Review Article Acoustic Absorption of Natural Fiber Compositesdownloads.hindawi.com/journals/je/2016/5836107.pdf · Review Article Acoustic Absorption of Natural Fiber Composites

Review ArticleAcoustic Absorption of Natural Fiber Composites

Hasina Mamtaz Mohammad Hosseini FouladiMushtak Al-Atabi and Satesh Narayana Namasivayam

School of Engineering Taylorrsquos University 47500 Subang Jaya Selangor Malaysia

Correspondence should be addressed to Hasina Mamtaz hasina ctgyahoocom

Received 27 November 2015 Revised 21 February 2016 Accepted 17 April 2016

Academic Editor Mariatti bt Jaafar

Copyright copy 2016 Hasina Mamtaz et alThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The current study is a bibliographic observation on prevailing tendencies in the development of acoustic absorption by naturalfiber composites Despite having less detrimental environmental effects and thorough availability natural fibers are still unsuitablefor wide implementation in industrial purposes Some shortcomings such as the presence of moisture contents thicker diameterand lower antifungus quality hold up the progress of natural fiber composites in staying competitive with synthetic compositesThe review indicates the importance of the pretreatment of fresh natural fiber to overcome these shortcomings However thepretreatment of natural fiber causes the removal of moisture contents which results in the decrease of its acoustic absorptionperformance Incorporation of granular materials in treated fiber composite is expected to play a significant role as a replacementfor moisture contents This review aims to investigate the acoustic absorption behavior of natural fiber composites due to theincorporation of granular materials It is intended that this review will provide an overview of the analytical approaches for themodeling of acoustic wave propagation through the natural fiber composites The possible influential factors of fibers and grainswere described in this study for the enhancement of low frequency acoustic absorption of the composites

1 Introduction

The advancement of controlling noise by sound absorptionoffers a great opportunity to study the acoustic attenuationtechnique of various porous materials The available com-mercial sound absorptive materials used in outdoor andindoor applications can be classified as granular cellularand fibrous Fibrous materials can be either natural orsynthetic The acoustic panels made from natural fibers areless hazardous to human health and more eco-friendly thanthose made of conventional synthetic fibers [1] Thereforegrowing concern for human health and safety issues hasencouraged manufacturers and engineers to seek alternativematerials from natural fibers as a replacement for syntheticfibers

In recent years researchers like [2ndash4] started working onthe fabrication of fiber composites with the combination ofplastic and rubber based granular materials The incorpora-tion of granular materials such as rubber crumb increases thebulk density and flow resistivity of the composite material

which has a significant effect in enhancing low frequencyacoustic absorption In addition chemical concentrationfiber-grain composition ratio fiber size and grain size mayalso be vital factors for improving low frequency soundabsorptionThe combination of natural or conventional fiberand rubber granularmaterials exhibits an encouraging soundabsorption performance at low frequency region when com-pared with either pure natural fiber or granular compositesBut from the point of environmental impact and healthhazard issues these nonrecyclable conventional absorptivematerials do not only cause environmental pollution but alsocontribute to global warming by emitting CO

2gas

To eliminate these problems a few researchers like [5ndash8] directed their attention in finding sustainable eco-friendlycomposites with the combination of natural fiber and rubbergranular materials or conventional fiber and biogranularmaterials which can be named as fibrogranular compositesAn encouraging performance of these fibrogranular com-posites was observed in the evaluation of many indoor andoutdoor applications

Hindawi Publishing CorporationJournal of EngineeringVolume 2016 Article ID 5836107 11 pageshttpdxdoiorg10115520165836107

2 Journal of Engineering

Table 1 Advantages and disadvantages of natural fibers [17 18]

Advantages DisadvantagesAre biodegradable cheaper and eco-friendly and have low specificweight

Have lower antifungus durability moisture and fire resistantqualities

Are abundantly available and high electrical resistant Have a negative impact on climate change (CO2absorption)

Have good thermal and acoustic insulating properties Exhibit lower acoustic absorption compared to synthetic fibersdue to a larger diameter

Have low toxicity and less human health hazards during processingand handling

Have poor fiber-matrix adhesion and moisture resistance whichcauses increase in volume for swelling of the fibers

A handful of researchers have focused on natural fibercomposites with the combination of natural fiber and gran-ular materials The objective of this review is to presentresearch development in the area of sound absorption ofnatural fiber composites combined with granular materialsThe aim of the review is to observe the expansion of thisfield from conventional fibrogranular composites to naturalfibrogranular composites for acoustic absorption purposesThe effective physical parameters for enhancing the lowfrequency absorption in the materials are also highlightedin this review In addition three well-known models weredemonstrated for evaluating the acoustic parameters of fibro-granular composites

2 Natural Fiber Composites

Due to their biodegradable lightweight cheaper nontoxicand nonabrasive qualities natural fibers are receiving muchattention in composites as a substitute for synthetic fibers foracoustic absorption purposes The natural fibers with desir-able physical andmechanical properties are exhibited as highperformance composites with environmental and economicadvantages [15] Many potential candidates are available inthe form of natural fibers for use as sustainable acousticabsorbers The fibers of coir corn paddy sisal and bananaare some examples Fiberglass mineral wool and glass woolare examples of synthetic fibers The acoustic performance ofsynthetic sound absorptive materials is higher than that ofnatural sound absorptive materials because of their thinnerdiameter and antifungus quality but they have a higherenvironmental impact than the natural fibers [16]

In recent years natural fiber reinforced resinpolymercomposites have earned a lot of attention due to theirlightweight abundant cost efficient biodegradable and eco-friendly nature Moreover these materials are cheaper andenvironmentally superior to glass fiber reinforced composites[26] However due to low interfacial adhesion poormoistureresistance and the low antifungus quality of natural fibercomposites these materials are still not quite as popular assynthetic based composites

Researchers are trying to improve the quality of naturalfibers through chemical treatment prior to compositeproduction to overcome these shortcomings It was reportedthat mercerization or alkaline treatment reduces the fiberdiameter and upgrades the quality by improving its adhesive

and antifungus quality [17] The reduction of fiber diameterenhances low frequency sound absorption by providinga more tortuous path and higher surface area which inturn increases the air flow resistivity of fibrous materialThe increase of air flow resistivity causes loss of soundenergy through friction of sound waves with air moleculesand thus improves low frequency sound absorption[9]

The study analyzes the limitations of natural fibers toachieve their acoustic absorption performance at a desiredlevel Some of the advantages and disadvantages of naturalfibers are furnished in Table 1 [17 18]

3 Pretreatment of Natural Fiber

To achieve fiber fitness fiber quality fiber strength and abetter fiber-matrix adhesion in the composite pretreatmentof natural fiber is needed for commercial use in parallel withsynthetic fiber There are various pretreatment techniquesavailable to tune the fiber according to the research require-ments Examples includemercerization or alkaline treatmentgraft copolymerization and plasma treatment Among themalkaline treatment or mercerization serves the purpose ofthis research as this process reduces the fiber diameterIt is a common method of producing high quality fibersMercerization increases the surface roughness of fiber byremoving some important substances like lignin pectin andhemicelluloses of the fiber Although the removal of thesesubstances lowers the acoustic absorption performance ofthe material it allows better fiber-binder interface adhesionfiber fitness longevity and antifungus quality and mostimportantly reduces the diameter of the fibers [11 17 27]

Figures 1 2 and 3 demonstrate the inner structure of coirfiber and the appearance of coir fiber before and after alkalinetreatment respectively It is evident from these three imagesthat alkaline treatment causes a reduction in fiber diameterwith the removal of moisture contents

Figure 3 shows the reduction in fiber diameter due tothe alkaline treatment at the cost of the removal of moisturecontents Figure 4 shows that the increase in chemicalconcentration results in the decrease of fiber diameter andfiber strength as well It was reported that 6 of alkalitreated coir fiber-epoxy resin composite showed a satisfactoryfiber diameter reduction with better mechanical strengthcompared to untreated composites [11]

Journal of Engineering 3

Lignin

Cellulose

Hemicellulose

Figure 1 The inner structure of coir fiber [9]

Figure 2The image of fiber structure before alkaline treatment [10]

Figure 3 The image of coir fiber structure after alkaline treatment[10]

NaOH treatment

NaOH concentration ()

028

027

026

025

024

023

022

021

02

Fibe

r dia

met

er (m

m)

0 2 4 6 8 10

02743

02542

0241

0231702287

0218

Figure 4 Effect of NaOH concentration on fiber diameter [11]

4 Fibrogranular Composites

Fibrous materials are usually composed of groups of orificesformed by interfiber voids and within-fiber voids The soundabsorption of fibrous materials is controlled by these innerand within-fiber voids Two common kinds of fibrous mate-rials are natural and synthetic The granular materials arewidely accepted as porous sound absorptivematerial for theirsustainability longevity and noncombustible and moistureresistant qualities The granular materials contain pores intheir grains where the sound absorption takes place due toviscosity Usually there are two kinds of granular materialsconsolidated and unconsolidated or loose granular materialsIn consolidated granular materials the particles are relativelyrigid and macroscopic and their dimensions are greater thanthose of the internal voids by many orders of magnitudeUnconsolidated materials are assemblages of loosely packedindividual particlesThe example of some granular absorbingmaterials are granular clays sands gravel limestone chipsand soil which are perfect for controlling outdoor soundpropagation [1 28 29]

Fibrogranular composites are the incorporation of gran-ulates made of natural rubber or plastic materials into afibrous matrix The performance of the fibrogranular com-posite is the summation of the individual components inwhich there is a more favorable balance between intrinsicadvantages and disadvantages In a fibrogranular compositethe advantage of one component supplements the lacking ofthe other to get a resultant balanced performance Further-more in a fibrogranular composite each component helpsin optimizing the acoustic properties of the other materialin order to absorb the sound at the desired frequency so asto yield the highest overall sound absorption Swift et al [13]reported that in a rubber granular composite the binder fillsthe small pores and forms bridges between the grains Thisreduces overall porosity and increases the tortuosity and flowresistivity of the material The investigation confirmed theconsiderable effect of the binder in predicting the acousticproperties of the granular composite

A fibrogranular composite is usually a high resistivematerial with low permeability This phenomenon causes thematerial to acquire higher flow resistivity resulting in higheracoustic absorption at low frequency region However lowpermeability can be a useful factor for the enhancement oflow frequency acoustic absorption but it should be withina limit which will allow the material to go through thecomposite Otherwise the compactness of the material maycause the reflection instead of the absorption of the soundwaves Anumerical simulationwas reported byBerbiche et al[30] in order to reconstruct the permeability by solving theinverse problem using waves reflected by some high resistiveplastic foam samples at different frequency bandwidths inthe Darcy regime Their method is considered as simplecompared to the conventional method as it is independentof frequency and porosity

Generally natural fibers need to be mixed with additivesto improve their characteristics for commercial acousticabsorption uses Some natural fibers such as kenaf hempcoir corn date palm sugar cane and jute composites are


Table 2 Acoustic performances of various fibrogranular composites

Year Components Frequency (Hz) SAC Ref2008 Nylon 66 fibers + PVC 1000 085 [19]2008 Nylon fibers + RG 1000 091 [19]2010 Coconut coir fiber + RG 1600 09 [5]2011 PVC + Nylon fiber 1000 07ndash10 [20]2012 Pine sawdust + RG + PU 1000 085 [21]2012 Ground tire rubber + fiber 1000ndash2000 08ndash10 [3]2013 RG + fiber + RG (multilayer panels) 1000ndash1500 55ndash65 [22]2013 Cotton fiber + RG 500 074 [23]SAC RG and PU are the sound absorption coefficient rubber grain and polyurethane respectively

Table 3 Influence of porous layer thickness on low frequency acoustic absorption of various fibrous and granular materials

Materials SAC at 119891 = 500HzThickness

10mm 20mm 30mm 40mm 50mmPolypropylene 0061 0072 0080 0135 0199Gravelite 0066 0079 0101 0138 0185Rubber 0089 0116 0220 0395 0586Mineral wool 0089 0187 0401 0702 0786High-silica sand 0115 0181 0319 0356 0418

made with resin coated fiber particulate particle strandsveneers and rubber granular materials These natural fibercomposites have good sound absorption properties by them-selves The effective sound absorption of any compositematerial can be achieved when it has a more tortuous pathhigher surface area higher flow resistivity and low porositywithin it at the optimal range [31] A general rule of thumbstates that the free spaces within and between fibers can besignificantly diminished by the incorporation of any granularmaterials to achieve effective sound absorption performanceThe chronological details on the sound absorption coef-ficient of some fibrogranular composites are furnished inTable 2

The information illustrated in Table 3 opens scenariosof possible applications of natural fiber composite with thecombination of biogranulates as new sound absorbing mate-rials and points to areas of research for further improvementof their sound absorption performance in the low frequencyrange

5 Theoretical Considerations

51 Delany-Bazley Model TheDelany-Bazley [32] model is asimple and fast approximation technique for the estimation ofacoustic parameters of a layer of isotropic and homogenousporousmaterialThe acoustic parameters such as characteris-tic impedance (119885

119888) the propagation constant (119896) and surface

acoustic impedance (119885) can be obtained as [33 34]

119885119888= 12058801198880[1 + 0057119887minus0754 minus 119894 (0087119887minus0732)]

119896 =2120587119891

1198880

[0189119887minus0595 + 119894 (1 + 00978119887minus07)] (1)

Having surface acoustic impedance (119885) the sound absorp-tion coefficient (120572) at a normal incidence of the porous layerwhile backed with a rigid wall can be calculated as

119885 = 119885119888coth (119896 sdot 119889) (2)

where 1205880is air density 119888

0is speed of sound in air 119891 is sound

wave frequency 119889 is thickness of porous layer 119887 = 1205880119891120590

which is dimensionless parameter the model is applicableonly for 001 le 119887 le 10

The technique depends on only one intrinsic property ofthematerial which is flow resistivity to a certain range of 1000le 120590 le 50000Nsdotsmminus4 and porosity close to 1

52 Johnson-Champoux-Allard Model Johnson-Champoux-Allard model is a rigid frame model where the solid phaseof the frame remains motionless Five nonacoustical param-eters flow resistivity porosity tortuosity viscous characteris-tics length and thermal characteristics length are involvedin this model Later two parameters relate the viscous andthermal losses respectively

Including the effects of viscosity the frame geometrydependent parameter viscous characteristic length (Λ) wasdefined by Johnson et al [35] as follows

Λ = 2int V2fluid119889119860

int V2fluid119889119881 (3)


In (17) the numerator denotes the velocity of fluid overthe pores surface area A and the denominator denotes thevelocity inside the pores volume V

Therelation between the viscous characteristic length andflow resistivity (120590)was noted by Johnson et al [35] as follows

Λ =1

119888(radic

8120578120572infin

120590120601) (4)

where c is a constant and is close to 1The expression of the effective density 120588(120596) of rigid

framed porous materials which was proposed by Johnson etal [36] is stated in

120588 (120596) = 120572infin1205880[

[

1 +120590120601

1198951205961205880120572infin

radic1 +41205722infin1205781205880120596

1205902Λ21205962]

]

(5)

According to Champoux and Allard [37] the thermal char-acteristic length (Λ1015840) which characterizes the high frequencybehavior of the bulk modulus119870(120596) is given by

Λ1015840 = 2int 119889119860

int119889119881= 2

119860

119881 (6)

whereA andV are the surface area of and volumeof the poresrespectively

In the case of fibrous materials with porosity close to 1 Λand Λ1015840 can be stated as in (7) and (8) respectively [38]

Λ =1

2120587119903119897 (7)

Λ1015840 =1

120587119903119897= 2Λ (8)

119897 =1

1205871199032 lowast 120588bulk120588fiber (9)

where 119897 is total length of fiber per unit volume 119903 is cross-sectional radius of fiber 120588bulk is bulk density of porousmaterial 120588fiber is density of fiber 120588bulk120588fiber is fraction of fiberexisting in porous material

The expression of the bulk modulus119870(120596) of rigid framedporous materials which was proposed by Champoux andAllard [37 38] is stated in

119870 (120596) =1205741198750

120574 minus (120574 minus 1) [1 minus 119895 (8120578Λ101584021198731199011205880120596)radic1 + 119895 (Λ10158402119873

119901120588012059616119896)]

minus1 (10)

where 120578 is viscosity of air Λ1015840 is thermal characteristiclength 120596 is angular frequency 120574 is ratio of specific heat atconstant pressure to specific heat at constant volume 119875

0is

atmospheric pressure119873119901is Prandtl number 120588

0is density of

airThe expression for characteristic impedance 119885

119888(120596) the

complexwave number 119896119888(120596) and surface acoustic impedance

119885 can be estimated by the following equations [38 39]

119885119888(120596) =

1

120601radic120588 (120596) sdot 119870 (120596)

119896119888(120596) = 120596radic

120588 (120596)

119870 (120596)

119885 = 119885119888(120596) sdot coth (119896

119888(120596))

(11)

53 Biot-Allard Model Allardrsquos model [40] in addition tohis extension to Biot [41] is an elastic frame method forthe porous material which is saturated with viscous fluidIn this model the frame (fiber) is assumed as elastic cylin-drical fiber which deals with the study of the frame-fluidinteraction Hence both frame (fiber) and fluid (air) are inmotion

The frequency dependent bulk modulus of fluid 119870119891(120596)

inside the pore which is assumed to be the only parameter tocharacterize the air filling pores is defined as [40]

119870119891(120596) =

1205741198750

120574 minus (120574 minus 1) [1 + (8120578119895Λ10158402

1198731199011205961205880) (1 + 119895120588

0(120596119873119901Λ10158402

16120578))12

]minus1 (12)


Allard [40] derived the elasticity coefficients 119875 119876 and 119877 interms of Biotrsquos experiments as follows

119875 = 43119873 + 119870

119887+(1 minus 120593)

2

120593119870119891

119876 = 119870119891(1 minus 120593)

119877 = 119870119891120593

(13)

The bulk modulus of frame119870119887can be evaluated as

119870119887=2119873 (] + 1)3 (1 minus 2])

(14)

where119873 is shear modulus ] is Poisson coefficientThe dynamic rigidity of the elastic solid was characterized

by the shear modulus and Poisson coefficient The derivationof the kinetic energy helps in the evaluation of the equationof motion in an elastic medium The parameters 120588lowast

11 120588lowast12

and 120588lowast22 which help to identify the inertial coupling between

frame and fluid can be estimated as [40]

120588lowast11= 120588bulk + 120588119886 minus 119895120590120593

2119866 (120596)

120596

120588lowast12= minus120588119886+ 1198951205901205932

119866 (120596)

120596

120588lowast22= 1205931205880+ 120588119886minus 1198951205901205932

119866 (120596)

120596

(15)

where

119866120596= (1 +

41198951205722infin1205781205880120596

1205902Λ21205932)

12

120588119886= 1205880120593 (120572infinminus 1) = Inertial coupling term

(16)

120572infin

is the tortuosity of the frame which is defined as [42]

120572infinasymp

1

radic120593 (17)

According to Biot [41] there are two compression wavesand one shear wave which propagate in porous media Onecompression wave is air borne which mostly transmits inair and another one is frame borne which propagates inboth of them A rotational wave called shear wave is alsoframe borne which is considered when the sound wavespropagate at oblique incidence The study only analyzes thepropagation of sound at normal incidence and hence onlytwo compression waves are considered here

To calculate the ratio of frame and fluid velocity thesquared wave numbers of two compression waves can beevaluated as

12057521=

1205962

2 (119875119877 minus 1198762)[119875120588lowast22+ 119877120588lowast11minus 2119876120588lowast

12minus radicΔ]

12057522=

1205962


12+ radicΔ]

(18)

where

Δ = (119875120588lowast22+ 119877120588lowast11+ 2119876120588lowast

12)2

minus 4 (119875119877 minus 1198762) (120588lowast11120588lowast22minus 120588lowast12

2

) (19)

The squared wave numbers are useful to calculate the ratio offrame and fluid velocity

120583119894=1198751205752119894minus 1205962120588lowast

11

1205962120588lowast12minus 1198761205752119894

(20)

As two compression waves simultaneously propagate inboth media four characteristic impedances related to thepropagation in air 119885119886

119894or frame 119885119891

119894can be evaluated as

119885119886119894= (119877 +

119876

120583119894

)120575119894

120593120596

119885119891

119894= (119875 + 119876120583

119894)120575119894

120596

(21)

where 119894 = 1 2 in the case of (20) and (21)The surface acoustic impedance at normal incidence (119885)

of the material with thickness 119889 which is the function of theabove characteristic impedances can be calculated as

119885 = minus119895(119885119891

111988511988621205832minus 119885119891

211988511988611205831)

119863 (22)

where

119863 = (1 minus 120593 + 1205931205832) [119885119891

119894minus (1 minus 120593)119885119886

1198941205831] 1199051198921205752119889

+ (1 minus 120593 + 1205931205831) [11988511988621205832(1 minus 120593) minus 119885

119891

2] 1199051198921205751119889

(23)

Hence the sound propagation in elastic materials is modeledby implementing the above-mentioned formulation

Having the surface acoustic impedance (119885) the absorp-tion coefficient (120572) at a normal incidence of the porous layerwhile backed with a rigid wall can be calculated as

120572 = 1 minus10038161003816100381610038161003816100381610038161003816

119885 minus 1198850

119885 + 1198850

10038161003816100381610038161003816100381610038161003816

2

(24)

where 1198850= 12058801198880which is impedance of the air

The effectiveness of any porous material depends on thevalue of its sound absorption coefficient which is close to onewith an absorption plane on a large frequency range

6 Effective Factors for Low FrequencyAcoustic Absorption

61 Fiber Size Fiber diameter is the most important physicalgeometrical parameter for enhancing the sound absorptionperformance of any fibrous material The decrease in fiberdiameter leads to an increase in the value of the sound absorp-tion coefficient This is because more fibers are required toreach the same volume density at the same thickness ofthe sample material This results in a more tortuous path


and higher airflow resistance As a result the acousticalperformance of the sample material increases due to theviscous friction through air vibration [31]

The accession of thinner fibers due to the reduction offiber diameter results in a high specific surface area andmoremicropores in equal volume density of the sample materialThis increases the value of the sound absorption coefficientdue tomore friction of airmolecules with a larger surface area[43] Furthermore thin fiber moves more easily than thickfiber in sound waves which causes vibration in the air andthis enhances absorption bymeans ofmore viscous losses dueto air vibration [44]

These observations indeed help us to show that fiberdiameter is an important parameter in enhancing the soundabsorption in the low frequency region The significantenhancement in low frequency absorption was found dueto the reduction of coir fiber diameter in the numericalsimulation of Nor et al [9] for the range of fiber sizes from100 to 250120583m at 50mm constant thickness of the samplematerial The study reported the gradual increase and shift ofthe peak of the sound absorption coefficient with the decreaseof fiber diameter towards the low frequency region

A strong influence of fiber fineness on the sound absorp-tion performance of the nonwoven fabrics was reported byShahani et al [12] They stated that finer fiber with reduceddiameter absorbed the sound more efficiently than the thickcoarse fiber The finer fibers enhance the sound absorptionperformance of nonwoven fabric material by reducing thepossible connectivity of pores The variation of the soundabsorption performance at different fiber diameters is illus-trated in Figure 5

62 Grain Size Voronina and Horoshenkov [45] developeda new empirical model which relates the characteristicimpedance and propagation constant with characteristic par-ticle dimension porosity tortuosity and the specific densityof grain base The study reported a reliable prediction ofthe acoustic performance of a loose granular mix of grainbase 04ndash35mm and specific densities between 200 and1200 kgm3 in the frequency range 250ndash4000Hz

Sakamoto et al [6] investigated the sound absorbingcharacteristics of two biogranular materials rice and buck-wheat husks They revealed the effectiveness of rice husk andbuckwheat husk as sound absorbing materials They foundthat the value of the sound absorption coefficient of ricehusk is 05 and buckwheat husk is 45 at 500Hz and 40mmthickness

Swift et al [13] reported that the flow resistivity isdirectly proportional to the internal surface area of thegranular composite material while the internal surface areais inversely proportional to the grain size They confirmedthat unconsolidated granulates of grain sizes between 071and 1mm and consolidated material of grain size lt2mmcontribute higher flow resistivity on the condition of applyingthe binder at a suitable ratio Their report can be explainedby the fact that smaller grains show higher flow resistivitythan larger grains leading to higher acoustic absorptionperformance

1

095

09

085

08

075

Soun

d ab

sorp

tion

coeffi

cien

t

250 500 1000 2000 4000

Frequency (Hz)

V5 - 17denV3 - 12denV1 - 8den

V4 - 15denV2 - 10den

Figure 5 Variation of the sound absorption coefficient at differentfiber diameters [12]

Flow

resis

tivity

(Nsm

minus4)

0 05 1 15 2 25 3 35 4

Average particle size (mm)

NonconsolidatedConsolidated

106

105

104

103

102

Figure 6 Influence of the grain size on the flow resistivity ofconsolidated and unconsolidated granular materials [13]

A comparison study of flow resistivity of consolidated andunconsolidated grain materials is shown in Figure 6 for eachgrain size

Their report can be explained by the fact that smallergrains show higher flow resistivity than the larger grainsresulting in higher acoustic absorption performance for bothgrain types

63 Bulk Density The density of a material is often asignificant factor governing its sound absorption qualitiesThe investigation of materials density is very important asthe current study is dealing with the combined density of twomaterials such as fibrous and granular material Koizumi etal [31] stated that the increase in sample density causes anincrease in sound absorption at medium and high frequencyregionsThey explained that with increases in the number of

8 Journal of EngineeringSo

und

abso

rptio

n co

effici

ent

Frequency (Hz)

10

09

08

07

06

05

04

03

02

01

00

125 250 500 1k 2k 4k

Thickness50mmAir space0mm

Density20kgm3

30kgm3

40kgm3

50kgm3

Figure 7Variation of sound absorption coefficients at different bulkdensities [14]

fibers per unit area the sample density increases As a resultenergy loss of sound waves increases due to the increaseof surface friction which leads to an increase in soundabsorption performance

Tiuc et al [46] reported that the sound absorptioncoefficient for flexible polyurethane foam with a densityof 60 kgm3 was higher than glass wool with a density of15 kgm3 atmediumandhigh frequency rangesThe influenceof the bulk density was observed in the acoustic performanceof bamboo wool materialsThe increase in bulk density of thebamboo wool material moved the peak value of the soundabsorption coefficient from the high to the low frequencyrange [14] Figure 7 presents the variation of the soundabsorption coefficient at different bulk densities of bamboowool material

64 Sample Layer Thickness According to general guide-lines of absorption phenomena inside a porous material along dissipative process of viscosity and thermal conductionbetween the air and absorbing material within the compositeimproves the absorption This improved sound absorptionis due to the increased thickness of the sample materialNor et al [9] demonstrated the significant role of fiberlayer thickness on acoustic absorption of fresh and industrialcoir fiber They implemented the Johnson-Allard rigid framemodel to estimate the acoustic absorption performance ofcoir fiber at different thicknesses They found that for bothcases increasing the coir fiber layer thickness increases theabsorption and moves the absorption peak towards the lowfrequency region

Increasing the sample layer thickness has a signifi-cant effect on enhancing the sound absorption at the lowfrequency region of the porous material while there isan insignificant effect at the higher frequency range [47]

Table 4 List of the sound absorption coefficients of different fibrousmaterial at different frequencies

Materials Fiber diameter (120583m) SAC at 119891 = 500Hz RefCotton 135 050

[24 25]

Flax 218 040Ramie 244 040Wool 371 020Jute 812 020Sisal 213 010

The effective absorption of the incident sound wave occurswhen the thickness of the material is one-tenth of itswavelength [48] The influence of layer thickness on thesound absorbing properties of various fibrous and granularmaterials is furnished in Table 3 at the frequency of 500Hzfor five-layer thicknesses

From the information provided in Table 3 it is clearlyevident that increasing sample layer thickness of any poroussound absorption material promotes the sound absorptioncoefficient at the low frequency region

7 Results and Discussions

Based on the investigation of various analytical and exper-imental overviews various potential factors were foundto enhance the low frequency acoustic absorption Thesefactors are fiber size grain size bulk density sample layerthickness and so forth According to researchers decreasingfiber diameter resulted in the increase of fiber content inthe composite and absorption by means of more viscousfriction of air molecules with a larger surface area Hencethe decrease in fiber diameter causes the dramatic increase inthe flow resistivity as well as sound absorption performanceof the fiber materials towards low frequency [31 49] Thevariation of the values of sound absorption coefficients withthe values of various fiber diameters is furnished in Table 4

Investigations carried out bymany researchers confirmedthe clear relationship between the absorption spectra andthe size of the granular particles Pfretzschner [4] statedthat the sound absorption efficiency of rubber granularmaterials depends on its particlesrsquo size and layer thicknessThe absorption increases to its maximum with decreases ingrain size and most optimum sound absorption is acquiredfor rubber grain sizes between 05 and 1mm [13]

A comparison study was made by Mahzan et al [50]among rice husk rubber granulate and woods shavedmaterials to validate the effectiveness of rice husk as anacoustic materialTheir result demonstrated that the acousticperformance of 25 rice husk together with a polyurethanebinder is superior to rubber and woods shaved materialTable 5 presents the comparison study of sound absorptioncoefficients for rice husk with rubber and woods shavedmaterials

The acoustic absorption performance of a fibrogranularcomposite was better among simple rubber granulates cotton


Table 5 A comparison study of the acoustic performance ofbiogranular and rubber granular materials

Materials SACRice husk 09Rubber grains 0583Woods shaved 0484

Table 6 Acoustic absorption study of fibrous granular and fibro-granular composites [23]

Materials SAC at 500HzThickness

30mm 40mm 50mmCotton fiber-rubber granulate 029 042 074Cotton fiber 034 037 062Rubber granulate 012 018 026

fiber and cotton fiber-rubber granulate composites A com-parison study is furnished in Table 6 for the sound absorptioncoefficient at frequency 500Hz and different layer thicknessesof these three materials [23]

The information provided in Table 3 is also a clearindication of the significant contribution of the increasein sample layer thickness for enhanced acoustic absorptionperformance of three types of materials

8 Conclusion

Natural fibers have already confirmed their potentiality inreplacing common synthetic fibrous materials for acousticabsorption purposes However in real world applicationsnatural fibers should be pretreated to improve their antifun-gus quality and life expectancy The study highlighted thepossible ways to improve the acoustic behavior of naturalfiber composites as high quality absorbers in combinationwith biobased granular materials

The alkaline treatment process causes the reductionof fiber diameter at the cost of the removal of moistureabsorbents such as oil cellulose and wax of the naturalfiber thus improving adhesion and antifungus qualities of thecomposite However limited research was reported on theeffect of the sound absorption performance due to alkalinetreatment More research is needed on the effect of themercerization or alkaline treatment for acoustic absorptionperformance

In fibrogranular compositematerials there is goodpoten-tial in filling the small pores by the granular componentand the formation of bridges between the fibers as wellThis contributes a higher surface area within the compositeMaterials with higher density show increased absorptionperformance since the density has a great influence on theporosity and flow resistivity of the composite

The acoustic absorption of natural fiber composites canbe estimated by using the Delany-Bazley Biot-Allard andJohnson-Champoux-Allard analytical models The Delany-Bazley model is the only method that shows the general

absorption pattern at overall broadband frequency withoutgiving any information on the peaks and resonance of theframeThe other twomodels give accurate information aboutpeaks and resonance of the frame

Reduction in fiber diameter causes an increase in thefiber content and hence a high specific surface area in thecomposites Thus the loss of more energy due to the viscousfriction of airmoleculeswith higher surface area increases thevalue of the sound absorption coefficient at the low frequencyregion

Influence of grain size has a considerable effect on theacoustic properties of granular compositematerials For largegrains the absorption is generally low due to low flowresistivity but for smaller grains the absorption increasesdue to high flow resistivity and tortuosity The maximumsound absorption 095 was found for rubber grain sizes 05ndash1mm Biogranular materials such as rice husk have a betterpotential for commercialization as low frequency soundabsorbent material compared to rubber and wood shavingsat its optimum percentage with polyurethane binder

Sample layer thickness also plays an important role inenhancing low frequency sound absorption The reason isthe increase in layer thickness causing the incident soundwaves to lose more energy as they take a longer path throughthe material In thicker materials the impinged sound waveshave to undergo a long dissipative procedure of viscosity andthermal conduction in the air within the composite

The review rests great hopes in developing the new nat-ural fiber composite material with the use of biobased grainsfor acoustic absorption purposes The manufacture of thesenew materials by combining waste residues will contributeto environmental protection and sustainable acoustic absorp-tion solutions that are cheaper than the traditional alterna-tives Extensive investigation is needed for the improvementof lower frequency sound absorption performance consider-ing the various effective physical parameters of the material

Competing Interests

The authors declare that they have no competing interests

References

[1] J P Arenas and M J Crocker ldquoRecent trends in porous sound-absorbingmaterialsrdquo SoundampVibration vol 44 no 7 pp 12ndash182010

[2] R Maderuelo-Sanz J M Barrigon Morillas M Martın-Castizo V Gomez Escobar and G Rey Gozalo ldquoAcousticalperformance of porous absorber made from recycled rubberand polyurethane resinrdquo Latin American Journal of Solids andStructures vol 10 no 3 pp 585ndash600 2013

[3] R Maderuelo-Sanz A V Nadal-Gisbert J E Crespo-Amorosand F Parres-Garcıa ldquoA novel sound absorber with recycledfibers coming from end of life tires (ELTs)rdquo Applied Acousticsvol 73 no 4 pp 402ndash408 2012

[4] J Pfretzschner Rubber Crumb as Granular Absorptive AcousticMaterial Instituto de Acustica Madrid Spain 2002

[5] S Mahzan A M Ahmad Zaidi N Arsat M N M Hatta MI Ghazali and S R Mohideen ldquoStudy on sound absorption


properties of coconut coir fibre reinforced composite withadded recycled rubberrdquo International Journal of IntegratedEngineering vol 2 no 1 pp 29ndash34 2010

[6] S Sakamoto Y Takauchi K Yanagimoto and S WatanabeldquoStudy for sound absorbing materials of biomass tubule etcrdquoJournal of Environment and Engineering vol 6 no 2 pp 352ndash364 2011

[7] A Borlea T Rusu O Vasile and A Gheorghe ldquoSoundproofing materials with recycled rubber particles and sawdustrdquoin Proceedings of the 23rd Symposium of the Institute of SolidMechanics (SISOM rsquo12) pp 291ndash296 Bucharest Romania May2012

[8] B Ekici A Kentli andH Kucuk ldquoImproving sound absorptionproperty of polyurethane foams by adding tea-leaf fibersrdquoArchives of Acoustics vol 37 no 4 pp 515ndash520 2012

[9] M J M Nor M Ayub R Zulkifli N Amin andM H FouladildquoEffect of different factors on the acoustic absorption of coirfiberrdquo Journal of Applied Sciences vol 10 no 22 pp 2887ndash28922010

[10] H Gu ldquoTensile behaviours of the coir fibre and related com-posites after NaOH treatmentrdquoMaterials amp Design vol 30 no9 pp 3931ndash3934 2009

[11] A Karthikeyan and K Balamurugan ldquoEffect of alkali treatmentand fiber length on impact behavior of coir fiber reinforcedepoxy compositesrdquo Journal of Scientific amp Industrial Researchvol 71 no 9 pp 627ndash631 2012

[12] F Shahani P Soltani and M Zarrebini ldquoThe analysis ofacoustic characteristics and sound absorption coefficient ofneedle punched nonwoven fabricsrdquo Journal of Engineered Fibersamp Fabrics vol 9 no 2 pp 84ndash92 2014

[13] M J Swift P Bris and K V Horoshenkov ldquoAcoustic absorptionin re-cycled rubber granulaterdquo Applied Acoustics vol 57 no 3pp 203ndash212 1999

[14] N TsujiuchiI T Koizumi Y Ohshima and T Kitagawa AnOptimal Design and Application of Sound-Absorbing MaterialMade of Exploded Bamboo Fibers Department of MechanicalEngineering Doshisha University Kyoto Japan 2002

[15] M Avella G La Rota E Martuscelli et al ldquoPoly(3-hydroxybutyrate-co-3-hydroxyvalerate) and wheat straw fibrecomposites thermal mechanical properties and biodegra-dation behaviourrdquo Journal of Materials Science vol 35 no 4pp 829ndash836 2000

[16] F Asdrubali ldquoGreen and sustainable materials for noise controlin buildingsrdquo in Proceedings of the 19th International Congresson Acoustics Madrid Spain 2007

[17] S Kalia B S Kaith and I Kaur ldquoPretreatments of naturalfibers and their application as reinforcing material in polymercompositesmdasha reviewrdquo Polymer Engineering amp Science vol 49no 7 pp 1253ndash1272 2009

[18] F Asdrubali ldquoSurvey on the acoustical properties of newsustainable materials for noise controlrdquo in Proceedings of theEuronoise 2006 Tampere Finland 2006

[19] A Khan Vibro-acoustic products from re-cycled raw materialsusing a cold extrusion process a continuous cold extrusionprocess has been developed to tailor a porous structure frompolymeric waste so that the final material possesses particularvibro-acoustic properties [PhD thesis] University of BradfordBradford UK 2008

[20] H Benkreira A Khan and K V Horoshenkov ldquoSustainableacoustic and thermal insulation materials from elastomericwaste residuesrdquo Chemical Engineering Science vol 66 no 18pp 4157ndash4171 2011

[21] T Rusu and O Vasile ldquoInvestigation composite materials for itssound absorption propertiesrdquo Romanian Journal of Acoustics ampVibration vol 9 no 2 pp 123ndash126 2012

[22] E Julia J Segura A Nadal J M Gadea and J E Crespo ldquoStudyof sound absorption properties of multilayer panels made fromground tyre rubbersrdquo Fascicle of Management and TechnologicalEngineering vol 1 pp 147ndash150 2013

[23] J Turkiewicz and J Sikora ldquoSound absorbing materials fromrecycled rubber productsrdquo Mechanics and Control vol 32 no3 pp 117ndash121 2013

[24] D J Oldham C A Egan and R D Cookson ldquoSustainableacoustic absorbers from the biomassrdquoApplied Acoustics vol 72no 6 pp 350ndash363 2011

[25] W D Yang and Y Li ldquoSound absorption performance ofnatural fibers and their compositesrdquo ScienceChinaTechnologicalSciences vol 55 no 8 pp 2278ndash2283 2012

[26] S V Joshi L T Drzal A K Mohanty and S Arora ldquoArenatural fiber composites environmentally superior to glass fiberreinforced compositesrdquoComposites Part A Applied Science andManufacturing vol 35 no 3 pp 371ndash376 2004

[27] H Demir U Atikler D Balkose and F Tıhmınlıoglu ldquoTheeffect of fiber surface treatments on the tensile and watersorption properties of polypropylene-luffa fiber compositesrdquoComposites Part A Applied Science and Manufacturing vol 37no 3 pp 447ndash456 2006

[28] J Sikora and J Turkiewicz ldquoSound absorption coefficients ofgranular materialsrdquo Mechanics and Control vol 29 no 3 pp149ndash157 2010

[29] G Iannace C Ianniello LMaffei andR Romano ldquoSteady-stateair-flow and acoustic measurement of the resistivity of loosegranular materialsrdquo Journal of the Acoustical Society of Americavol 106 no 3 pp 1416ndash1419 1999

[30] A Berbiche M Sadouki Z Fellah et al ldquoExperimental deter-mination of the viscous flow permeability of porous materialsby measuring reflected low frequency acoustic wavesrdquo Journalof Applied Physics vol 119 no 1 Article ID 014906 2016

[31] T Koizumi N Tsujiuchi and A Adachi ldquoThe development ofsound absorbing materials using natural bamboo fibersrdquo HighPerformance Structures and Materials vol 4 pp 157ndash166 2002

[32] M E Delany and E N Bazley ldquoAcoustical properties of fibrousabsorbentmaterialsrdquoApplied Acoustics vol 3 no 2 pp 105ndash1161970

[33] F-C Lee and W-H Chen ldquoAcoustic transmission analysis ofmulti-layer absorbersrdquo Journal of Sound and Vibration vol 248no 4 pp 621ndash634 2001

[34] I P Dunn and W A Davern ldquoCalculation of acousticimpedance of multi-layer absorbersrdquo Applied Acoustics vol 19no 5 pp 321ndash334 1986

[35] D L Johnson J Koplik and L M Schwartz ldquoNew pore-sizeparameter characterizing transport in porous mediardquo PhysicalReview Letters vol 57 article 2564 1986

[36] D L Johnson J Koplik and R Dashen ldquoTheory of dynamicpermeability and tortuosity in fluid-saturated porous mediardquoJournal of Fluid Mechanics vol 176 pp 379ndash402 1987

[37] Y Champoux and J-F Allard ldquoDynamic tortuosity and bulkmodulus in air-saturated porous mediardquo Journal of AppliedPhysics vol 70 no 4 pp 1975ndash1979 1991

[38] J F Allard Propagation of Sound in Porous Media ModellingSound Absorbing Materials Elsevier Application Science NewYork NY USA 1993


[39] N Kino T Ueno Y Suzuki and H Makino ldquoInvestigationof non-acoustical parameters of compressed melamine foammaterialsrdquo Applied Acoustics vol 70 no 4 pp 595ndash604 2009

[40] J Allard Sound Propagation in Porous Media Modelling SoundAbsorbing Materials Elsevier London UK 1993

[41] M Biot ldquoGeneralized theory of acoustic propagation in porousdissipative mediardquo The Journal of the Acoustical Society ofAmerica vol 34 no 9A pp 1254ndash1264 1962

[42] K Attenborough ldquoModels for the acoustical characteristics ofair filled granular materialsrdquo Acta Acustica vol 1 pp 213ndash2261993

[43] R Asmatulu W Khan and M B Yildirim ldquoAcoustical prop-erties of electrospun nanofibers for aircraft interior noisereductionrdquo inProceedings of the ASME InternationalMechanicalEngineering Congress and Exposition American Society ofMechanical Engineers Lake Buena Vista Fla USA November2009

[44] T J Cox and P Drsquoantonio Acoustic Absorbers and DiffusersTheory Design and Application Taylors amp Francis New YorkNY USA 2009

[45] NNVoronina andKVHoroshenkov ldquoA new empiricalmodelfor the acoustic properties of loose granular mediardquo AppliedAcoustics vol 64 no 4 pp 415ndash432 2003

[46] A E Tiuc O Vasile U Anamaria-Didona T Gabor and HVermeuan ldquoThe analysis of factors that influence the soundabsorption coefficient of porous materialsrdquo Polyurethane vol40 pp 105ndash108 2014

[47] M Ibrahim and R Melik ldquoPhysical parameters affectingacoustic absorption characteristics of fibrous materialsrdquo inProceedings of the Mathematical and Physical Society of Egyptp 46 1978

[48] M Coates and M Kierzkowski ldquoAcoustic textilesmdashlighterthinner and more sound-absorbentrdquo Technical Textiles Interna-tional vol 11 no 7 pp 15ndash18 2002

[49] K U Ingard Notes on Sound Absorption Technology NoiseControl Foundation Poughkeepsie NY USA 1994

[50] S Mahzan A Zaidi A Mujahid M I Ghazali M N Yahyaand M Ismail ldquoInvestigation on sound absorption of rice-husk reinforced compositerdquo in Proceedings of the MalaysianTechnical Universities Conference on Engineering and Technology(MUCEET rsquo09) pp 19ndash22 Kuantan Malaysia June 2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Table 1 Advantages and disadvantages of natural fibers [17 18]

Advantages DisadvantagesAre biodegradable cheaper and eco-friendly and have low specificweight

Have lower antifungus durability moisture and fire resistantqualities

Are abundantly available and high electrical resistant Have a negative impact on climate change (CO2absorption)

Have good thermal and acoustic insulating properties Exhibit lower acoustic absorption compared to synthetic fibersdue to a larger diameter

Have low toxicity and less human health hazards during processingand handling

Have poor fiber-matrix adhesion and moisture resistance whichcauses increase in volume for swelling of the fibers

A handful of researchers have focused on natural fibercomposites with the combination of natural fiber and gran-ular materials The objective of this review is to presentresearch development in the area of sound absorption ofnatural fiber composites combined with granular materialsThe aim of the review is to observe the expansion of thisfield from conventional fibrogranular composites to naturalfibrogranular composites for acoustic absorption purposesThe effective physical parameters for enhancing the lowfrequency absorption in the materials are also highlightedin this review In addition three well-known models weredemonstrated for evaluating the acoustic parameters of fibro-granular composites

2 Natural Fiber Composites

Due to their biodegradable lightweight cheaper nontoxicand nonabrasive qualities natural fibers are receiving muchattention in composites as a substitute for synthetic fibers foracoustic absorption purposes The natural fibers with desir-able physical andmechanical properties are exhibited as highperformance composites with environmental and economicadvantages [15] Many potential candidates are available inthe form of natural fibers for use as sustainable acousticabsorbers The fibers of coir corn paddy sisal and bananaare some examples Fiberglass mineral wool and glass woolare examples of synthetic fibers The acoustic performance ofsynthetic sound absorptive materials is higher than that ofnatural sound absorptive materials because of their thinnerdiameter and antifungus quality but they have a higherenvironmental impact than the natural fibers [16]

In recent years natural fiber reinforced resinpolymercomposites have earned a lot of attention due to theirlightweight abundant cost efficient biodegradable and eco-friendly nature Moreover these materials are cheaper andenvironmentally superior to glass fiber reinforced composites[26] However due to low interfacial adhesion poormoistureresistance and the low antifungus quality of natural fibercomposites these materials are still not quite as popular assynthetic based composites

Researchers are trying to improve the quality of naturalfibers through chemical treatment prior to compositeproduction to overcome these shortcomings It was reportedthat mercerization or alkaline treatment reduces the fiberdiameter and upgrades the quality by improving its adhesive

and antifungus quality [17] The reduction of fiber diameterenhances low frequency sound absorption by providinga more tortuous path and higher surface area which inturn increases the air flow resistivity of fibrous materialThe increase of air flow resistivity causes loss of soundenergy through friction of sound waves with air moleculesand thus improves low frequency sound absorption[9]

The study analyzes the limitations of natural fibers toachieve their acoustic absorption performance at a desiredlevel Some of the advantages and disadvantages of naturalfibers are furnished in Table 1 [17 18]

3 Pretreatment of Natural Fiber

To achieve fiber fitness fiber quality fiber strength and abetter fiber-matrix adhesion in the composite pretreatmentof natural fiber is needed for commercial use in parallel withsynthetic fiber There are various pretreatment techniquesavailable to tune the fiber according to the research require-ments Examples includemercerization or alkaline treatmentgraft copolymerization and plasma treatment Among themalkaline treatment or mercerization serves the purpose ofthis research as this process reduces the fiber diameterIt is a common method of producing high quality fibersMercerization increases the surface roughness of fiber byremoving some important substances like lignin pectin andhemicelluloses of the fiber Although the removal of thesesubstances lowers the acoustic absorption performance ofthe material it allows better fiber-binder interface adhesionfiber fitness longevity and antifungus quality and mostimportantly reduces the diameter of the fibers [11 17 27]

Figures 1 2 and 3 demonstrate the inner structure of coirfiber and the appearance of coir fiber before and after alkalinetreatment respectively It is evident from these three imagesthat alkaline treatment causes a reduction in fiber diameterwith the removal of moisture contents

Figure 3 shows the reduction in fiber diameter due tothe alkaline treatment at the cost of the removal of moisturecontents Figure 4 shows that the increase in chemicalconcentration results in the decrease of fiber diameter andfiber strength as well It was reported that 6 of alkalitreated coir fiber-epoxy resin composite showed a satisfactoryfiber diameter reduction with better mechanical strengthcompared to untreated composites [11]


Lignin

Cellulose

Hemicellulose




NaOH treatment


028

027

026

025

024

023

022

021

02

Fibe

r dia

met

er (m

m)

0 2 4 6 8 10

02743

02542

0241

0231702287

0218




















119896 =2120587119891

1198880

[0189119887minus0595 + 119894 (1 + 00978119887minus07)] (1)


119885 = 119885119888coth (119896 sdot 119889) (2)








Λ = 2int V2fluid119889119860

int V2fluid119889119881 (3)




Λ =1

119888(radic

8120578120572infin

120590120601) (4)



120588 (120596) = 120572infin1205880[

[

1 +120590120601

1198951205961205880120572infin

radic1 +41205722infin1205781205880120596

1205902Λ21205962]

]

(5)


Λ1015840 = 2int 119889119860

int119889119881= 2

119860

119881 (6)



Λ =1

2120587119903119897 (7)

Λ1015840 =1

120587119903119897= 2Λ (8)

119897 =1




119870 (120596) =1205741198750


119901120588012059616119896)]

minus1 (10)


0is


0is density of


119888(120596) the



119885119888(120596) =

1

120601radic120588 (120596) sdot 119870 (120596)

119896119888(120596) = 120596radic

120588 (120596)

119870 (120596)

119885 = 119885119888(120596) sdot coth (119896

119888(120596))

(11)




119870119891(120596) =

1205741198750

120574 minus (120574 minus 1) [1 + (8120578119895Λ10158402

1198731199011205961205880) (1 + 119895120588

0(120596119873119901Λ10158402

16120578))12

]minus1 (12)



119875 = 43119873 + 119870

119887+(1 minus 120593)

2

120593119870119891

119876 = 119870119891(1 minus 120593)

119877 = 119870119891120593

(13)


119870119887=2119873 (] + 1)3 (1 minus 2])

(14)



11 120588lowast12




2119866 (120596)

120596

120588lowast12= minus120588119886+ 1198951205901205932

119866 (120596)

120596

120588lowast22= 1205931205880+ 120588119886minus 1198951205901205932

119866 (120596)

120596

(15)

where

119866120596= (1 +

41198951205722infin1205781205880120596

1205902Λ21205932)

12


(16)

120572infin


120572infinasymp

1

radic120593 (17)



12057521=

1205962


12minus radicΔ]

12057522=

1205962


12+ radicΔ]

(18)

where


12)2


2

) (19)


120583119894=1198751205752119894minus 1205962120588lowast

11

1205962120588lowast12minus 1198761205752119894

(20)


119894or frame 119885119891


119885119886119894= (119877 +

119876

120583119894

)120575119894

120593120596

119885119891

119894= (119875 + 119876120583

119894)120575119894

120596

(21)



119885 = minus119895(119885119891

111988511988621205832minus 119885119891

211988511988611205831)

119863 (22)

where

119863 = (1 minus 120593 + 1205931205832) [119885119891

119894minus (1 minus 120593)119885119886

1198941205831] 1199051198921205752119889


119891

2] 1199051198921205751119889

(23)



120572 = 1 minus10038161003816100381610038161003816100381610038161003816

119885 minus 1198850

119885 + 1198850

10038161003816100381610038161003816100381610038161003816

2

(24)













1

095

09

085

08

075

Soun

d ab

sorp

tion

coeffi

cien

t

250 500 1000 2000 4000

Frequency (Hz)




Flow

resis

tivity

(Nsm

minus4)

0 05 1 15 2 25 3 35 4



106

105

104

103

102






und

abso

rptio

n co

effici

ent

Frequency (Hz)

10

09

08

07

06

05

04

03

02

01

00

125 250 500 1k 2k 4k


Density20kgm3

30kgm3

40kgm3

50kgm3








[24 25]

















8 Conclusion










Competing Interests


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Lignin

Cellulose

Hemicellulose




NaOH treatment


028

027

026

025

024

023

022

021

02

Fibe

r dia

met

er (m

m)

0 2 4 6 8 10

02743

02542

0241

0231702287

0218




















119896 =2120587119891

1198880

[0189119887minus0595 + 119894 (1 + 00978119887minus07)] (1)


119885 = 119885119888coth (119896 sdot 119889) (2)








Λ = 2int V2fluid119889119860

int V2fluid119889119881 (3)




Λ =1

119888(radic

8120578120572infin

120590120601) (4)



120588 (120596) = 120572infin1205880[

[

1 +120590120601

1198951205961205880120572infin

radic1 +41205722infin1205781205880120596

1205902Λ21205962]

]

(5)


Λ1015840 = 2int 119889119860

int119889119881= 2

119860

119881 (6)



Λ =1

2120587119903119897 (7)

Λ1015840 =1

120587119903119897= 2Λ (8)

119897 =1




119870 (120596) =1205741198750


119901120588012059616119896)]

minus1 (10)


0is


0is density of


119888(120596) the



119885119888(120596) =

1

120601radic120588 (120596) sdot 119870 (120596)

119896119888(120596) = 120596radic

120588 (120596)

119870 (120596)

119885 = 119885119888(120596) sdot coth (119896

119888(120596))

(11)




119870119891(120596) =

1205741198750

120574 minus (120574 minus 1) [1 + (8120578119895Λ10158402

1198731199011205961205880) (1 + 119895120588

0(120596119873119901Λ10158402

16120578))12

]minus1 (12)



119875 = 43119873 + 119870

119887+(1 minus 120593)

2

120593119870119891

119876 = 119870119891(1 minus 120593)

119877 = 119870119891120593

(13)


119870119887=2119873 (] + 1)3 (1 minus 2])

(14)



11 120588lowast12




2119866 (120596)

120596

120588lowast12= minus120588119886+ 1198951205901205932

119866 (120596)

120596

120588lowast22= 1205931205880+ 120588119886minus 1198951205901205932

119866 (120596)

120596

(15)

where

119866120596= (1 +

41198951205722infin1205781205880120596

1205902Λ21205932)

12


(16)

120572infin


120572infinasymp

1

radic120593 (17)



12057521=

1205962


12minus radicΔ]

12057522=

1205962


12+ radicΔ]

(18)

where


12)2


2

) (19)


120583119894=1198751205752119894minus 1205962120588lowast

11

1205962120588lowast12minus 1198761205752119894

(20)


119894or frame 119885119891


119885119886119894= (119877 +

119876

120583119894

)120575119894

120593120596

119885119891

119894= (119875 + 119876120583

119894)120575119894

120596

(21)



119885 = minus119895(119885119891

111988511988621205832minus 119885119891

211988511988611205831)

119863 (22)

where

119863 = (1 minus 120593 + 1205931205832) [119885119891

119894minus (1 minus 120593)119885119886

1198941205831] 1199051198921205752119889


119891

2] 1199051198921205751119889

(23)



120572 = 1 minus10038161003816100381610038161003816100381610038161003816

119885 minus 1198850

119885 + 1198850

10038161003816100381610038161003816100381610038161003816

2

(24)













1

095

09

085

08

075

Soun

d ab

sorp

tion

coeffi

cien

t

250 500 1000 2000 4000

Frequency (Hz)




Flow

resis

tivity

(Nsm

minus4)

0 05 1 15 2 25 3 35 4



106

105

104

103

102






und

abso

rptio

n co

effici

ent

Frequency (Hz)

10

09

08

07

06

05

04

03

02

01

00

125 250 500 1k 2k 4k


Density20kgm3

30kgm3

40kgm3

50kgm3








[24 25]

















8 Conclusion










Competing Interests


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






















119896 =2120587119891

1198880

[0189119887minus0595 + 119894 (1 + 00978119887minus07)] (1)


119885 = 119885119888coth (119896 sdot 119889) (2)








Λ = 2int V2fluid119889119860

int V2fluid119889119881 (3)




Λ =1

119888(radic

8120578120572infin

120590120601) (4)



120588 (120596) = 120572infin1205880[

[

1 +120590120601

1198951205961205880120572infin

radic1 +41205722infin1205781205880120596

1205902Λ21205962]

]

(5)


Λ1015840 = 2int 119889119860

int119889119881= 2

119860

119881 (6)



Λ =1

2120587119903119897 (7)

Λ1015840 =1

120587119903119897= 2Λ (8)

119897 =1




119870 (120596) =1205741198750


119901120588012059616119896)]

minus1 (10)


0is


0is density of


119888(120596) the



119885119888(120596) =

1

120601radic120588 (120596) sdot 119870 (120596)

119896119888(120596) = 120596radic

120588 (120596)

119870 (120596)

119885 = 119885119888(120596) sdot coth (119896

119888(120596))

(11)




119870119891(120596) =

1205741198750

120574 minus (120574 minus 1) [1 + (8120578119895Λ10158402

1198731199011205961205880) (1 + 119895120588

0(120596119873119901Λ10158402

16120578))12

]minus1 (12)



119875 = 43119873 + 119870

119887+(1 minus 120593)

2

120593119870119891

119876 = 119870119891(1 minus 120593)

119877 = 119870119891120593

(13)


119870119887=2119873 (] + 1)3 (1 minus 2])

(14)



11 120588lowast12




2119866 (120596)

120596

120588lowast12= minus120588119886+ 1198951205901205932

119866 (120596)

120596

120588lowast22= 1205931205880+ 120588119886minus 1198951205901205932

119866 (120596)

120596

(15)

where

119866120596= (1 +

41198951205722infin1205781205880120596

1205902Λ21205932)

12


(16)

120572infin


120572infinasymp

1

radic120593 (17)



12057521=

1205962


12minus radicΔ]

12057522=

1205962


12+ radicΔ]

(18)

where


12)2


2

) (19)


120583119894=1198751205752119894minus 1205962120588lowast

11

1205962120588lowast12minus 1198761205752119894

(20)


119894or frame 119885119891


119885119886119894= (119877 +

119876

120583119894

)120575119894

120593120596

119885119891

119894= (119875 + 119876120583

119894)120575119894

120596

(21)



119885 = minus119895(119885119891

111988511988621205832minus 119885119891

211988511988611205831)

119863 (22)

where

119863 = (1 minus 120593 + 1205931205832) [119885119891

119894minus (1 minus 120593)119885119886

1198941205831] 1199051198921205752119889


119891

2] 1199051198921205751119889

(23)



120572 = 1 minus10038161003816100381610038161003816100381610038161003816

119885 minus 1198850

119885 + 1198850

10038161003816100381610038161003816100381610038161003816

2

(24)













1

095

09

085

08

075

Soun

d ab

sorp

tion

coeffi

cien

t

250 500 1000 2000 4000

Frequency (Hz)




Flow

resis

tivity

(Nsm

minus4)

0 05 1 15 2 25 3 35 4



106

105

104

103

102






und

abso

rptio

n co

effici

ent

Frequency (Hz)

10

09

08

07

06

05

04

03

02

01

00

125 250 500 1k 2k 4k


Density20kgm3

30kgm3

40kgm3

50kgm3








[24 25]

















8 Conclusion










Competing Interests


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Λ =1

119888(radic

8120578120572infin

120590120601) (4)



120588 (120596) = 120572infin1205880[

[

1 +120590120601

1198951205961205880120572infin

radic1 +41205722infin1205781205880120596

1205902Λ21205962]

]

(5)


Λ1015840 = 2int 119889119860

int119889119881= 2

119860

119881 (6)



Λ =1

2120587119903119897 (7)

Λ1015840 =1

120587119903119897= 2Λ (8)

119897 =1




119870 (120596) =1205741198750


119901120588012059616119896)]

minus1 (10)


0is


0is density of


119888(120596) the



119885119888(120596) =

1

120601radic120588 (120596) sdot 119870 (120596)

119896119888(120596) = 120596radic

120588 (120596)

119870 (120596)

119885 = 119885119888(120596) sdot coth (119896

119888(120596))

(11)




119870119891(120596) =

1205741198750

120574 minus (120574 minus 1) [1 + (8120578119895Λ10158402

1198731199011205961205880) (1 + 119895120588

0(120596119873119901Λ10158402

16120578))12

]minus1 (12)



119875 = 43119873 + 119870

119887+(1 minus 120593)

2

120593119870119891

119876 = 119870119891(1 minus 120593)

119877 = 119870119891120593

(13)


119870119887=2119873 (] + 1)3 (1 minus 2])

(14)



11 120588lowast12




2119866 (120596)

120596

120588lowast12= minus120588119886+ 1198951205901205932

119866 (120596)

120596

120588lowast22= 1205931205880+ 120588119886minus 1198951205901205932

119866 (120596)

120596

(15)

where

119866120596= (1 +

41198951205722infin1205781205880120596

1205902Λ21205932)

12


(16)

120572infin


120572infinasymp

1

radic120593 (17)



12057521=

1205962


12minus radicΔ]

12057522=

1205962


12+ radicΔ]

(18)

where


12)2


2

) (19)


120583119894=1198751205752119894minus 1205962120588lowast

11

1205962120588lowast12minus 1198761205752119894

(20)


119894or frame 119885119891


119885119886119894= (119877 +

119876

120583119894

)120575119894

120593120596

119885119891

119894= (119875 + 119876120583

119894)120575119894

120596

(21)



119885 = minus119895(119885119891

111988511988621205832minus 119885119891

211988511988611205831)

119863 (22)

where

119863 = (1 minus 120593 + 1205931205832) [119885119891

119894minus (1 minus 120593)119885119886

1198941205831] 1199051198921205752119889


119891

2] 1199051198921205751119889

(23)



120572 = 1 minus10038161003816100381610038161003816100381610038161003816

119885 minus 1198850

119885 + 1198850

10038161003816100381610038161003816100381610038161003816

2

(24)













1

095

09

085

08

075

Soun

d ab

sorp

tion

coeffi

cien

t

250 500 1000 2000 4000

Frequency (Hz)




Flow

resis

tivity

(Nsm

minus4)

0 05 1 15 2 25 3 35 4



106

105

104

103

102






und

abso

rptio

n co

effici

ent

Frequency (Hz)

10

09

08

07

06

05

04

03

02

01

00

125 250 500 1k 2k 4k


Density20kgm3

30kgm3

40kgm3

50kgm3








[24 25]

















8 Conclusion










Competing Interests


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119875 = 43119873 + 119870

119887+(1 minus 120593)

2

120593119870119891

119876 = 119870119891(1 minus 120593)

119877 = 119870119891120593

(13)


119870119887=2119873 (] + 1)3 (1 minus 2])

(14)



11 120588lowast12




2119866 (120596)

120596

120588lowast12= minus120588119886+ 1198951205901205932

119866 (120596)

120596

120588lowast22= 1205931205880+ 120588119886minus 1198951205901205932

119866 (120596)

120596

(15)

where

119866120596= (1 +

41198951205722infin1205781205880120596

1205902Λ21205932)

12


(16)

120572infin


120572infinasymp

1

radic120593 (17)



12057521=

1205962


12minus radicΔ]

12057522=

1205962


12+ radicΔ]

(18)

where


12)2


2

) (19)


120583119894=1198751205752119894minus 1205962120588lowast

11

1205962120588lowast12minus 1198761205752119894

(20)


119894or frame 119885119891


119885119886119894= (119877 +

119876

120583119894

)120575119894

120593120596

119885119891

119894= (119875 + 119876120583

119894)120575119894

120596

(21)



119885 = minus119895(119885119891

111988511988621205832minus 119885119891

211988511988611205831)

119863 (22)

where

119863 = (1 minus 120593 + 1205931205832) [119885119891

119894minus (1 minus 120593)119885119886

1198941205831] 1199051198921205752119889


119891

2] 1199051198921205751119889

(23)



120572 = 1 minus10038161003816100381610038161003816100381610038161003816

119885 minus 1198850

119885 + 1198850

10038161003816100381610038161003816100381610038161003816

2

(24)













1

095

09

085

08

075

Soun

d ab

sorp

tion

coeffi

cien

t

250 500 1000 2000 4000

Frequency (Hz)




Flow

resis

tivity

(Nsm

minus4)

0 05 1 15 2 25 3 35 4



106

105

104

103

102






und

abso

rptio

n co

effici

ent

Frequency (Hz)

10

09

08

07

06

05

04

03

02

01

00

125 250 500 1k 2k 4k


Density20kgm3

30kgm3

40kgm3

50kgm3








[24 25]

















8 Conclusion










Competing Interests


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















1

095

09

085

08

075

Soun

d ab

sorp

tion

coeffi

cien

t

250 500 1000 2000 4000

Frequency (Hz)




Flow

resis

tivity

(Nsm

minus4)

0 05 1 15 2 25 3 35 4



106

105

104

103

102






und

abso

rptio

n co

effici

ent

Frequency (Hz)

10

09

08

07

06

05

04

03

02

01

00

125 250 500 1k 2k 4k


Density20kgm3

30kgm3

40kgm3

50kgm3








[24 25]

















8 Conclusion










Competing Interests


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










und

abso

rptio

n co

effici

ent

Frequency (Hz)

10

09

08

07

06

05

04

03

02

01

00

125 250 500 1k 2k 4k


Density20kgm3

30kgm3

40kgm3

50kgm3








[24 25]

















8 Conclusion










Competing Interests


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















8 Conclusion










Competing Interests


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Review Article Acoustic Absorption of Natural Fiber Compositesdownloads.hindawi.com/journals/je/2016/5836107.pdf · Review Article Acoustic Absorption of Natural Fiber Composites