sound-absorbing materials, such as slag wool, glass wool, perlite, and other

inorganicsound-absorbingmaterials; foammaterials, suchasfoamconcrete,foamplastic,and

other sound-absorbing foam materials; sound-absorbing building materials, such as absorbent

Acoustic stucco, microporous acoustic tiles, ceramic acoustic panels, etc. The new sound-

absorbing material not only has the excellent acoustic performance of flexible fibre-shaped

sound-absorbing materials (such as glass fibre wool) but also must have the stable mechanical

propertiesofothermud-powder-likesound-absorbingmaterials(suchasclaysoundabsorption)

[14].

Inorganic fibre materials such as rock wool, glass wool and slag wool have excellent sound

absorption performance, light capacity, non-combustible, non-corrosive, and thermal

insulation.

Andothercharacteristicsandthepriceisrelativelylow,makingitthemostwidelyusedsound-

absorbing material in acoustic engineering, but it is easy to break due to its soft quality,quiet

strength,andbrittlefibre.Intheconstructionandinstallationproject,fibredustwillbeformed

polluted environment. Therefore, in actual use, a covering material is used to prevent the

fibres from scattering. Commonly used are glass fibre cloth, as well as microporous veneer,

glass fibre felt, sprayed neoprene, and high perforation aluminium foil and other covering

materials. Most of these covering layers can maintain the sound absorption properties of glass

wool[15].

2.3 A study of Finite Element Method

The finite element method (FEM) is a modern computing method that has emerged in the rapid

development of electronic computers. In the 1950s, the finite element method was replaced for

thefirsttime inthefieldofcontinuummechanics. Throughcontinuousdevelopment, the objects

that can be analyzed by the finite element analysis method have also expanded from elastic

materials to plastics, viscoelasticity and composite materials. The finite element method will

develop the research scope from statics to dynamics, stability and flow problems; The elastic

planeproblemextendstotheplateandshellproblemandthespaceproblem[16].

Finite elements are those discrete elements that can be combined to represent the actual

continuous domain. The concept of finite element analysis has actually been proposed long

ago. For example, when calculating the perimeter of a ring, a polygon (a finite number of

9

linear factors) can be used to approximate a circle. The finite element method was originally

used to calculate the structural strength of the aircraft, but because of its convenience,

practicality and effectiveness, it has aroused great interest. Scientists use it to solve

engineeringproblems.Withtherapiddevelopmentandpopularizationofcomputertechnology

and the rapid development of finite element method, it can be used not only to analyze

engineering strength but also to calculate almost all fields of science and technology. It has

becomeacolorful,widelyused,practicalandeffectivenumericalanalysismethod.[17].

The operating principle of FEA is to simulate real physical systems by using mathematical

approximation methods, such as: the load and geometric characteristics of objects. By using

interactive and simple elements, a real system with infinite unknowns is transformed into a

systemwithfiniteunknowns[17].

In the process of solving problems, finite element analysis is to replace complex problems

with simple problems and then solve them. In the solution process, it is to understand the

things to be studied as composed of many small interconnected sub-domains that it considers

finite elements. Assuming that when each unit has a suitable (simpler) approximate solution,

the analysis of the approximate solution can reduce the overall satisfactory results and get the

final answer. However, because this method turns the elements of the actual problem into

approximate solutions, this solution is not completely accurate, and the answer is an

approximate solution. Since most practical problems cannot obtain accurate answers

completely, the finite element analysis method can not only adapt to various complicated

shapes but also have high calculation accuracy. Therefore, the finite element analysis method

isaneffectiveengineeringanalysismethod.[17].

Necessarystepsforfiniteelementanalysis:

Step1:Undertheconditionsgivenaccordingtotheactualproblem,whendefiningandsolving

themodel,therearethefollowingaspects:

Definition of geometric characteristics of practical problems: In solving practical problems, it

is necessary to determine the approximate physical properties and geometric characteristics,

element types, and material types of the research objects. In addition to this, it is necessary to

determine the load, the connectivity between each element, the function of things, the shape

(area,length)oftheelementsused,andtheboundaryconditions.[17].

Step2:Split

The region to be solved is divided into discrete sets of finite elements. The shape of the

10

component (unit) is, in principle arbitrary. Two-dimensional problems generally ustriangular

elements or rectangular elements, and three-dimensional space can use tetrahedron or

polyhedron.Theverticesofeachunitarecallednodes(ornodes)[18].

Figure3:Two-dimensionalgridimage[18]

Step3:Unitanalysis

Performing slice interpolation, expand the unknown function at any point in the division unit

with the shape function in the division unit and the function value on the discrete grid point,

establishalinearinterpolationfunction[18]

Step4:Solvetheapproximatevariationalequation

The finite element method is used to disperse the continuum, and the numerical method is

used to solve various mechanical and physical problems by peaceful interpolation. The finite

elementmethoddispersesthecontinuumintofiniteunits.The structuralunitoftherodsystem

is each member. The unit of the continuum is the unitary body of different shapes (triangle,

quadrilateral, hexahedron, etc.). The field function for each element is a simple field function

that contains only a limited number of parameters and sets of unspecified nodes. Among the

field functions of these elements, the field function of the whole continuum can be roughly

represented. According to the energy equation or the weighted residual equation, a finite

number of algebraic equations with indeterminate parameters can be established, and the

numerical solution of the finite element method is as follows. It is obtained by solving this

discrete equation. The finite element method is used to solve linear and nonlinear problems.

Established various finite element models such as fitted, unadjusted, mixed, hybrid and semi-

fitted. The finite element method is very efficient, versatile and widely used. There are many

important or special programming systems for engineering design. Items Limited by

Computer Aided Design Technology. This method is also used in computer aided

manufacturing[18].

According to the existing literature review, several sound-absorbing materials will be

11

identified by finite element analysis and finite element analysis was performed on the sound-

absorbing materials using finite element analysis software. In addition, a suitable sound-

absorbingmaterialshouldbefinalized

2.4 Economic anechoic chamber material-polyurethane acoustic

sponge

As noise pollution is increasingly recognized as a serious and worldwide public health

problem. Therefore, the issue of noise control has received considerable attention. Therefore,

the need for sound-absorbing materials meets the requirements of low-cost, lightweight, and

wide-frequency absorption materials. Therefore, predicting the acoustic performance of noise

absorbers is crucial. Porous materials such as foam are often used in noise control. The same

foam is also suitable for the internal wall veneer of the anechoic room. Because this material

can generate air friction and viscous friction within the polymer battery and between adjacent

polymer chains, these foams canact as soundabsorbers by converting sound energy intoheat.

Insummary,polyurethaneacousticfoamisoneofthemostsuitablefoamsofthistype.

Polyurethane acoustic material, usually porous polyurethane foam, which combines the sound

absorption mechanism of general porous materials and the damping sound absorption

mechanismofflexiblematerials,hasgoodsoundabsorptionandsoundinsulationperformance,

and is a popular type. The new acoustic material has the following advantages compared with

commonly used fibrous sound-absorbing materials such as ultra-fine glass wool, rock wool,

slagwool,etc.:

1) Light weight, the density of polyurethane foam is very small, generally 10-200kg/N3,

whichisdifficulttoachieveformanyfibrousmaterials;

2) The sound absorption coefficient is high. The average sound absorption coefficient of

polyurethane foaminthe range of125-2000Hz canreachmorethan 0.50.The maximum

sound absorption coefficient of sound products in the middle and low frequency regions

canreachmorethan0.95;

3) Itiseasytoprocess,andthepolyurethanematerialiseasytoform,moldableand citable;

4) No dust pollution, is an environmentally friendly sound absorption and insulation

materialThisisalsounmatchedbymanyfibrousmaterials;

5) Waterproof,Moisture-proof,Moth-proof;

6) Awiderange ofadaptabilitynotonlycanbeuseddirectly,butalsocanbeattachedwitha

12

varietyofcladdingmaterialsonthesurfacefordecorationPlace[19].

The acoustic performance of polyurethane foam acoustic materials is related to the open cell

type of foam materials. The absorption coefficient of open cell foam is larger than that of

closedcellfoam.Table1.

Table1:Acousticabsorptioncoefficientofpolyurethanefoam[20]

frequency/Hz 125 250 350 500 1000 2000 4000

Opentype 0.14 0.22 0.31 0.69 0.53 0.83 0.73

Closetype 0.12 0.18 0.20 0.27 0.19 0.63 0.22

With polyester acoustic sponge can absorb electromagnetic energy and convert it into heat

energy. This material can be used as the main wall material when constructing an anechoic

chamberwithaspecialformandthickness.

The absorption characteristic that can absorb electromagnetic waves originates from the loss

part of the complex dielectric constant A, which is caused by the carbon loading of the

polyurethane foam in the material of the anechoic chamber. In order to maximize the

absorption capacity, the dielectric absorption medium should be in a region where electrical

energy accounts for a large portion of the total field energy.With a metal-backed surface, the

electric field energy is zero on the metal surface and is maximized at a quarter wavelength

awayfromthemetalsurface.Due tothisbasic limitation,whendesigningadielectricabsorber

with good performance for electromagnetic compliance (EMC), its length at the lowest

operatingfrequencyisalwaysatleastaboutonequarterofthewavelength[21]

The main sound-absorbing material analyzed in this study is the lightweight inherent fire-

proof and sound-proof foam board from Mega sorber for construction applications:

Megasorber FM sound-absorbing board. The sound insulation board has excellent sound

insulation and heat insulation effects and is suitable for construction and engineering

applications because it is easy to handle, cut and install, and is very light. The FM panel uses

Mega sorbet ’ s patented sound-absorbing surface material, Soundmesh G8, to provide

maximum sound absorption, especially in the mid- and low-frequency range (US Patent

8167085, Canadian Patent 2674986, Australian Patent 200926197). The unique Soundmesh

G8 coating is very durable. It is essentially fireproof. Traditional fireproof facing materials

andsoundreflectingfilmfacings(suchasaluminumfoil,polyesterfilmandpolyurethanefilm)

13

have almost noorzeroandpreventnoise frombeingabsorbedbythefoambelow.In contrast,

Soundmesh G8 has been carefully designed and adjusted to maximize sound absorption [22].

According to these data, it has been proved that this material can have a better sound

absorptioneffect.Ifthefiniteelementmodelcanbeusedtosuccessfullysimulatethematerial,

itshowsthatthecompletedfiniteelementmodelissuccessful.

Figure4:Megaserver’spatentedsoundabsorptionsystem[22]

Figure5:Thesound-absorbingmaterialsparticipatinginthetest,fromlefttorightareFM100,

FM50G-G,FM50G-W

2.5 A study of Finite Element modelling of porous materials

The finite element model is a calculation model for finite element analysis. It provides all

necessary raw data for finite element calculation. The process of establishing a finite element

14

model is called finite element modeling. It is the key to the entire finite element analysis

process. Whether the model is reasonable or not will directly affect the accuracy of the

calculation results, the length of the calculation time, the size of the storage capacity, and the

completionofthecalculationprocess.[34]

Finiteelementmodelingsteps:

 Problemdefinition

Before the finite element analysis, the shape, size, working condition, material type,

calculation content, general law of stress and deformation of the analysis object should be

carefully analyzed. Only by correctly mastering the specific characteristics of the analysis

object cana reasonable finite element model be established. Generallyspeaking, the following

points should be clarified when defining an analysis problem: structure type, analysis type,

analysis content, calculation accuracy requirements, model scale, and general laws of

calculationdata.

 Geometricmodelestablishment

Whenbuildinga geometric model,you needtosimplify, modify, andprocessshapes andsizes

according to the specific characteristics of the object in order to adapt to the characteristics of

finite element analysis.A geometric model is a description of the shape and size of an

analytical object, also known as the geometric solution domain. It is abstracted according to

the actual shape of the object, but not completely copied. Therefore, the dimensional

characteristics, shape, and size of a geometric model may be exactly the same as the original

structure, or there may be some differences. In order to realize automatic network division, a

geometric model needs to be established in the computer. The representation of geometric

model in computer includes solid model, curved surface model and wire frame model. The

specific form is related to the structure type. For example, plate and shell structure adopts

curved surface model, space structure adopts solid model, and rod system adopts Wireframe

models,etc.

 Unitselection

Before dividing the network, you must first determine which unit to use, including the type,

shape and order of the unit. Unit selection should be comprehensively considered based on

factors such as structure type, shape characteristics, stress and deformation characteristics,

accuracy requirements and hardware conditions. For example, if the structure is an irregular

space structure with a very complex shape, you should choose tetrahedral spatial solid

15

elements instead of pentahedral or hexahedral elements. If the accuracy requirements are

higherandthecomputercapacityislarger,youcanchoosethesecondaryortertiaryunit.Ifthe

structure is a relatively regular beam structure and the beam deformation is dominated by

bending deformation, it is more appropriate to choose non-coordinating elements than

coordinating elements. In addition, the selection of the unit type must be limited to the unit

library provided by the analysis software used, which means that only units supported by the

software can be used. In this sense, the richer the unit library of the software, the wider its

applicationrange,andthestrongerthemodelingfunction.

 Unitcharacteristicdefinition

Inadditiontoshowingacertainexternalshape(grid),theunitshouldalsohaveasetofinternal

characteristic data required for calculation. These data are used to define material properties,

physicalproperties,auxiliarygeometricfeatures,cross-sectionalshapeandsize,etc.Therefore,

before generating the unit, we should first define various characteristic tables describing the

characteristicsoftheunit.

 Meshing

Meshing (abbreviated as meshing) is the central task of establishing a finite element model.

The steps describedabove andbelow are allcarriedoutaroundmeshing. The rationalityof the

modelislargelydeterminedbythegridform.Therefore,subnettingisaverycriticalstepinthe

modeling process. It needs to consider many issues, such as the number of grids, density,

quality, layout, and displacement coordination. Networking is also the most workload and

time-consuming link in the modeling process. In order to improve the modeling speed,

automatic or semi-automatic network splitting methods are widely used. Automatic network

division refers to the automatic division of the grid by the computer through certain human

control based on the geometric model. The semi-automatic method is a human-computer

interaction method. It defines nodes and forms units by humans, and automatically numbers

nodes and units by software, and provides some auxiliary means to speed up the generation of

nodesandunits.

 Modelcheckingandprocessing

Generally speaking, the mesh model divided by automatic or semi-automatic method cannot

be used for analysis immediately. Due to the complexity of the structure shape and the grid

generation process, there are more or less problems with the grid, such as poor quality,

overlapping nodes or elements, unreasonable numbering sequence, etc. These problems will

affect the calculation accuracy and time, or Produce unreasonable calculation results, or even

16

abort the calculation. Therefore, the grid model should be checked and dealt with accordingly

afterthenetworkisdivided.

 Definitionofboundaryconditions

Themeshcombinationgeneratedbydividingthenetworkdefinesthenodeandelementdata.It

is not a complete finite element model, so it cannot be directly used for calculation. Boundary

conditions reflect the interactionbetween the analysis object and the outside worldand are the

manifestations of actual working conditions on the finite element model. Only when complete

boundary conditions are defined, can the required calculation results be calculated. For

example, when force and displacement constraints are imposed on the model, the deformation

and stress distribution of the structure can be calculated. The establishment of boundary

conditionsgenerallyrequires twosteps. One istoquantifythe actual operatingconditions, that

is,toexpresstheoperatingconditionsasmathematicalforms thatcanbedefinedonthemodel,

such as determining the distribution law of surface pressure, heat transfer coefficient of

convective heat transfer, and contact The surface contact stiffness, dynamic load action law,

etc.,this part of the workmay sometimes be verycomplicated, andoftenneedtorelyon some

test data. The second link is to define the quantified working conditions as the boundary

conditions on the model, such as element face force and edge force, inertial body force, and

convective heat transfer on the surface of the element. Whena reasonable gridform is divided

andthecorrectboundaryconditionsaredefined,acompletefiniteelementmodelisestablished.

Atthistime,thecorrespondinganalysisprogramcanbe calledtocalculatethemodel,andthen

the calculation results can be displayed and processed and research. However, for complex

analysis objects, due to many uncertain factors, it is sometimes impossible to model

successfully once through the modeling process described above, but through "modeling-

calculation-analysis, and comparison of calculation results. "Model revision" is an iterative

processtograduallymake themodelmorereasonable.Therefore,inthemodelingprocess,itis

necessary to conduct appropriate trial calculations and adopt modeling ideas ranging from

simpletocomplex,fromroughtoprecise.[35]

2.6 A study of Johnson-Champoux-Allard (JCA) Model

Johnson-Chamoux-Allard model is currently a generalized acoustic model that can accurately

describe the sound absorption characteristics of rigid framework porous metal materials in a

wide frequency range. The model contains five basic macro-acoustic parameters of materials.

At the same time, these five basic parameters have clear physical meanings. The five acoustic

parameter values are: Flow resistivity; Porosity; Tortuosity; Viscous characteristics lengths;

17

Thermalcharacteristicslengths.

 Porosity

Porosity refers to the percentage of the volume of pores in the bulk material to the total

volume of the material in its natural state. Porosity includes true porosity, closed porosity and

pre-porosity. Another concept corresponding to the porosity of the material is the density of

the material. Density indicates the degree to which the material is filled with solids. It

quantitatively reflects the content of solids inside the material, and its effect on the properties

ofthematerialisjusttheoppositeof theporosity. Theporosityorcompactness ofthe material

directlyreflects the compactness of the material. A high porosity of a material indicates a low

degreeofcompaction.

 Tortuosity

Tortuosityofporesisanimportantparameterdescribingtheseepagechannel.Thetortuosityis

defined as the ratio of the actual length of the seepage channel to the apparent length (macro

distance) passing through the seepage medium, that is, the true length of the particle's

trajectory in the channel when the seepage fluid particle passes through the medium unit

distance[36].

 Flowresistivity

Flow resistivity directly reflects some structural characteristics of the material, and flow

resistance is used to establish the relationship between the structure of the material and some

of the acoustic characteristics of the material (such as: attenuation characteristics, sound

absorptioncharacteristics,etc.)

 Viscouscharacteristicslengths

The viscous characteristic length (usually represented by the letter Λ) is a parameter used to

describe the viscous effect at medium and higher acoustic frequencies. This parameter has

beenintroducedbyJohnson,KoplikandDashen

 Thermalcharacteristicslengths

The concept of thermal characteristic length is used to calculate the volume elasticity

coefficient of air in porous materials in the high frequency range, which is used to represent

theinfluenceofgeometricfactorsontheeffectivevolume elasticitycoefficientK.Thethermal

characteristiclength,usuallyrepresentedbyletter ′

18

The JCA model is establishedbased on the BIOT theory considering the viscous inertia effect

and heat dissipation effect of porous media. The pore shape is defaulted to be cylindrical, and

the air-saturated porous material with rigid skeleton is regarded as having the same dynamic

density and dynamic bulk modulus. Efficacious fluid. In Workbench, after installing

Acoustic's ACT plug-in, when the JCA model is selected, the corresponding parameters that

need to be entered in the model will appear in the drop-down menu as shown in the figure

below. Enter the parameters, and you can use the JCA porous model to calculate the acoustic

structure:

3. METHOD

3.1 Finite Element Method

3.1.1Introduction

In this report, ANSYS will be used to perform finite element analysis on the model, and the

method used is called the finite element method. This paper uses the finite element analysis

software ANASYS to numerically simulate the impedance tube. The numerical simulation

uses the finite element analysis method, which is a method to solve the approximate solution

of the boundary value problem of partial differential equations. This method divides the

problem area, minimizes the error function, and generates a stable solution. Finally, the

simulation results are matched with the experimental results of the impedance tube on the

Megasorber FM sound-absorbing panel, and a finite element analysis model that can be used

tosimulateunknownmaterialsisobtained.

3.1.2Theory

In dealing with the fluid structure coupling problem of the acoustic field, the finite element

analysis method can be used to deal with the Navier-Stokes equation and the structural

dynamic equation of the fluid with fluid momentum and flow continuity. The discretized

structuraldynamicequationcanbeexpressedas[23]

19 (1)

Whenthefluidisacompressible,non-viscous,non-flowinguniformfluid,Thefollowing

acousticwaveequationisasimplifiedNavier-Stokesequation:

1

∇ ()

WherePistheinstantaneoussoundpressure,tisthetimevariable,cisthespeedofsound.

Inthefiniteelementmethod,thediscretesoundfieldwaveequationis:

When (t)

isFluidmassmatrix

isFluidstiffnessmatrix

isCouplingmassmatrix

Tofullydescribethefluid-solidcouplingproblem,thefluidpressuretermactingonthe

interfacebetweenthestructureandthefluidneedstobeaddedtotherightofthestructural

dynamicequation(1)

ᦙ

(t)

Fluidpressureloadvector Afterdiscretizationbyfiniteelement:

ᦙ

ᦙ

(t)

Formula(4)becomes:

(㤮)

Combining formula (3) and formula (6), the complete sound field-solid coupling equation is

obtained(7)

(7)

쳌

쳌

2 0

When

= istheCouplingmassmatrix

쳌

sthecouplingstiffnessmatrix.

쳌

Accordingtothediscretizationmatrix(7)of thecouplingbetweenthe elasticstructureandthe

fluid, the displacement and the sound pressure at the S node of the structure surface can

beobtained.Whentheacousticboundaryontheboundaryisdampedtofullabsorption(thatis,

the acoustic impedance on the boundary is changed to the plane wave impedance), the

coupling vibration and acoustic radiation of the elastic structure and the fluid in the

unboundedfluidregioncanbeapproximatelycalculated

3.1.3AcousticanalysisbasedonANASYS

Themainfocusofthisarticleistomodelthethree-dimensionalimpedancetubewiththefinite

element method. The rapid development of computer technology provides a foundation for

solving the coupled acoustic and vibration problems of complex structures. In theory, the

finite element analysis method is the most convenient numerical method for calculating

structural vibration and sound radiation [24]. In order to study the sound absorption

performance of this porous material, the finite element method (FEM) is used here. By

establishing a finite element model, the relationship between sound absorption coefficient and

frequency is studied, and the influence of mesh size on sound absorption quality is studied.

Finally, the finite element results are comparedwith the impedance tube experiment results to

establish that the model canrunwell sothat the modelcanbe usedtosimulate other materials

thatcannotbeobtained.

Finiteelementmodelbuildingprocess:

 SetupaHarmonicAcousticsanalysis

21

 Geometry

Create the geometry for the impedance tube air space and foam sample (two bodies). Select

bothbodies,rightclickandformamulti-bodypart,Asfollows:

Part of creating impedance tube material: Create→ Primitives → Cylinder. The operation is

Add Material. Origin Definition of this cylinder (x,y, z) m= (0,0,0) m. Axis Definition of this

cylinder,(x,y,z)m=(0,0,-0.1)m.Here0.1mrepresentsthethicknessofthematerial.

Impedance tube sound transmission part: Create→ Primitives → Cylinder. The operation is

Add Frozen. Origin Definition of this cylinder (x, y, z) m= (0,0,0) m. Axis Definition of this

cylinder, (x, y, z) m= (0,0,1.982) m. According to the measurement results in the laboratory,

thetubelengthoftheimpedancetubeis1.982m.

Figure6:Geometricmodelingofimpedancetube

 EngineeringData

22

IntheANSYSWorkbenchmainwindowselectEngineeringdata.

Right click on “Air”, select “duplicate”. This gives it the necessary basic properties such as

density and speed of sound. Rename the new material something meaningful like “Foam”.

Thenselectthatnewmaterialanddoubleclick“Johnson-Champoux-Allard” under“Perforated

Materials” and enter some meaningful values for the variables. This adds the remaining

requiredpropertiesforthefoammaterial.

Figure7:EngineeringDataoftheimpedancetubemodel

In Figure 7: Engineering Data of the impedance tube model, materials 1-7 are used to study

the influence of Fluid Resistivity, Porosity, Tortuosity, Viscous Characteristic Length, and

23

Thermal Characteristic Length on the sound absorption coefficient of the material. Material

FM100andmaterialFM50arematchingvalueswithMegasorberFMsound-absorbingboard.

 Model

1.Thetwobodieshavethecorrectmaterialsselected(AirandFoamrespectively)

2.Thetwobodiesarebothdefinedasacousticsregions

3.Boundaryconditionsetc.areapplied

4.Under “Analysis settings” may switch “Far-field radiation surface” (Under “Advanced”) to

“Off”

Figure8:Modelingprocessdiagramofimpedancetube

24

 Mesh

According to the data of the impedance tube experiment, it is determined that between 200hz

and2600hz,thebodyelementsizingofthematerialis0.05m

Figure9:ElementsizedistributionofModel

Get more results by changing the value of the JCA Model coefficient. Compare the

experimental value obtained from the laboratory with the sound absorption coefficient

calculated by ANSYS to calculate the error. Summarize all results and look for relationships.

Theresultsarelistedin"Results"and"Appendix".

Figure10:MaterialFM50,soundpressuredistributiondiagramat2600hz

25

3.2 Johnson-Champoux-Allard (JCA) Model

3.2.1Introduction

The porous sound-absorbing material has a large number of thin tubes, narrow slits and

cavities, etc. If the thin tubes or slits are arranged neatly, as shown in Figure 11(c), the sound

density and acoustic impedance of the material are those of a single tube or slit. Divide the

value by the porosity . However, in actual materials, thin tubes or slits are randomly

distributed, as shown in Figure 11(b), and there are even dead-tube cavities. But if there are

only holes, as shown in Figure 11(a), it does not constitute a sound-absorbing material.

Although the porous sound-absorbing material is a random combination of thin tubes, its

characteristics are still within the framework of the basic characteristics of a single tube or a

narrowslot.

Figure11:Structureofporousmaterials [25]

Intheactualporoussound-absorbingmaterial,theeffectivedensityofairis[25]

쳌

Where

ᾐ

x represents the structural constant of the two materials. When the micropores in the material

are randomly distributed, its value is 3; is the porosity; =2 f represents the angular

frequency; representsthematerialflowresistanceconstant,anditsexpressionis

Thespeedofsoundcinthematerialis:

Acousticimpedanceratio:

26

Where

ᦙ

isthebulkmodulusinthetube,anditsformulais:

ᦙ

1

1( 1)

ᦙ 1(1)

Where

( 1)

is the ratio of air's constant pressure specific heat toconstantvolume specific heat; is the

pressure in the air at 15 ; is the perforated plate constant; J(x) is the Bessel

ᾐ

functionofthefirstkind. ℃

t

쳌 쳌

쳌 1

t 㤮t

t

쳌 쳌 쳌

1 쳌 (1 )

1

The propagation of sound waves in porous materials is more complicated. The JCA model is

based on the Biot theory considers the viscous inertia effect of porous media [26] and the

thermal dissipationeffect [27] toestablish a generalized acoustic model,which can accurately

describethesoundabsorptioncharacteristicsofrigid frameworkmaterialsina widefrequency

range. widely used. The model considers the shape of the pores to be cylindrical and saturates

the rigid skeleton with more air. Porous materials are regarded as equivalent fluids with the

same dynamic density and dynamic bulk modulus. The expressions of dynamic density and

dynamicbulkmodulus[28]

In 1987, Johnson Koplik and Dashen [JKD87] proposed a semi-phenomenological model to

describethecompositedensityofacousticporous materialswitha fixedskeletonandarbitrary

poreshapes.Theexpressionis

1

t

1 1

In 1991, Champoux and Allard [CA91] introduced the dynamic bulk modulus expression of

thesameporousmaterialbasedonthepreviousworkofJohnsonandothers.

27

1

1

1

t

1 1

Where is the air density, a is the tortuosity factor, is the static flow resistance rate, and

isthevi scosityCharacteristiclength, istheadiabatic constant, istheairpressure,andNp r

is the Prandtl number. For porou s materials with arbitrary pore shapes, the thermal

characteristiclength ’mustbeusedinsteadof

Viscosity characteristic length refers to the radial dimensionof the connecting part between

two holes, which is usedto describe the viscous effect of sound waves inthe middle and high

frequency range. This parameter can be obtained by standing wave tube method or ultrasonic

technology.Itsexpression[28]:

1t

1

Wheresisthesectionshapefactor.

3.2.2EstimationofJCAparameters

 Porosity

Open porosity, commonly referred to as "porosity", refers to the ratio of the fluid volume

occupied by the continuous fluid phase to the total volume of the porous material. The

opening rate is usually identified by the Greek letters. However, in Biot’s original work, it is

usedtorepresentthisparameter. [29]

Porosityreferstotheratioofthevolumeofthefluidareatothetotalvolumeofthefluidinthe

porousmedium.Theformulaforporosityderivedfromthegeometricmodelisasfollows:

Where

Volumeoffluidarea:

Totalvolumeoffluidinporousmedia:

 Fluidresistivity

28

Fluid resistivity (commonly called resistivity) is used to describe the acoustic behavior of

porous materials. Usually identified by the symbol . The dimension in the International

SystemofUnitsisNsm^{-4}

Themathematicaldefinitionofthestaticairflowresistivity, is:

∇

The static airflow resistance rate partially characterizes the viscous inertia effect at low

frequencies (when the size of the viscous boundary layer is equal to the characteristic size of

thehole).

 Tortuosity

In the high frequency range ( →∞), the inertial effect dominates the viscous effect. This

tendency results in a very small viscous boundary layer in porous media, so fluids tend to

behave asidealfluids.Thisincompressiblefluidflowproblemcoincideswiththeconductivity

problem [30] where the fluid in the porous medium is assumed to be a conductive fluid with

an insulating solid (skeleton) phase. This fluid-electrical analogy is established by assuming

that the current density corresponds to the local fluid acceleration, the potential difference

across the electrical domain corresponds to the pressure difference across the fluid domain,

and the resistivity corresponds to the density of the fluid in the porous medium. This analogy

simplifies the inertial fluid flow problem to the Laplace equation of the conduction problem,

asfollows[27]:

∇

∇ aΩ

a aΩ

When E is the scaled electric field, −∇q is the fluctuation part of the periodic scalar field Q,

and e is the unit vector field of the fluid flow direction in the unit cell [31] The degree of

curvature( )canbeestimatedasfollows:

 Viscouscharacteristiclength

Johnsonetal.[26] introducesthe parameterviscositycharacteristic lengthΛ of theratioofthe

weighted pore volume to the wet surface in the periodic unit. This parameter takes into

accounttheviscouseffectofthefluidsurfaceinterfaceandcanbeestimatedasfollows:

29

h

 Thermalcharacteristiclength

Similar to the parameter , Champoux and Allard [27] introduced the parameter thermal

characteristic length ( ') in the periodic unit as the doubling ratio of the fluid volume to the

wet surface area. This parameter takes into account the heat dissipation in the periodic unit

andcanbeestimatedasfollows:

'

h

In the results, the influence of these five coefficients on the sound absorption coefficient of

sound-absorbingmaterialswillbeexplainedindetail.

Table2:SummaryofJCAparameterstable[37]

Parametername Parametervaluerange

Porosity [0.70,0.99]

Tortuosity [1.00,3.00]

Fluidresistivity( }) [ , ]

t t 㤮

Viscouscharacteristicle⚱ngth(um) 1[1 1,3 15 0]

Thethermalcharacteristiclengthisrelatedto

Thermalcharacteristiclength(um)

themaximumsizeofthehole.

The thermal characteristiclength Λ 'relatedtothe size hole cannotbe measureddirectly.For a

given porous material, its value can be estimated from (i) 2D or 3D acquisition of the

microstructure of the material for analysis, (ii) measurement in a standing wave tube at an

audiblefrequency,or(iii)ultrasoundobtainedbymeasuringatfrequency[37].

3.3 Impedance Tube

This part was done by my partner Zi Yi Kam. I really feel that he wants the data and

informationIprovided.

3.3.1Introduction

30

The standing wave tube (also called impedance tube) method allows fast, easy, but fully

repeatable measurement of the absorption coefficient. The impedance tube also allows

accurate measurement of the normally incident acoustic impedance, and only requires a small

sample of the absorbing material. The sketch of the B&K Libo installation is shown below.

The loudspeaker generates sound waves, which propagate along the pipe and are reflected

from the testsample.The phase interference betweenthe incidentandreflectedpipe waves on

thetestsamplewillcauseastandingwavepatterntoforminthepipe.

Figure12:SketchofB&KLiboinstallation[32]

Another method of determining the absorption properties of materials, which is also widely

used today, involves placing a unit area of material (for example, one-meter square) in a

special reverberation chamber. The difference in the reverberation time of the material

produces the absorption performance of the material. This method is usually more expensive,

requires precisely calibrated sensors and a specially designed reverberation chamber, and is

not very convenient. Although this method cannot produce normal incident acoustic

impedance data, it is superior to the absorption characteristics of random incident acoustic

waves and is more suitable for determining the absorption characteristics that depend on the

sizeofthematerial.

Therefore, when designing the anechoic room, in order to determine the sound-absorbing

materialsintheroom,impedancetubeexperimentscanbeusedtotestthetargetmaterials.

3.3.2laboratoryapparatus

1) Oscilloscope

2) RMS

3) Frequencycounter

4) Signalgenerator

5) Amplifier

6) MicrophoneTrolley

7) Rail

8) Tube

31

9) SampleHolder

Figure13Experimentalinstrumentdiagramofimpedancetube [33]

3.3.3Experimentalsteps

MeasurementofAcousticAbsorptionUsingaStandingWaveTube[33]

1) Beforetheexperiment,itisnecessarytonumberandrecordthespecimenthicknessand

material.

2) Correlatethepositionoftheprobetipwiththescaleprovidednexttothemicrophonetrolley

anddeterminetheprobepositionthatwillbegeneratedwhentheprobetipcontactsthesample.

3) Placethesampleintheholderandclampposition.

4) RecordbackgroundnoiselevelvoltageEo

5) Setthesignalgeneratorto150Hzandmovethetrambackandforthtodeterminethelocal

maximumandminimumvaluesofthestandingwavegenerated.Whenthemaximumvalueis

located,checktheoutputwaveformoftheoscilloscopetoensurethatthesignalisnotcutoff.

Ifso,reducethewaveformamplitudeonthesignalgenerator.

6) Recordthemaximumandminimumvoltages(suchastheeffectivevaluevoltagesEminand

Emax).

7) CalculatetheStandingWaveRatiousing

,andthenthereflectioncoefficient

⚱쳌 a1

a a ⚱a ᦙ a1

8) Repentforfrequencybetween150Hzand5000Hz

32

1 t

1

9) Calculatethewavelength 1t

(쳌⚱쳌쳌⚱a)

10) Calculatethereflectionphasechangeas

t쳌⚱a1

( 1)

11) Loosenthesampleholderandplacetheperforateddiskinfrontofthesample.Closetothe

sideofthemicrophone,repeatsteps5-10.

12) Ineachtest,checkyourdatabycheckingthespeedofsoundaccordingtothegenerated

frequencyandmeasuredwavelength:

Figure14:Sketchoftheexperimentaldevice

4. RESULT & DISCUSSION

4.1 Chapter introduction

ThisChapterdescribes theuse offiniteelementanalysis software ANASYStoanalyze sound-

absorbing materials. The main results have three aspects. 1. The influence of Johnson-

Champoux-Allard (JCA) Model coefficient of sound-absorbing material on the sound-

33

absorbing coefficient. 2. The matching result of the finite element model result and the

impedance tube experiment result. 3. The influence of material thickness on sound absorption

coefficient.

A total of 7 materials were set up in this research. The JCA model coefficients of the 7

materialsareasfollows:

PleaseseeAppendixAforthedetailsoftheaboveexperimentalresults

Table3.JCAModelcoefficientsofsevenmaterialsanalyzedbyfiniteelementmodel

Johson-Champoux-Allard 1 2 3 4 5 6 7

FluidResistivity(Nsm^-4) 7000 2000 12000 7000 7000 7000 7000

Porosity 0.8 0.8 0.8 0.9 0.8 0.8 0.8

Tortuosity 1.5 1.5 1.5 1.5 2.5 1.5 1.5

ViscousCharacteristic

50 50 50 50 50 200 50

Length(um)

ThermalCharacteristic

200 200 200 200 200 200 800

Length(um)

According to the above summary table, Table 2: JCA parameter summary table. First,

establish the JCA parameters of material 1 as shown in the above table: Table 3. JCA Model

coefficients of seven materials analyzed by finite element model. In order to explore the

influence of JCA parameters on the sound absorption coefficient, the influence of different

parametervaluesonmaterialsiscomparedbychangingonlyonesetofparameterseachtime.

4.2 The relationship between fluid resistivity and absorption coefficient

of materials

In order tostudy the influenceof FluidResistivityonthe attractioncoefficient ofthe material,

threesetsofcontrolexperimentsweresetup.Theyarematerial1,material2,andmaterial3.

Figure15:Theinfluenceoffluidresistivityonfluid(fluidresistivity=2000,7000,12000)

34

According to the image, the three materials have basically the same sound absorption

coefficient at 200hz: 0.625. As the frequency increases, the three groups of materials all reach

the maximum sound absorption coefficient around 350hz, and the coefficient of material 2 is

the largest at this time. Subsequently, the sound absorption coefficients of the three groups of

materials gradually decreased from 350hz to 750hz. This is after the minimum sound

absorption coefficient of material 2 is 0.74.750hz, the sound absorption coefficients of the

three groups of materials gradually become stable, all between 0.85-0.9. When the Fluid

Resistivity of the material becomes smaller, the sound absorption coefficient of the material

will have larger fluctuations at low decibels (200hz-1200hz). If it is to be used as an indoor

material in an anechoic room, it must be able to absorb sound at all basic frequencies. In

summary, the sound-absorbing material used in the anechoic chamber should have a large

FluidResistivity.

4.2 The relationship between material Porosity and absorption

coefficient

By comparing the relationship between the sound absorption coefficient and frequency of

material 1 andmaterial 4, the influence of porosity onthe attractive coefficient of the material

isstudied.

Figure16:TheinfluenceofPorosityonfluid(Porosity=0.8and0.9)

According to the above figure, the growth curves of material 1 and material 4 at 200hz-350hz

are basically the same, but after 350hz, the sound absorption coefficient of material 4 is about

0.04 higher than that of material 1. In addition, the curve trends of the two materials are

exactly the same, and both show a downward trend between 350hz and 750hz, and gradually

stabilize after 750hz. In summary, since the Porosity of material 4 is greater than that of

material 1, the sound absorbing material with high Porosity can absorb sound better when the

sound absorbed is higher. As an acoustic laboratory, the anechoic room often needs to test

35

high-frequency sound segments, and the greater the Porosity of the indoor sound-absorbing

material, the better experimental results can be obtained. When choosing the sound-absorbing

material room of the anechoic room, you should choose Porosity material, and when creating

confidencesound-absorbingmaterial,thePorosityofthematerialshouldbecloseto1.

4.3 The relationship between material Tortuosity and absorption

coefficient

By comparing material 1 and material 5, we can know the effect of Tortuosity of the material

onthesoundabsorptioncoefficientofthematerial

Figure17:TheinfluenceofTortuosityonfluid(Tortuosity=1.5and2.5)

Accordingtothefigureabove,therelationshipcurve betweenthesoundabsorptioncoefficient

andfrequencyofmaterial5lookslikethecurveofmaterial1hasshiftedtotheleft.Thesound

absorption coefficient of material 5 is higher than that of material 1 at around 200hz, and the

sound absorption coefficient of material 1 is better than that of material 5 at other frequency

stages. The reasonfor this is that the Tortuosity of material 5 is higher than that of material 1.

By observing the curve, we can clearly know that material 1 is better than material 5. In

summary, astheinteriormaterialof theanechoicchamber, theTortuosityof thematerial tobe

usediscloseto1.

4.4 The relationship between material Viscous Characteristic

Length(um) and absorption coefficient

36

By comparing material 1 and material 6, we can know the effect of Viscous Characteristic

Length(um)ofthematerialonthesoundabsorptioncoefficientofthematerial.

Figure18:TheinfluenceofViscousCharacteristicLengthonfluid(ViscousCharacteristic

Length=50and200um)

According to the above figure, the frequency at which material 1 and material 6 reach the

maximum sound absorption coefficient is different. By observing the curves of the two

materials, the curve of material 6 obviously fluctuates more. Moreover, the sound absorption

coefficient of material 6 after 600hz is basically between 0.8-1. Material 6 can have a good

sound absorption effect at certain specific frequencies. However, as the indoor material of the

anechoic chamber,it is oftennot onlyfortestingthe frequencyofa large span,if material 6is

used.It is very likelythat a larger errorwill occur.By comparingthe curves of material 1 and

material 6, it can be found that the Viscous Characteristic Length of the sound-absorbing

materialshouldnotbetoolarge.

4.5 The relationship between material Thermal Characteristic

Length(um) and absorption coefficient

Figure19:TheinfluenceofThermalCharacteristicLengthonfluid(ThermalCharacteristic

Length=200and800um)

37

By comparing material 1 and material 7, we can know the effect of Thermal Characteristic

Length(um)ofthematerialonthesoundabsorptioncoefficientofthematerial

According to the above figure, the sound absorption coefficient of material 7 between 200hz

to 350hz and 700hz to 1300hz is lower than that of material 1, while the sound absorption

coefficients of the two materials are basically the same at other frequency stages. It can be

seen that material 7 is slightly worse than material 1. According to the characteristics of the

two materials, the Thermal Characteristic Length of material 7 is much larger than Viscous

Characteristic Length, and the difference between the two coefficients is 16 times, while the

two coefficients of material 1 are only 4 times different. In summary, when choosing sound-

absorbing materials, you should not choose materials whose Thermal Characteristic Length

andViscousCharacteristicLengtharetoodifferent.

4.6 The matching result of the finite element model result and the

impedance tube experiment result.

Figure20:MatchingresultofimpedancetubeexperimentofmaterialFM100withfiniteelement

model

Figure21:MatchingresultofimpedancetubeexperimentofmaterialFM50G-Gwithfinite

elementmode

38

Figure22:MatchingresultofimpedancetubeexperimentofmaterialFM50G-Wwithfinite

elementmodel

Accordingtotheabovefigure,thefiniteelementanalysismodelIconstructedcansimulatethe

three sound-absorbing materials provided by Megasorber. According to the curve, it can be

known that the JAC Model coefficients of 3 materials are very close. This proves that the

materialsofthethreesoundinsulationboardsarethesame.

Table4:Materialcharacteristicsmatchedbythefiniteelementanalysismodelaccordingtothe

experimentalresultsoftheimpedancetube

Johson-Champoux-Allard FM100 FM 50G-G FM 50G-W

FluidResistivity (Nsm^-4) 13000 13000 13000

Porosity 0.99 0.99 0.99

Tortuosity 1.01 1.01 1.01

Viscous CharacteristicLength(um) 200 200 200

Thermal CharacteristicLengrh(um) 800 800 800

According to the matching results, the Porosity and Tortuosity of the three materials are the

same. Because these three materials are good sound-absorbing materials, and their sound-

absorbing characteristics are relatively good, it is known that the Porosity of the sound-

absorbingmaterialsusedinthedesign ofthe anechoicchamber needstobe close to1, andthe

Tortuosity of the sound-absorbing materials also needs to be close to 1. In this simulation, the

material Viscous Characteristic displayed by the three materials is the same. In addition, the

three groups of materials have a unified feature, that is, they all have poor absorption of low-

frequencysoundsources.Thisisnotonlyshowninthesimulationvalue,butalsocanbefound

based on the results of the impedance tube experiment. But FM100 has better sound

absorption effect on low frequency sound sources than FM50. This is due to the different

thicknessofthematerials.Pleaseseetheappendixforthetwodataofthethreematerials.

39

4.7 The influence of material thickness on sound absorption coefficient

Figure23:TherelationshipbetweenthesoundabsorptioncoefficientandfrequencyofFM50with

differentthicknesses

According to the figure above, when the material becomes thicker, the material can have a

good absorptioneffect onthe low-frequencysoundrange.However,whenthethicknessof the

material becomes thinner, the material will have a good absorption effect on the high-

frequencysoundrange.Basedontheabove results,make aguess.Sincetheprincipleofsound

absorption by sound-absorbing materials is to convert sound energy into heat energy, the

energy of low-frequency sound is very small. When low-frequency sound enters the thin

sound-absorbing material, the sound energy cannot be fully converted into heat energy, and

there is a sound energy that can penetrate Over sound-absorbing materials. All thin sound-

absorbing materials have poor absorption of low-frequency sounds. Thick sound-absorbing

materials can avoid this problem. In the face of high-frequency sound, because more heat is

converted, thicker materials will dissipate heat worse than thinner ones. Therefore, the

thickness of the sound-absorbing material will be a little short of absorbing mid and high-

frequency sound. Both are personal conjectures and need further testing. Because of the flat

surfaceusedintheexperimentandsimulationprocess,thesoundisaccepted.Inthenextstudy,

it is necessary to study whether the sound absorption coefficient will be affected when the

surfaceofthesoundabsorbingmaterialisirregular.

40

5. CONCLUSION AND FURTHER WORK

5.1 Conclusion

The main purpose of this paper is to test the known and unknown sound-absorbing materials

through the finite element analysis method and the impedance tube experiment method.

Accordingtoliterature,poroussound-absorbingmaterialisakindofsound-absorbingmaterial

often used in anechoic chambers.In order to verify the characteristics of the material and the

correctness of the model, the Megasorber FM acoustic panel was simulated and compared

withthemeasurementresultsprovidedbyZiYiKam.

Accordingtotheavailabledata,thefinite element model hasset upseven groupsof materials.

The characteristics of the materials are shown in Table 2. JCA Model coefficients of seven

materials analyzed by finite element model. Acoustic simulations were performed on these

seven groups of materials in the environment of 200hz to 2600hz, and the relationship

between the sound absorption coefficient and frequency of the seven groups of materials was

analyzed based on the data obtained. And the seven groups of materials can be used as a

control experiment with each other, and the impression of the material's jca model coefficient

on the material is analyzed based on the obtained results. Please see Appendix A for the

simulationexperimentresultsofthesevengroupsofmaterials.

Finally, by comparing the results of the experiment and the model, a well-functioning model

was obtained. In the process of model research, not only did we understand that the fluid

resistance, Porosity, Tortuosity, Viscous Characteristic Length, and Thermal Characteristic

Length of the material would be affected by the sound absorption coefficient. The higher the

frequency, the stronger the material's ability to transform sound energy. In order to achieve a

soundabsorptioncoefficientcloseto1,itisalsounderstoodthat thePorosityofthematerialis

required to be close to 1, and the Tortuosity of the material is close to 1. Due to the collected

data, the optimal mesh size is specified. The finite element results are compared with the

experimentalresults.Due tothecollecteddata,theoptimal gridsize isspecified. Accordingto

the research results, an equation was proposed to obtain the optimal mesh size to simulate the

model,andtheanswerclosesttotheexperimentaldatawasobtained.

Based on the above results, if someone needs to design an anechoic chamber, the results and

modelofthisreportwillbeagoodstartingpointforthedesign.

41

5.2 Recommendation for future research

Since only the characteristics of sound-absorbing materials in the anechoic chamber are

studiedinthisreport,theshapeofsound-absorbingmaterialsandthesuperpositionofmultiple

sound-absorbingmaterialsneedtobesimulatedandanalyzedinfuturework.

 According to the study of the two Megasorber FM Sound Absorbing Panels in the report, it

is found that when the material thickness is different, the absorption efficiency of sound

sources of different frequencies is different. Thin materials have a better absorption effect

onhighfrequencysoundsources. Low-frequencysoundsources absorbbetter.Accordingto

the guess of the result, if the surface of the sound-absorbing material is set as a wedge-

shaped block, the material cannot have a good sound-absorbing effect for sound sources of

any frequency. The shape of all sound-absorbing materials is the focus of future research.

According to the research in this report, it is most appropriate to set the surface of the

sound-absorbing material of the anechoic chamber to protrude outward. Please refer to

Figure 2 for the specific style; The reflection of sound waves on the walls of the anechoic

chamberisminimized.

 Another key point in the design of the anechoic chamber is the combination of multiple

materials. According to the study of the two specifications of Megasorber FM Sound

Absorbing Panels, FM100 and FM50, the two materials have different sound absorption

effects for different frequencies.Therefore, in the design of the anechoic chamber, the

silencing material used is not a single porous silencing material, but a material

superimposed with multiple sound-absorbing materials according to the needs of the

anechoic chamber. This will make the design of the anechoic chamber more

perfect.According to the research in this report, FM100is a good sound-absorbing material,

but its absorption effect for low-frequency sound energy is poor. When choosing another

sound-absorbing material, its JCA model coefficient should reach: Porosity still needs to be

close to 1,Tortuositycanbe increasedappropriately, Characteristic Length onfluid=200um

is a suitable choice, and Thermal Characteristic Length should also be smaller. The fluid

resistivity can also be smaller. Such materials are better than FM100 and FM50 in the

conversion of low-frequency sound energy. The above conclusions come from 4.1 to 4.5 in

thefourthsectionofthisarticle.

42

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45

APPENDIX

Appendix A Finite element model data

Table5:Dataofmaterial1simulatedbythemodel

Figure24:Therelationshipbetweenthefrequencyofmaterial1andthesoundabsorption

coefficient

46

Table6:Dataofmaterial2simulatedbythemodel

Figure25:Therelationshipbetweenthefrequencyofmaterial2andthesoundabsorption

coefficient

Table7:Dataofmaterial3simulatedbythemodel

47

Figure26:Therelationshipbetweenthefrequencyofmaterial3andthesoundabsorption

coefficient

Table8:Dataofmaterial4simulatedbythemodel

Figure27:Therelationshipbetweenthefrequencyofmaterial4andthesoundabsorption

coefficient

48

Table9:Dataofmaterial5simulatedbythemodel

Figure28:Therelationshipbetweenthefrequencyofmaterial5andthesoundabsorption

coefficient

Table10:Dataofmaterial6simulatedbythemodel

49

Figure29:Therelationshipbetweenthefrequencyofmaterial6andthesoundabsorption

coefficient

Table11:Dataofmaterial7simulatedbythemodel

Figure30:Therelationshipbetweenthefrequencyofmaterial7andthesoundabsorption

coefficient

50

Table12:DataofFM100,Thick=0.1msimulatedbythemodel

Table13:DataofFM50G-GThick=0.05msimulatedbythemodel

Table14:DataofFM50G-GThick=0.1msimulatedbythemodel

51

Table15:DataofFM50G-GThick=0.15msimulatedbythemodel

Table16:DataofFM50G-WThick=0.05msimulatedbythemodel

52

Appendix B Impedance tube experiment data

Table17:ExperimentaldataofimpedancetubeofmaterialFM100

Figure31:TherelationshipbetweenthefrequencyofthematerialFM100andthesound

absorptioncoefficient

Table18:ExperimentaldataofimpedancetubeofmaterialFM50G-G

53

Figure32:TherelationshipbetweenthefrequencyofthematerialFM50G-Gandthesound

absorptioncoefficient

Table19:ExperimentaldataofimpedancetubeofmaterialFM50G-W

Figure33:TherelationshipbetweenthefrequencyofthematerialFM50G-Wandthesound

absorptioncoefficient

54