research article viscoelastic characterization of long...

Research ArticleViscoelastic Characterization of Long-Eared Owl Flight FeatherShaft and the Damping Ability Analysis

Jia-li Gao1 Jin-kui Chu1 Le Guan1 Hai-xin Shang1 and Zhen-kun Lei2

1 Key Laboratory for Precision amp Non-Traditional Machining of Ministry of Education Dalian University of TechnologyDalian 116024 China

2 State Key Laboratory of Structural Analysis for Industrial Equipment Dalian University of Technology Dalian 116024 China

Correspondence should be addressed to Jin-kui Chu chujkdluteducn

Received 25 May 2014 Revised 28 July 2014 Accepted 29 July 2014 Published 28 August 2014

Academic Editor Mickael Lallart

Copyright copy 2014 Jia-li Gao et alThis is an open access article distributed under theCreative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Flight feather shaft of long-eared owl is characterized by a three-parameter model for linear viscoelastic solids to reveal its dampingability Uniaxial tensile tests of the long-eared owl pigeon and golden eagle flight feather shaft specimens were carried out based onInstron 3345 single columnmaterial testing system respectively and viscoelastic response of their stress and strain was described bythe standard linear solid model Parameter fitting result obtained from the tensile tests shows that there is no significant differencein instantaneous elasticmodulus for the three birdsrsquo feather shafts but the owl shaft has the highest viscosity implyingmore obviousviscoelastic performance Dynamic mechanical property was characterized based on the tensile testing results Loss factor (tan 120575)of the owl flight feather shaft was calculated to be 1609 plusmn 0238 far greater than those of the pigeon (0896 plusmn 0082) and goldeneagle (1087 plusmn 0074) It is concluded that the long-eared owl flight feather has more outstanding damping ability compared to thepigeon and golden eagle flight feather shaft Consequently the long-eared owl flight feathers can dissipate the vibration energymore effectively during the flying process based on the principle of damping mechanism for the purpose of vibration attenuationand structure radiated noise reduction

1 Introduction

Noise pollution is a major problem in the main urban trafficarea recently especially the airport neighborhoods adverselyaffecting the lives of millions of people and animals Evolvinga silent flight most genera of owls are not audible to manand more importantly to their prey How flight noise can beefficiently reduced may be learned from owls

Since more than a century ago the research regarding themechanisms that enable the nearly silent flight of owls hasremained an interesting field for theoretical and experimentalresearch Mascha and Graham discovered and innovativelyconcluded three mechanisms of the owl feathers that sup-posedly enabled the silent flight (1) comb-like structure atthe leading edge of the wings (2) long and soft fringes atthe trailing edge and (3) soft downy upper surface of thefeathers [1 2] These three mechanisms have been gradually

identified [3ndash6] and accepted by the bionic researchers [7ndash13] The reported biological studies of the noiselessly flyingowls show that owl wing feather has significantly long softfeather material and unique morphological structure whichare different from other bird feathers

However material research of the owl feathers is stillnot fully carried out and is away from material biomimeticsynthesis so that bionic studies about the owl feather arealmost all based on the outline edges Though Bachmannet al experimentally measured the flexural stiffness of theowl primary feather shaft cortex [14] a more comprehensivemechanical characterization of owl feather is necessary Inaddition its comparison with other bird feathers is stillinsufficient

Stiff strong but lightweight shaft is the key force bearingstructure in an owl feather for its gliding flight Interactingwith the flow field during flight feather shafts are subjected

Hindawi Publishing CorporationShock and VibrationVolume 2014 Article ID 709367 9 pageshttpdxdoiorg1011552014709367

2 Shock and Vibration

to bendmainly under aerodynamic loads [15 16] Because rel-ative movement caused by the feather vibration and frictionduring flight would lead to the radiation noise [17] amplitudestability of the feather shaft directly affects the vibration ofthe whole feather structure and noise radiation Dampingfactor as an important physical parameter can be used tocharacterize the vibration attenuation capability of the owlfeather shaft and compared with other birdrsquos shafts Conse-quently on account of the assumption that the investigationof biomimetic materials inspired by the quiet flying owlsmight lighten a new way to obtain more excellent mufflingperformance in addition to the morphological bionic designwe present our study on the viscoelastic characterization ofowl flight feather materials and the analysis of their vibrationdamping ability so as to provide further insight into theowlrsquos silent flight mechanism and bionic design in our furtherresearch in view of material acoustics [18 19]

The research presented in this paper focuses on theviscoelastic characterization of flight feather shaft of long-eared owl (Asio otus Strigiformes) pigeon (Columba liviaColumbiformes) and golden eagle (Aquila chrysaetos Fal-coniformes) to reveal the damping ability of their dynamicfeathers on wings Here long-eared owl is the main researchobject with noise reduction function [20] Its flight generallyconsists of an initial flapping phase followed by a glidingphase and a short flapping during touchdown [21] Pigeon is atypical flapping flight bird which differs from the long-earedowl and has a smaller size than the owl Golden eagle involvesthe same flight style as the long-eared owl and its size is largerthan the long-eared owl Both of the pigeon and golden eagledo not have the silent flight ability The aim is to comparethe viscoelastic performance of owl feather with other noisyflying birds without the impact of flying style and bird size onnoise generation

Feather shaft can be regarded as a slender beam sothe shear effect on its bending deformation can be ignoredHence normal stress accounts for the bending deformationof feather shaft Therefore uniaxial tensile tests of the threetypes of the prepared flight feather shaft specimens wereconducted on Instron 3345 single column materials testingsystem to investigate the relationship of strain and normalstress of the shafts at first Then viscoelasticity of feathershaft material was studied employing the standard linearviscoelastic solid model And then based on the viscoelasticmaterial parameters obtained from the tensile testing resultsdynamic mechanical property at a constant temperaturewas analyzed And tan 120575 of the long-eared owl pigeonand golden eagle flight feather shaft was calculated for adamping ability comparison between the three types of flightfeathers Relationship between damping ability and vibrationattenuation for owl feather shaft was briefly discussed at last

2 Materials and Methods

21 Feather Material and Anatomy of Feather Shafts Flightfeathers of long-eared owl pigeon and golden eagle wereobtained from Dalian Forest Zoo (Liaoning China) Itis noted that feathers are collected with no harm to the

birdsrsquo life complying with the Animal Protection Act Barbson both sides of the feather shaft were removed by thescalpel blade Trimmed feather shafts were rinsed twice withdeionized water for 30 minutes and naturally dried on cleanfilter paper at room temperature All the specimens werecleaned and prepared in the cleanroom of key laboratoryfor precision and nontraditional machining of Ministry ofEducation Dalian University of Technology

The tested specimenswere selected from the feather shaftsaccording to the following rules

(a) the same relative position that the testing samplesare selected in the same proportion position on flightfeather shafts of the long-eared owl pigeon andgolden eagle

(b) the same aspect ratio that the ratio of the shaft lengthto maximum cross-sectional diameter is unified forall the testing parts one end of the testing sectionis marked according to the selection method (a) atfirst and its maximum diameter size is measured bya spiral micrometer subsequently The other end islocated away from the marked position with a gaugelength of fifteen times the maximum diameter

After marking the testing portion in accordance with theabove methods specimen including the testing section andsufficient extension parts on its two sides for clamping iscut out as is shown in Figure 1 Before the test is startedreinforcement of the clamping parts is necessary in orderto avoid damage of the specimen caused by gripping Twoextension parts were inserted in flat boxes which are fullof liquid epoxy structural adhesive (WD3003) with highbonding strength and excellent performance to resist thecompression Clamping structures were obtained when theliquid adhesive was solidified into a block after 24 hoursMeanwhile thin aluminium sheets with strong ductility werepasted on gripping interface of the adhesive to preventcontamination of the experimental equipment

22 Experimental Instrument and Procedures Instron 3345single columnmaterials testing system (Instron Corporationthe United States) is used for uniaxial tensile test as isshown in Figure 2The whole system is equipped with a 5 kNload cell a displacement sensor a speed-controlled guidescrew driving device (range 0005mmmin to 1000mmminaccuracy plusmn5 of the point value) andwedge clamps with thegripping force of 50 kN that one clamp is connected to theload cell while the other is secured to the machine Both theload accuracy and the strain accuracy are plusmn5 of indicatedvalue for the materials testing system

During the experiments the material testing systemrecorded the stretching force every 01 seconds and the one-to-one sampling time until the testing specimen was frac-tured Digital image correlation (DIC) was applied to analyzethe deformation mechanisms [22] Firstly two high contrastmarkers were spotted on the lateral wall of the specimenSecondly high-speed camera was used to obtain chargecoupled device (CCD) images before and after the tensiledeformation in the experimental process The corresponding

Shock and Vibration 3

(a) (b)

Testedspecimen

Clampingpart

Clampingpart

(c)

Figure 1 Schematic drawings of flight feather and the sampling of tensile tested specimen (a) Complete feather (b) Feather shaft afterremoving the vane with scissors (c) Tested specimen with extension parts on its two sides for clamping

Load transducer

High-speedcamera

DIC analysis

Displacementmonitoring

F d

Figure 2 Schematic of the tensile test The test specimen (feathershaft) was center-mounted onto the wedge clamps Tensile force (119865)was measured while the specimen was pulled at a constant rate of05mmmin Tensile process was recorded by a high speed cameraand the strain of the specimen was calculated from DIC analysisof the CCD images DIC analysis was applied with the purpose ofexcluding the influence caused by the sample debonding clampingand the measurement error of samplersquos initial length

elongated deformation of the specimen was computed fromthe extremum of correlation coefficient by the correlationcalculation of the CCD images finally CCD images of eachloading in the whole test were recorded and the real strain ateach observing time was calculated All samples were testedat a constant room temperature of 22∘C and humidity of 55

3 Results

31 Morphological Characterization of the Feather Shaft CrossSection Intersecting surface of the long-eared owl pigeonand golden eagle flight feather shaft was morphologically

C

M

C-s

(a)

C

M

C-s

(b)

CM

C-s

(c)

Figure 3 Flight feather shaft cross-section and scanning cross-section of the cortex (a) Cross-section of long-eared owl feather(b) Cross-section of pigeon feather (c) Cross-section of golden eaglefeather C Cortex M Medulla C-s Cross-section of the cortex

characterized as shown in Figure 3The general morphologyof the rachis is very similar in the three species All shafts havean approximate shape of a box girder each shaft consists ofa solid compact shell (cortex) and is filled by the medullawhich contains air-filled keratinized epithelial cells withan average diameter of 10ndash20 120583m [23] Noteworthy is the


asymmetry of the cross section of a considerable part of theflight feather shaft

According to the reported literatures the feather shaftgives rise to X-ray diffraction patterns of great complexitythat they have been described as the most complex knownfor the naturally occurring fibrous substances And furtherstudy suggests that120573-keratin structure is proposed to accountfor the principal features of the X-ray pattern and for somephysical properties of the feather shaft Cortex is composedof two different 120573-keratin fiber layers where the inner layerfiber direction is along the shaft and the outer keratinfiber direction is circumferential Due to its high hardnessand great flexibility cortex bears most bending stresses inthe flight process The compact keratin was found to beapproximately 100 times stiffer than themedullary foam [24]consistent with an earlier finding of Purslow and Vincentthat the medullary foam and transverse septa contributeonly 16 to the overall bending stiffness of the feathershaft [25] Because the medullary foam appears to play aminor structural role calculation of the medulla structure isnegligible in this study and our research is focused on thecortex for all flight feather shafts

Cross-sectional area of the fractured position of thefeather shaft cortex was calculated using image extractionmethod Cross-sectional area of the tested long-eared owlspecimen is 1360plusmn0103mm2 cross-sectional area of pigeonspecimen is 0308 plusmn 0024mm2 and cross-sectional area ofgolden eagle specimen is 1511 plusmn 0273mm2

32 Mechanical Behavior of the Flight Feather Shafts Figure 4gives a description of the flight feather shaft of long-earedowl pigeon and golden eagle specimens before and afterexperiments respectively Fractured positions are mostlylocated near to the thin end of the gauge length for shaftspecimensThe fracture mode of the shafts is ductile fractureInfluence caused by the sample fixation clamping andadhesive debonding can be avoided since tensile strain iscalculated by DIC analysis

Figure 5 presents typical stress-strain curves of long-eared owlrsquos and pigeonrsquos flight feather shaft Stress (120590) of theshaft relative to the cross-sectional area (119860) is given by theformula 120590 = 119865119860where 119865 is the tensile force In addition theformula for the strain (120576) is also given as 120576 = 1198711015840119871 where 119871is the feather shaftrsquos initial gauge length and 1198711015840 is the drawnshaft length respectively Nonlinear stress-strain relationshipis a common feature for all shafts in Figure 5 And it can alsobe found in Figure 5 that stress versus strain curve curvatureof the owl shaft is larger than the other two curves

4 Discussions

41 Viscoelastic Behavior andModel Analysis The above uni-axial tensile test results reveal a nonlinear material behaviorBased on the reported achievements in relation to naturalbiological composite materials asymmetrical geometry vis-coelastic property and inhomogeneous density are inherentcharacteristics for feather shaft leading to the nonlinear

response between stress and strain during the loading pro-cess In this study the selected testing samples from long-eared owl pigeon and golden eagle feather shaftwere straightas far as possible in length direction and the cortex sustainedmost of the tensile stress Therefore asymmetrical geometryand inhomogeneous density of the material are not thedeterminate factors for nonlinear mechanical response As aresult it is suggested that viscoelastic property might be themajor factor causing the nonlinear stress-strain relationshipof the feather shaft

In consideration of the nature of the tested material andthe applied testing method we employed a three-parameterstandard linear solid [26] to describe the nonlinear stress-strain relation of feather shaftThis nonlinearmodel is subjectto uniaxial tensile test The model consists of a single elasticelement (spring) (elastic modulus 119864

1) and a Kelvin element

with an elastic element (elastic modulus 1198642) and a viscous

element (dashpot) (coefficient of viscosity 120578) in parallel Theconstitutive law in differential equation form for the standardlinear solid model is

120590 +120578

1198641+ 1198642

=11986411198642

1198641+ 1198642

120576 +1198641120578

1198641+ 1198642

120576 (1)

Delay time (120591119888= 120578119864

2) and relaxation time (120591

119877= 120578(119864

1+1198642))

are two important internal time parameters for viscoelasticmaterial And for the standard linear solid model 120591

119888and 120591119877

only relate to material constants (1198641 1198642 120578)

In our test shaft specimens were tested at a constantrate Therefore mechanical behavior was studied under thecondition of constant strain ratio (119879) Stress response wasinvestigated under the whole strain history Strain expressionis as follows

120576 (119905) = 119879119905 (2)

Employing Boltzmannrsquos superposition method constitutiveequation of the stress response with a loading history ofconstant strain ratio is obtained

120590 (119905) = int

120591=infin

120591=infin

119864 (119905 minus 120591) 119889120576 (120591) = 119864 (119905) lowast 119889120576 (119905)

=1198641119879

1198641+ 1198642

[1198642119905 +

1198641120578

1198641+ 1198642

(1 minus 119890minus((1198641+1198642)120578)119905

)]

(3)

Dynamic behavior of viscoelastic materials is analyzed whenalternating stress (4) with angular frequency (120596) is appliedThus strain response of the viscoelastic solid can be expressedin (5)

120590 (119905) = 1205900119890119894120596119905

(4)

120576 (119905) = 119866 (119894120596) 120590 (119905) = 119866 (119894120596) 1205900119890119894120596119905

(5)

119866(119894120596) is defined as complex compliance an elastic constantwhich is equal to the ratio of strain and stress It changesonly with frequency and is a characterization of dynamic


Wedgeclamps

Markersfor DICanalysis

Fracturedposition

(a1) (a2) (a3)

(a)

Fracturedposition

(b1) (b2) (b3)

(b)

Fracturedposition

(c1) (c2) (c3)

(c)

Figure 4 Experimental specimens in the clamps scale bar 1mm (a1) Fixed long-eared owl specimen before test (a2) Breaking long-earedowl specimen after tensile process (a3) Breaking point close-up of the owl specimen (b1) Fixed pigeon specimen before test (b2) Breakingpigeon specimen after tensile process (b3) Breaking point close-up of the pigeon specimen (c1) Fixed golden eagle specimen before test (c2)Breaking golden eagle specimen after tensile process (c3) Breaking point close-up of the golden eagle specimen

mechanical properties of material in stable vibration Com-plex compliance is used and is to be presented as follows

119866 (119894120596) = 1198661(120596) + 119894119866

2(120596) (6)

where1198661and119866

2are identified as storage compliance and loss

compliance respectively Equations (4) and (5) are put into

(1) thus complex compliance 119866(119894120596) of the standard linearsolid model can be obtained in

119866 (119894120596) =1198641+ 1198642+ 120578119894120596

(11986411198642)2

+ (1198641120578120596)2

times [(1198641+ 1198642) 11986411198642+ 1198641(120578120596)2

minus 1198642

1

120578119894120596]

(7)


0 2 4 6 80

50

100

150

200

250

Stre

ss (M

Pa)

Strain ()

OwlEaglePigeon

Figure 5 Relationships of the stress and strain for long-eared owland pigeon shafts

Viscoelastic parameters can be derived from the storagecompliance and loss compliance One parameter is the lossfactor (tan 120575) where 120575 is an indication of the phase lagbetween the stress and strain tan 120575 represents the dampingability of the viscoelastic material and can be quantified bythe ratio of the loss modulus to storage modulus

tan 120575 = minus1198662 (120596)1198661(120596)

=((120578119864

2) minus (120578 (119864

1+ 1198642))) 120596

1 + (1205781198642) sdot (120578 (119864

1+ 1198642)) 1205962

=(120591119888minus 120591119877)

radic120591119888120591119877

sdot120596radic120591119888120591119877

1 + 1205911198881205911198771205962

(8)

From (8) it can be easily found that the maximum of tan 120575 isobtained when radic120591

119888120591119877= 1 and tan 120575 is close to zero when 120596

approaches either zero or extremum (infin)

42Determination of theMaterial Constants (1198641 1198642 120578) Least

square method was employed to formulation regression formaterial constants prediction The method of least squares isa standard approach to the approximate solution of overdeter-mined systems mostly used in data fitting The best fit in theleast squares sense minimizes the sum of squared residuals aresidual being the difference between an observed value andthe fitted value provided by a model Least squares problemsfall into two categories linear or ordinary least squares andnonlinear least squares depending on whether or not theresiduals are linear in all unknowns

In our test the measured strain performs a linearenlargement with the increase of time Relationship between

the measured stress and testing time exhibits a nonlinearcharacteristic due to stress relaxation for the viscoelasticmaterials SPSS statistical software was used following theprinciple of least square method for the linear fit of strainand loading time according to (2) firstly Strain ratio (119879) isdetermined by the slope of the fitted straight line And thennon-linear fitting of the stress and loading time is conductedon the base of (3) for viscoelastic parameters 119864

1 1198642 120578

43 Fitted Material Parameters of Long-Eared Owl and PigeonFlight Feather Shafts Uniaxial tensile tests of the long-earedowl pigeon and golden eagle flight feather shaft specimenswere performed and their fittedmaterial parameters based onthe three-parameter standard linear solid model were listedin Table 1 Five specimens were tested for each shaft samplegroup

From Table 1 it can be found that the golden eaglefeather shaft has the lowest instantaneous elastic modulus(1198641) ((7273 plusmn 661)MPa) and that of the pigeon feather shaft

((8841 plusmn 687)MPa) is the highest 1198641of the owl feather shaft

falls in between the pigeon and golden eagle shafts The con-clusion is in accordance with Worcesterrsquos investigation thatamong species larger birds have more flexible primaries thansmaller birds [27] However material parameters of Kelvinelement (elastic modulus (119864

2) of the spring and viscosity

coefficient (120578) of the dashpot) have greater dissimilarities 1198642

of long-eared owl flight feather shaft was (722 plusmn 149)MPalower than the one of pigeon feathers (2849 plusmn 718)Mpa andgolden eagle feathers (1315 plusmn 182)Mpa 120578 of long-eared owlfeathers feather shaft was (1706 plusmn 170) lowast 105Mpasdots higherthan that of pigeon feathers (799 plusmn 157) lowast 105Mpasdots andgolden eagle feathers (1100plusmn120)lowast 105MpasdotsThis indicatesthat the long-eared owl flight feather shaft is more like atypical viscoelastic material but the pigeon and golden eagleflight feather shafts aremore like elasticmaterials with a lowerviscosityThus more internal energy dissipation would occurby long-eared owl flight feather due to its molecular frictionduring the deformation process on the basis of viscoelastictheory

44 tan 120575 of Long-Eared Owl and Pigeon Flight Feather Shaftstan 120575 of the tested long-eared owl pigeon and golden eagleflight feather shafts is calculated for damping ability char-acterization from the fitted material parameters of uniaxialtensile test results according to (8) when alternating stress isapplied to the specimens at constant testing temperature

Figure 6 illustrates the loss tangent (tan 120575) of the long-eared owl pigeon and golden eagle flight feather shafts AndTable 2 lists their peak value of tan 120575 It is found that tan 120575maxof the long-eared owl flight feather shafts (1609 plusmn 0238) ishigher than the pigeon feather shafts (0896 plusmn 0082) andgolden eagle shafts (1087 plusmn 0074) In other words dampingability of the long-eared owl flight feather is better than thepigeon and golden eagle feather Therefore long-eared owlflight feather would dissipate more energy from the wingvibration in the flying process The owl feather can restrainthe resonance response more effectively due to its largedamping factor Thus high damping ability is concluded to


Table 1 Fitting parameters based on the viscoelastic model from tensile tests for the long-eared owl pigeon and golden eagle flight feathershafts

Sample Cross-sectionalarea 119860 (mm2)

Gauge length 119871(mm)

Elastic modulus1198641

(MPa)Elastic modulus1198642

(MPa)Coefficient of

viscosity 120578 (MPasdots)owl1 1432 3894 8210 625 1620290owl2 1474 3428 8989 554 1684931owl3 1279 2954 8318 896 1966866owl4 1384 3840 8760 860 1747912owl5 1230 3416 9930 673 1510543pigeon1 0280 1984 10087 2411 597359pigeon2 0324 2298 9590 2314 981513pigeon3 0330 2132 11103 3851 836727pigeon4 0282 2108 10201 3373 680685pigeon5 0322 2346 10404 2296 896814eagle1 1197 3948 7023 1333 1047637eagle2 1784 4214 6674 1073 1107921eagle3 1710 4348 7255 1197 1265107eagle4 1624 3786 8396 1455 938756eagle5 1242 3897 7016 1515 1141217

0 5 10 15 2000

05

10

15

20

tan 120575

(TRTC)12

120596

o1 p1 e1o2 p2 e2o3 p3 e3o4 p4 e4o5 p5 e5

Figure 6 Internal friction spectrum of feather shaft specimens

be an important factor to reduce or eliminate the mechanicalvibration and free vibration of the owl feathers as soon aspossible As a result noise caused by wing vibration andfeather friction from the relative motion would effectively besuppressed by the long-eared owl

5 Conclusion

Flight feather shafts of long-eared owl pigeon and goldeneagle were mechanically characterized based on Instron 3345single column material testing system at a constant loadingrate Nonlinear response of their stress and strain obtainedfrom the uniaxial tensile tests was described by the standardlinear solid model to reveal the viscoelastic characteristicof dynamic feathers on owls pigeons and golden eagleThe parameter fitting result of the three-parameter modelindicates that the long-eared owl flight feather shaft is morelike a typical viscoelastic material but the pigeon and goldeneagle flight feather shafts aremore like elastic materials with alower viscosityThus more internal energy dissipation wouldoccur by long-eared owl flight feather due to its molecularfriction during the deformation process on the basis ofviscoelastic theory

In order to compare the damping ability of the three birdsrsquofeather shaft more intuitively dynamic mechanical propertyat a constant temperature was characterized based on theparameter fitting result of the three-parameter model Lossfactor (tan 120575) of the long-eared owl flight feather shaft wascalculated to be 1609 plusmn 0238 far greater than those of thepigeon (0896 plusmn 0082) and golden eagle (1087 plusmn 0074) Itis concluded that the long-eared owl flight feather has moreoutstanding damping ability compared to pigeon and goldeneagle flight feather shaft Consequently the flight feathers ofthe long-eared owl can dissipate the vibration energy moreeffectively in the form of heat during the flying process basedon the principle of damping mechanism Because relativemovement caused by the feather vibration and friction wouldlead to the radiation noise large damping factor which isefficient in rapid vibration attenuation could be assumed toreduce the flight noise greatly for the flight feather shaft


Table 2 Peak value of the loss tangent (tan 120575) of the feather shaft specimens

Owl specimen tan 120575max Pigeon specimen tan 120575max Eagle specimen tan 120575max

1 1746 1 0919 1 10522 1954 2 0914 2 11573 1447 3 0932 3 11404 1522 4 0754 4 11095 1376 5 0963 5 0976

In this paper noise reduction mechanism for long-earedowl was investigated from the viscoelastic viewpoint of flightfeather materials We hope the conclusion would offer a newperspective for the research in this area

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank Dalian Forest Zoo forproviding the feather samples of long-eared owl pigeon andgolden eagle The authors also appreciate the constructivesuggestions of Dr Xuanping Wang from the Institute ofAdvanced Manufacturing Technology Dalian University ofTechnology at various stages of the work Financial supportfor this research was provided by the National Basic ResearchProgram of China (Grants 2011CB302101 and 2011CB302105)and theNationalNatural Science Foundation ofChina (Grantno 51305057)

References

[1] R Graham ldquoThe silent flight of owlsrdquo Journal of the RoyalAeronautical Society vol 38 pp 837ndash843 1934

[2] E Mascha ldquoUber die Schwungfedernrdquo Zeitschrift fur Wis-senschaftliche Zoologie vol 77 pp 606ndash651 1903

[3] T Bachmann ldquoThe silent flight of owlsrdquo Integrative and Com-parative Biology vol 52 article E9 2012

[4] T Bachmann H Wagner and C Tropea ldquoInner vane fringesof barn owl feathers reconsidered morphometric data andfunctional aspectsrdquo Journal of Anatomy vol 221 no 1 pp 1ndash82012

[5] K Chen Q Liu G Liao et al ldquoThe sound suppressioncharacteristics of wing feather of owl (Bubo bubo)rdquo Journal ofBionic Engineering vol 9 no 2 pp 192ndash199 2012

[6] T Bachmann and H Wagner ldquoThe three-dimensional shapeof serrations at barn owl wings towards a typical naturalserration as a role model for biomimetic applicationsrdquo Journalof Anatomy vol 219 no 2 pp 192ndash202 2011

[7] TGeyer E Sarradj andC Fritzsche ldquoMeasurement of the noisegeneration at the trailing edge of porous airfoilsrdquo Experimentsin Fluids vol 48 no 2 pp 291ndash308 2010

[8] T Geyer E Sarradj and C Fritzsche ldquoPorous airfoils noisereduction and boundary layer effectsrdquo International Journal ofAeroacoustics vol 9 pp 787ndash820 2010

[9] T Geyer E Sarradj and C Fritzsche ldquoSilent owl flightcomparative acoustic wind tunnel measurements on preparedwingsrdquo Acta Acustica United with Acustica vol 99 no 1 pp139ndash153 2013

[10] M Herr ldquoDesign criteria for low-noise trailing-edgesrdquo inProceedings of the 13th AIAACEAS Aeroacoustics Conference2007

[11] M S Howe ldquoNoise produced by a sawtooth trailing edgerdquoJournal of the Acoustical Society of America vol 90 no 1 pp482ndash487 1991

[12] GM Lilley ldquoA study of the silent flight of the owlrdquoAIAA papervol 2340 pp lndash6 1998

[13] G M Lilley ldquoThe prediction of air frame noise and comparisonwith experimentrdquo Journal of Sound and Vibration vol 239 no4 pp 849ndash859 2001

[14] T Bachmann J Emmerlich W Baumgartner J M Schneiderand H Wagner ldquoFlexural stiffness of feather shafts geometryrules over material propertiesrdquo Journal of Experimental Biologyvol 215 no 3 pp 405ndash415 2012

[15] A Ennos J Hickson and A Roberts ldquoFunctional morphologyof the vanes of the flight feathers of the pigeon Columba liviardquoThe Journal of Experimental Biology vol 198 pp 1219ndash12281995

[16] J J Videler Avian Flight Oxford University Press New YorkNY USA 2005

[17] M Azoulay A Veprik V Babitsky and N Halliwell ldquoDis-tributed absorber for noise and vibration controlrdquo Shock andVibration vol 18 no 1-2 pp 181ndash219 2011

[18] M R Mofakhami H H Toudeshky and S H Hashemi ldquoNoisereduction evaluation ofmulti-layered viscoelastic infinite cylin-der under acoustical wave excitationrdquo Shock and Vibration vol15 no 5 pp 551ndash572 2008

[19] SMHasheminejad andN Safari ldquoDynamic viscoelastic effectson sound wave diffraction by spherical and cylindrical shellssubmerged in and filled with viscous compressible fluidsrdquo Shockand Vibration vol 10 no 5-6 pp 339ndash363 2003

[20] L Ren S Sun and C Xu ldquoNoise reduction mechanism of non-smooth leading edge of owlwingrdquo Journal of JilinUniversity vol38 pp 126ndash131 2008

[21] H D Gruschka I U Borchers and J G Coble ldquoAerodynamicnoise produced by a gliding Owlrdquo Nature vol 233 no 5319 pp409ndash411 1971

[22] Z Lei R Bai L Deng and W Qiu ldquoNoncontact opticalmeasurement of CTOA and CTOD for interface crack in DCBtestrdquo Optics and Lasers in Engineering vol 50 no 7 pp 964ndash970 2012

[23] W R Corning and A A Biewener ldquoIn vivo strains in pigeonflight feather shafts implications for structural designrdquo Journalof Experimental Biology vol 201 no 22 pp 3057ndash3065 1998

[24] R H C Bonser ldquoThemechanical properties of feather keratinrdquoJournal of Zoology vol 239 no 3 pp 477ndash484 1996


[25] P Purslow and J Vincent ldquoMechanical properties of primaryfeathers from the pigeonrdquoThe Journal of Experimental Biologyvol 72 pp 251ndash260 1978

[26] J D Achenbach andC C Chao ldquoA three-parameter viscoelasticmodel particularly suited for dynamic problemsrdquo Journal of theMechanics and Physics of Solids vol 10 no 3 pp 245ndash252 1962

[27] S E Worcester ldquoThe scaling of the size and stiffness of primaryflight feathersrdquo Journal of Zoology vol 239 no 3 pp 609ndash6241996

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VLSI Design



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to bendmainly under aerodynamic loads [15 16] Because rel-ative movement caused by the feather vibration and frictionduring flight would lead to the radiation noise [17] amplitudestability of the feather shaft directly affects the vibration ofthe whole feather structure and noise radiation Dampingfactor as an important physical parameter can be used tocharacterize the vibration attenuation capability of the owlfeather shaft and compared with other birdrsquos shafts Conse-quently on account of the assumption that the investigationof biomimetic materials inspired by the quiet flying owlsmight lighten a new way to obtain more excellent mufflingperformance in addition to the morphological bionic designwe present our study on the viscoelastic characterization ofowl flight feather materials and the analysis of their vibrationdamping ability so as to provide further insight into theowlrsquos silent flight mechanism and bionic design in our furtherresearch in view of material acoustics [18 19]

The research presented in this paper focuses on theviscoelastic characterization of flight feather shaft of long-eared owl (Asio otus Strigiformes) pigeon (Columba liviaColumbiformes) and golden eagle (Aquila chrysaetos Fal-coniformes) to reveal the damping ability of their dynamicfeathers on wings Here long-eared owl is the main researchobject with noise reduction function [20] Its flight generallyconsists of an initial flapping phase followed by a glidingphase and a short flapping during touchdown [21] Pigeon is atypical flapping flight bird which differs from the long-earedowl and has a smaller size than the owl Golden eagle involvesthe same flight style as the long-eared owl and its size is largerthan the long-eared owl Both of the pigeon and golden eagledo not have the silent flight ability The aim is to comparethe viscoelastic performance of owl feather with other noisyflying birds without the impact of flying style and bird size onnoise generation

Feather shaft can be regarded as a slender beam sothe shear effect on its bending deformation can be ignoredHence normal stress accounts for the bending deformationof feather shaft Therefore uniaxial tensile tests of the threetypes of the prepared flight feather shaft specimens wereconducted on Instron 3345 single column materials testingsystem to investigate the relationship of strain and normalstress of the shafts at first Then viscoelasticity of feathershaft material was studied employing the standard linearviscoelastic solid model And then based on the viscoelasticmaterial parameters obtained from the tensile testing resultsdynamic mechanical property at a constant temperaturewas analyzed And tan 120575 of the long-eared owl pigeonand golden eagle flight feather shaft was calculated for adamping ability comparison between the three types of flightfeathers Relationship between damping ability and vibrationattenuation for owl feather shaft was briefly discussed at last

2 Materials and Methods

21 Feather Material and Anatomy of Feather Shafts Flightfeathers of long-eared owl pigeon and golden eagle wereobtained from Dalian Forest Zoo (Liaoning China) Itis noted that feathers are collected with no harm to the

birdsrsquo life complying with the Animal Protection Act Barbson both sides of the feather shaft were removed by thescalpel blade Trimmed feather shafts were rinsed twice withdeionized water for 30 minutes and naturally dried on cleanfilter paper at room temperature All the specimens werecleaned and prepared in the cleanroom of key laboratoryfor precision and nontraditional machining of Ministry ofEducation Dalian University of Technology

The tested specimenswere selected from the feather shaftsaccording to the following rules

(a) the same relative position that the testing samplesare selected in the same proportion position on flightfeather shafts of the long-eared owl pigeon andgolden eagle

(b) the same aspect ratio that the ratio of the shaft lengthto maximum cross-sectional diameter is unified forall the testing parts one end of the testing sectionis marked according to the selection method (a) atfirst and its maximum diameter size is measured bya spiral micrometer subsequently The other end islocated away from the marked position with a gaugelength of fifteen times the maximum diameter

After marking the testing portion in accordance with theabove methods specimen including the testing section andsufficient extension parts on its two sides for clamping iscut out as is shown in Figure 1 Before the test is startedreinforcement of the clamping parts is necessary in orderto avoid damage of the specimen caused by gripping Twoextension parts were inserted in flat boxes which are fullof liquid epoxy structural adhesive (WD3003) with highbonding strength and excellent performance to resist thecompression Clamping structures were obtained when theliquid adhesive was solidified into a block after 24 hoursMeanwhile thin aluminium sheets with strong ductility werepasted on gripping interface of the adhesive to preventcontamination of the experimental equipment

22 Experimental Instrument and Procedures Instron 3345single columnmaterials testing system (Instron Corporationthe United States) is used for uniaxial tensile test as isshown in Figure 2The whole system is equipped with a 5 kNload cell a displacement sensor a speed-controlled guidescrew driving device (range 0005mmmin to 1000mmminaccuracy plusmn5 of the point value) andwedge clamps with thegripping force of 50 kN that one clamp is connected to theload cell while the other is secured to the machine Both theload accuracy and the strain accuracy are plusmn5 of indicatedvalue for the materials testing system

During the experiments the material testing systemrecorded the stretching force every 01 seconds and the one-to-one sampling time until the testing specimen was frac-tured Digital image correlation (DIC) was applied to analyzethe deformation mechanisms [22] Firstly two high contrastmarkers were spotted on the lateral wall of the specimenSecondly high-speed camera was used to obtain chargecoupled device (CCD) images before and after the tensiledeformation in the experimental process The corresponding


(a) (b)

Testedspecimen

Clampingpart

Clampingpart

(c)


Load transducer

High-speedcamera

DIC analysis


F d



3 Results


C

M

C-s

(a)

C

M

C-s

(b)

CM

C-s

(c)









4 Discussions







120590 +120578

1198641+ 1198642

=11986411198642

1198641+ 1198642

120576 +1198641120578

1198641+ 1198642

120576 (1)

Delay time (120591119888= 120578119864


119877= 120578(119864

1+1198642))


119888and 120591119877



120576 (119905) = 119879119905 (2)


120590 (119905) = int

120591=infin

120591=infin

119864 (119905 minus 120591) 119889120576 (120591) = 119864 (119905) lowast 119889120576 (119905)

=1198641119879

1198641+ 1198642

[1198642119905 +

1198641120578

1198641+ 1198642

(1 minus 119890minus((1198641+1198642)120578)119905

)]

(3)


120590 (119905) = 1205900119890119894120596119905

(4)

120576 (119905) = 119866 (119894120596) 120590 (119905) = 119866 (119894120596) 1205900119890119894120596119905

(5)



Wedgeclamps


Fracturedposition

(a1) (a2) (a3)

(a)

Fracturedposition

(b1) (b2) (b3)

(b)

Fracturedposition

(c1) (c2) (c3)

(c)



119866 (119894120596) = 1198661(120596) + 119894119866

2(120596) (6)

where1198661and119866




119866 (119894120596) =1198641+ 1198642+ 120578119894120596

(11986411198642)2

+ (1198641120578120596)2

times [(1198641+ 1198642) 11986411198642+ 1198641(120578120596)2

minus 1198642

1

120578119894120596]

(7)


0 2 4 6 80

50

100

150

200

250

Stre

ss (M

Pa)

Strain ()

OwlEaglePigeon



tan 120575 = minus1198662 (120596)1198661(120596)

=((120578119864

2) minus (120578 (119864

1+ 1198642))) 120596

1 + (1205781198642) sdot (120578 (119864

1+ 1198642)) 1205962

=(120591119888minus 120591119877)

radic120591119888120591119877

sdot120596radic120591119888120591119877

1 + 1205911198881205911198771205962

(8)








1 1198642 120578
















(MPa)Coefficient of


0 5 10 15 2000

05

10

15

20

tan 120575

(TRTC)12

120596




5 Conclusion






1 1746 1 0919 1 10522 1954 2 0914 2 11573 1447 3 0932 3 11404 1522 4 0754 4 11095 1376 5 0963 5 0976




Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)

Testedspecimen

Clampingpart

Clampingpart

(c)


Load transducer

High-speedcamera

DIC analysis


F d



3 Results


C

M

C-s

(a)

C

M

C-s

(b)

CM

C-s

(c)









4 Discussions







120590 +120578

1198641+ 1198642

=11986411198642

1198641+ 1198642

120576 +1198641120578

1198641+ 1198642

120576 (1)

Delay time (120591119888= 120578119864


119877= 120578(119864

1+1198642))


119888and 120591119877



120576 (119905) = 119879119905 (2)


120590 (119905) = int

120591=infin

120591=infin

119864 (119905 minus 120591) 119889120576 (120591) = 119864 (119905) lowast 119889120576 (119905)

=1198641119879

1198641+ 1198642

[1198642119905 +

1198641120578

1198641+ 1198642

(1 minus 119890minus((1198641+1198642)120578)119905

)]

(3)


120590 (119905) = 1205900119890119894120596119905

(4)

120576 (119905) = 119866 (119894120596) 120590 (119905) = 119866 (119894120596) 1205900119890119894120596119905

(5)



Wedgeclamps


Fracturedposition

(a1) (a2) (a3)

(a)

Fracturedposition

(b1) (b2) (b3)

(b)

Fracturedposition

(c1) (c2) (c3)

(c)



119866 (119894120596) = 1198661(120596) + 119894119866

2(120596) (6)

where1198661and119866




119866 (119894120596) =1198641+ 1198642+ 120578119894120596

(11986411198642)2

+ (1198641120578120596)2

times [(1198641+ 1198642) 11986411198642+ 1198641(120578120596)2

minus 1198642

1

120578119894120596]

(7)


0 2 4 6 80

50

100

150

200

250

Stre

ss (M

Pa)

Strain ()

OwlEaglePigeon



tan 120575 = minus1198662 (120596)1198661(120596)

=((120578119864

2) minus (120578 (119864

1+ 1198642))) 120596

1 + (1205781198642) sdot (120578 (119864

1+ 1198642)) 1205962

=(120591119888minus 120591119877)

radic120591119888120591119877

sdot120596radic120591119888120591119877

1 + 1205911198881205911198771205962

(8)








1 1198642 120578
















(MPa)Coefficient of


0 5 10 15 2000

05

10

15

20

tan 120575

(TRTC)12

120596




5 Conclusion






1 1746 1 0919 1 10522 1954 2 0914 2 11573 1447 3 0932 3 11404 1522 4 0754 4 11095 1376 5 0963 5 0976




Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















4 Discussions







120590 +120578

1198641+ 1198642

=11986411198642

1198641+ 1198642

120576 +1198641120578

1198641+ 1198642

120576 (1)

Delay time (120591119888= 120578119864


119877= 120578(119864

1+1198642))


119888and 120591119877



120576 (119905) = 119879119905 (2)


120590 (119905) = int

120591=infin

120591=infin

119864 (119905 minus 120591) 119889120576 (120591) = 119864 (119905) lowast 119889120576 (119905)

=1198641119879

1198641+ 1198642

[1198642119905 +

1198641120578

1198641+ 1198642

(1 minus 119890minus((1198641+1198642)120578)119905

)]

(3)


120590 (119905) = 1205900119890119894120596119905

(4)

120576 (119905) = 119866 (119894120596) 120590 (119905) = 119866 (119894120596) 1205900119890119894120596119905

(5)



Wedgeclamps


Fracturedposition

(a1) (a2) (a3)

(a)

Fracturedposition

(b1) (b2) (b3)

(b)

Fracturedposition

(c1) (c2) (c3)

(c)



119866 (119894120596) = 1198661(120596) + 119894119866

2(120596) (6)

where1198661and119866




119866 (119894120596) =1198641+ 1198642+ 120578119894120596

(11986411198642)2

+ (1198641120578120596)2

times [(1198641+ 1198642) 11986411198642+ 1198641(120578120596)2

minus 1198642

1

120578119894120596]

(7)


0 2 4 6 80

50

100

150

200

250

Stre

ss (M

Pa)

Strain ()

OwlEaglePigeon



tan 120575 = minus1198662 (120596)1198661(120596)

=((120578119864

2) minus (120578 (119864

1+ 1198642))) 120596

1 + (1205781198642) sdot (120578 (119864

1+ 1198642)) 1205962

=(120591119888minus 120591119877)

radic120591119888120591119877

sdot120596radic120591119888120591119877

1 + 1205911198881205911198771205962

(8)








1 1198642 120578
















(MPa)Coefficient of


0 5 10 15 2000

05

10

15

20

tan 120575

(TRTC)12

120596




5 Conclusion






1 1746 1 0919 1 10522 1954 2 0914 2 11573 1447 3 0932 3 11404 1522 4 0754 4 11095 1376 5 0963 5 0976




Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Wedgeclamps


Fracturedposition

(a1) (a2) (a3)

(a)

Fracturedposition

(b1) (b2) (b3)

(b)

Fracturedposition

(c1) (c2) (c3)

(c)



119866 (119894120596) = 1198661(120596) + 119894119866

2(120596) (6)

where1198661and119866




119866 (119894120596) =1198641+ 1198642+ 120578119894120596

(11986411198642)2

+ (1198641120578120596)2

times [(1198641+ 1198642) 11986411198642+ 1198641(120578120596)2

minus 1198642

1

120578119894120596]

(7)


0 2 4 6 80

50

100

150

200

250

Stre

ss (M

Pa)

Strain ()

OwlEaglePigeon



tan 120575 = minus1198662 (120596)1198661(120596)

=((120578119864

2) minus (120578 (119864

1+ 1198642))) 120596

1 + (1205781198642) sdot (120578 (119864

1+ 1198642)) 1205962

=(120591119888minus 120591119877)

radic120591119888120591119877

sdot120596radic120591119888120591119877

1 + 1205911198881205911198771205962

(8)








1 1198642 120578
















(MPa)Coefficient of


0 5 10 15 2000

05

10

15

20

tan 120575

(TRTC)12

120596




5 Conclusion






1 1746 1 0919 1 10522 1954 2 0914 2 11573 1447 3 0932 3 11404 1522 4 0754 4 11095 1376 5 0963 5 0976




Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 2 4 6 80

50

100

150

200

250

Stre

ss (M

Pa)

Strain ()

OwlEaglePigeon



tan 120575 = minus1198662 (120596)1198661(120596)

=((120578119864

2) minus (120578 (119864

1+ 1198642))) 120596

1 + (1205781198642) sdot (120578 (119864

1+ 1198642)) 1205962

=(120591119888minus 120591119877)

radic120591119888120591119877

sdot120596radic120591119888120591119877

1 + 1205911198881205911198771205962

(8)








1 1198642 120578
















(MPa)Coefficient of


0 5 10 15 2000

05

10

15

20

tan 120575

(TRTC)12

120596




5 Conclusion






1 1746 1 0919 1 10522 1954 2 0914 2 11573 1447 3 0932 3 11404 1522 4 0754 4 11095 1376 5 0963 5 0976




Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















(MPa)Coefficient of


0 5 10 15 2000

05

10

15

20

tan 120575

(TRTC)12

120596




5 Conclusion






1 1746 1 0919 1 10522 1954 2 0914 2 11573 1447 3 0932 3 11404 1522 4 0754 4 11095 1376 5 0963 5 0976




Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












1 1746 1 0919 1 10522 1954 2 0914 2 11573 1447 3 0932 3 11404 1522 4 0754 4 11095 1376 5 0963 5 0976




Acknowledgments


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









research article viscoelastic characterization of long...

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