Wilby FinalReport

8/18/2019 Wilby FinalReport

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i

Modal Characterization of a Thin Flat Plate in the Free-Free Condition

with Non-Contact Particle Velocity Measurements

by

Kevin Wilby

A Project Submitted to the Graduate

Faculty of Rensselaer Polytechnic Institute

in Partial Fulfillment of the

Requirements for the degree of

AS!"R #F "$GI$""RI$G in "%&A$I%A' "$GI$""RI$G

A((roved)

*****************************************"rnesto Gutierre+,iravete- Project Adviser

Rensselaer Polytechnic Institute

&artford- %onnecticut

.ecember /01/


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CONTENTS 12 Introduction 22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222 , 1 ,

/2 3ac4ground 22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222 , / ,

52 !heory6ethodology 22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222 , 7 ,

521 !heoretical Prediction of $atural Frequencies 2222222222222222222222222222222222222222222222 , 8 ,

52121 Analytical Prediction of $atural Frequencies 222222222222222222222222222222222222 , 8 ,

5212/ Finite "lement Prediction of $atural Frequencies 22222222222222222222222222222 , 9 ,

:2 Results and .iscussion 222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222 , 10 ,

:21 !est Setu( 22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222 , 10 ,

:2/ !est Results 22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222 , 15 ,

72 %onclusions222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222 , 18 ,

82 References 22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222 , 1; ,

A((endi< A = Analytical Prediction S(readsheet 2222222222222222222222222222222222222222222222222222222 , 19 ,

A((endi< 3 = icroflo>n Scan and Paint In(uts 2222222222222222222222222222222222222222222222222222222 , 1? ,


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LST OF T!"LES

!able 1 In(ut Parameters to !heoretical Predictions 22222222222222222222222222222222222222222222222222222 , 8 ,

!able / Analytically .erived $atural Frequencies 2222222222222222222222222222222222222222222222222222222 , ; ,

!able 5 %alculated $atural Frequencies from F"A 222222222222222222222222222222222222222222222222222222 , 9 ,

!able : easured $atural Frequencies from White $oise "


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LST OF F#$%ES

Figure 12 Picture of the !>o Platinum Wires in the icroflo>n from @5 2222222222222222222 , 5 ,

Figure /2 .irectionality of the icroflo>n PB Probe from @; 222222222222222222222222222222222222 , 5 ,

Figure 52 %om(arison of the Point res(onse from an Accelerometer- 'aser Cibrometer

and a icroflo>n Sensor @5 22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222 , 7 ,

Figure :2 Predicted ode Sha(es from @10 222222222222222222222222222222222222222222222222222222222222222222 , ; ,

Figure 72 F"A ode Sha(es D1st to 8

th odes From B((er 'eft to 'o>er RightE 2222222 , ? ,

Figure 82 Picture Sho>ing !est Setu( 2222222222222222222222222222222222222222222222222222222222222222222222222 , 10 ,

Figure ;2 Sha4er !est 'ine .iagram 2222222222222222222222222222222222222222222222222222222222222222222222222222 , 11 ,

Figure 92 !y(ical S(herical Piston %alibration Setu( D@15E 222222222222222222222222222222222222222 , 1/ ,

Figure ?2 easured Celocity Res(onse from a White $oise "er RightE 2222222 , 17 ,


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LST OF S&M"OLS

i hori+ontal half >aves

j vertical half >aves

natural frequency Di hori+ontal and j vertical half >avesE @&+

dimensionless frequency (arameter Di hori+ontal and j vertical half >avesE length of the (late DmetersE modulus of elasticity D(ascalsE ℎ thic4ness of the (late DmetersE mass (er unit area D4g6meter/E (oissons ratio

dis(lacement DmetersE scale factor DmetersE sqrtD,1E radian frequency DradiansE time DsecondsE velocity Dmeters6secondE acceleration Dmeters6second/EH (i


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LST OF !C%ON&MS

PB Pressure6Celocity

F"A Finite "lement Analysis

G Acceleration due to Gravity Dmeters6second/E


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!"ST%!CT

Structural acoustics is the study of the vibrations- and their (ro(agation through sol,

id objects2 !here are many industries that use vibratory analysis to (rovide insight to the

4ey strengths and >ea4nesses of structures2 !his (roject describes a novel ty(e ofmeasurement Dthe icroflo>n sensorE used to (erform a structural characteri+ation of a

flat (late and a((lies both analytical and finite element tools to validate the test results2

!he icroflo>n is a sensor that directly measures the (article velocity of the air moving

(ast it2 !he icroflo>n measurement system has been sho>n in this (roject to accurate,

ly ca(ture the dynamic res(onse of a structure2


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, 1 ,

'( ntroduction

Structural acoustics is the study of the vibrations- and their (ro(agation through solid

objects2 Bnderstanding the structural dynamics of a structure can (rovide valuable

information on its strengths and >ea4nesses for any given a((lication2 Cibratory analy,sis is constantly being (erformed in industry from assessing structural integrity in the

aeros(ace industry @1 to minimi+ing the acoustic res(onse of a structure in the automo,

tive industry @/2 @1 discusses a com(utational technique for assessing the integrity of

structures2 !his is a very (o>erful diagnostic tool that can (rovide indications of ma,

chine and structure >ear by monitoring the vibrations2 Signals related to rotational

harmonics for eaves2 Bnderstanding the structural re,

s(onse of the many moving (arts in a car is very im(ortant as the (erceived sound of a

car can be a major (art of its value2

Generally s(ea4ing all structural acoustic analyses can be bro4en do>n into three

ty(es) sim(listic analytical- detailed finite element and full or scale model testing2

!y(ically analytical models are used >herever (ossible because of their ease of use-

ho>ever- most real,life (roblems are much more com(le< then these models can re(li,

cate2 Finite element models give the ability to analy+e a structure >ell before its

actually built2 &o>ever- these models ta4e longer to build and analy+e than the analyti,

cal models and need a lot of validation for the results to be used for com(le< structures2

Scale model testing can be used as insight into the dynamics of the structure as >ell as

in(ut into the finite element models- ho>ever can (rove to be costly and may not fully

re(licate the full scale structure2 'astly- full scale testing is ty(ically the best to analy+e a

structure- ho>ever- does not have the ability to be analy+ed until the system is built- and

is usually the most costly solution2 !his (roject focuses on the testing as(ect of structural

acoustics and uses both analytical and finite element tools to validate the test results2


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)( "ac*+round

odal testing is a >ay to quantify the dynamic res(onse of a structure2 !y(ically- this is

done by eith a calibrated force hammer or a sha4erE and

then measuring its res(onse Dusually >ith accelerometersE2 !he (rocedure for these ty(esof tests can vary significantly based on the a((lication and in some cases can involve

long setu( times and6or long test duration2 Accelerometers can be mounted in many

>ays De2g2 threading them into a hole- glue- >ahich de(ending on the test can be

time consuming and (otentially affect the structural res(onse of the system D>ith the

added mass of the accelerometer itselfE2 $on,contact vibration measurements have the

advantage that there is no influence on the structural res(onse2 !his ty(e of measurement

can be (erformed >ith a sensor called icroflo>n @52 !he icroflo>n system (erforms

non,contact measurements that are relatively easy to generate for both quic4 loo4 and

more detailed analyses2

!he icroflo>n is a sensor that directly measures the (article velocity of the air

moving (ast it by the use of t>o heated (latinum >ires DFigure 1E2 As outlined in @5- the

icroflo>n sim(ly measures the difference in voltage caused by the heat of each

(latinum >ire that is lost due to convection2 3y using t>o >ires instead of one- and

loo4ing at the difference in voltage bet>een these t>o >ires- a highly directive meas,

urement of velocity can be (erformed2 !he PB (robe is a sensor (ac4age that combines

this icroflo>n technology >ith a small 169 (ressure sensor2 !his allo>s for a meas,

urement of intensity and acoustic im(edance Dbeyond just the velocity and (ressure

res(onseE2 Additionally- the highly directional nature of the velocity (robe DFigure /E

(rovides the ability for sound source locali+ation2 !his (roject focuses on the velocity

measurements- ho>ever- intensity and im(edance measurements are discussed in more

detail in @: and @7- res(ectively and sound source locali+ation is discussed in @8 as

>ell as @52


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(roject because it (rovides a visuali+ation of the velocity (rofile of the (late2 !hese

measurements >ill be com(ared to both analytical and finite element methods to validate

the measurement technique2 !he free,free boundary condition >as chosen because the

analytical and finite element methods should be very accurate for such a >ell researched

case2 S(ecific a((lications to this (roject are any industries that (erform modal analyses

Dsuch as the aeros(ace and automotive industriesE2


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,( TheoryMethodolo+y

!he icroflo>n is a sensor that directly measures the (article velocity of the air moving

(ast it and >ill be used in this (roject and com(ared to both analytical and finite element

(rediction methods2 !his com(arison involves the assum(tion that the (article velocity->hen measured in the very near field D>here the air can be a((roith the surface velocity of a structure2 !his assum(tion is en (robe2 Figure 5

sho>s the test setu( from @5 as >ell as the com(arison of the three sensors2

Fi+ure ,( Com.arison of the Point res.onse from an !ccelerometer/ Laser Vi0rometer and a

Microflown Sensor 1,2

!he structure in this re(ort >ill be a thin (late in the free,free condition2 As defined

in @?- a thin (late is one >ith a thic4ness that is less than 1610 the minimum lateral (late

dimension2 !he (late used in this (roject is made of steel and has the dimensions of 9in

by 1/in by J in2 !he free,free condition of a thin flat (late >as used to (rovide a condi,

tion that has been >ell investigated and the accuracy of the (rediction methods is 4no>n2

!he test setu( is a (late hung >ith ro(e- eo sha4ers- and measured >ith the

icroflo>n Scan and Paint system2 !his method is validated using @? and @10- using

theory of vibrations of (lates and by creating the finite element model and solving for

the natural frequencies2


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,(' Theoretical Prediction of Natural Fre3uencies

In this section- the natural frequencies of the thin flat (late are calculated by a te


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Where f ij is the natural frequency Din hert+E of the mode sequence of i hori+ontal half

>aves and j vertical half >aves- O ij is a dimensionless frequency (arameter- a is the

length of the (late- " is the modulus of elasticity- h is the thic4ness of the (late- is the

mass (er unit area- and Q is Poissons ratio2 !he values for the square of O ij >ere ta4en

from @? for a length of >idth ratio of 1272 !he !able 1 geometry and material (ro(erties

>ere used in this analysis2 !able / and Figure : sho> each calculated frequency and

mode sha(e- res(ectively2 $ote the different naming conventions used in @? and @10 Di

and j vs2 m and nE and that modes 1,8 using the @10 naming convention >ould be >ould

be @1-1- @/-0- @/-1- @0-5- @5-0- and @1-/2

Ta0le ) !nalytically 4eri5ed Natural Fre3uencies

Fi+ure 6( Predicted Mode Sha.es from 1'72

Mode

i()*

,e-uenc#

/

1 2(2* 680.1

2 3(1* 72.8

3 3(2* 1$76.2

4 1(3* 16.2

$ 4(1* 166.4

6 2(3* 2280.3

0 1 2 3 4

0

1

2

3

m

n


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,('() Finite Element Prediction of Natural Fre3uencies

A finite element analysis DF"AE >as (erformed to (redict the undam(ed natural fre,

quencies and mode sha(es of the thin flat (late in the free,free conditions2 !he model

>as built in &P"R"S& v1120 and the !able 1 geometry and material (ro(erties >ere

used2 #nce the model >as built- the natural frequencies >ere calculated using the mass

and stiffness of each element by im(orting the model into CI3"S,SA3"R2 !able 5

sho>s the calculated natural frequencies for each mode and Figure 7 sho>s a sna(shot

of the mode sha(e animation2 $otice ho> each of the mode sha(es corres(ond >ith the

analytical mode sha(es identified in Figure :2

Ta0le , Calculated Natural Fre3uencies from FE!

Mode

i()*

,e-uenc#

/

1 2(2* 678.1

2 3(1* 722.3

3 3(2* 1$63.0

4 1(3* 1680.8

$ 4(1* 143.7

6 2(3* 22$8.7


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Fi+ure 8( FE! Mode Sha.es 9'st to :

th Modes From $..er Left to Lower %i+ht;


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6( %esults and 4iscussion

Section 5 (rovided a (rediction of the natural frequencies of the (late by t>o different

methods Danalytical and finite elementE2 !he focus of this (roject is to use the

icroflo>n (article velocity sensor to measure the natural frequencies of this (late2 !henon,contact measurements that are (ossible >ith the icroflo>n system (rovide an easy

to use tool that can quic4ly (rovide a detailed analysis of the dynamics of a structure2

6(' Test Setu.

A thin flat (late made of steel and >ith the geometry of 9in by 1/in by16/in >as used in

this (roject2 !he (late had t>o holes drilled in it to (rovide a means for mounting it2 !he

(late >as hung by a ro(e to a((roo sha4ers >ere at,

tached to the structure and e test

results2 Figure ; sho>s a line diagram of the test setu(- >here the entire test >as run

using the icroflo>n Scan and Paint hard>are and soft>are2

Fi+ure :( Picture Showin+ Test Setu.

Sha4ers


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Fi+ure n Scan and Paint hard>are includes a PB (robe- a signal conditioner

DSF%,:E and a digiti+er DScout ://E2 !he PB (robe simultaneously measures (ressure

and velocity2 !he signal conditioner receives both the (ressure and velocity measure,

ments- and (rovides a calibrated correction to the signal2 !he digiti+er has t>o functions)

it receives the (ressure and velocity signals and sends them to the Scan and Paint soft,

>are and (rovides the sha4ers >ith the en Scan and Paint soft>are ta4es in the (ressure and velocity meas,

urements and the video feed from the camera2 !he camera is set u( (er(endicular to the

surface of interest2 !he (robe is then scanned by the user over the entire surface of

interest >hile maintaining a consistent distance Droughly 1,/ inches from the surfaceE

and aiming the (robe (er(endicular to the surface2 3oth the audio D(ressure and velocityE

and video signals are recorded >hile the (robe is scanned2 Although there is no actual

(ainting occurring- the icroflo>n Scan and Paint soft>are >ill follo> the (robe from

the video signal Dty(ically by follo>ing a brightly colored object attached to the (robeE

P

P P,essu,e P 5elocit#

hke, 2hke, 1

me,

ignl

onditione,

Mic,olown

"igitie,

9

:EM; :EM;

9

9

Mic,odot Mic,odot


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and synchroni+e it >ith the audio signal2 #nce the signals are synchroni+ed- the meas,

urements Dsuch as those in Section :2/E can be (rocessed and analy+ed2

!he icroflo>n PB (robe requires a s(ecial s(herical (iston calibrator to (erform

an official calibration of the sensor Dthis is (erformed once a yearE2 !he (rocedure for

this test is generally to eith a 4no>n signal- and use a reference

micro(hone to relate this signal to both (ressure and (article velocity @152 Figure 9

sho>s the s(herical (iston calibrator- the icroflo>n (robe and the reference micro,

(hone in a ty(ical setu(2

Fi+ure =( Ty.ical S.herical Piston Cali0ration Setu. 91',2;

It is also good (ractice to do a quic4 bench to( calibration to confirm that the (robe

is measuring correctly and that the a((ro(riate sensitivity is being a((lied2 !his is done

by ta4ing a standard accelerometer calibrator that (rovides a G of acceleration D1/0d3

re) GE on a flat vibrating surface at 100&+2 3y using "quation D/E- one can easily relate

acceleration res(onse and velocity measurements2

= #$% Since) & ''%( = = #$% Since) & ''%( = = ) #$% = D/E

S(herical Piston Reference icro(hone

PB Probe


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, 15 ,

Where < is dis(lacement- A is a scale factor- j is the sqrtD,1E- T is the radian fre,

quency- t is time- U is velocity- and V is acceleration2 !herefore- by (lacing the PB (robe

directly above the calibrator- and converting the velocity reading by sim(ly multi(lying

by T or /H100&+- the (robe can be quic4ly calibrated to the signal2

6() Test %esults

!he t>o sha4ers that >ere mounted to the (late >ere first eith >hite noise and

scanned using the Scan and Paint system2 Figure ? sho>s the measured velocity re,

s(onse of the (late Dan averaged linear s(ectrum of each locationE2 "ach of the (ea4s

sho>n re(resents a natural frequency of the (late2 !able : sho>s the measured natural

frequency for each of the first 8 modes Di2e2 the first 8 (ea4 frequenciesE2

Fi+ure >( Measured Velocity %es.onse from a ?hite Noise E@citation

102

103

104

10

20

30

40

50

60

70

P V L ( r e 5 0 e

- 9 m / s ) [ d B ]

[Hz]


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Ta0le 6 Measured Natural Fre3uencies from ?hite Noise E@citation

#nce the natural frequencies >ere identified >ith the >hite noise- the sha4ers >ere

then eith a sine >ave at each of the frequencies of the (ea4s sho>n in Figure ?2

Figure 10 sho>s the measured velocity (rofile for each of the first 8 modes2 !he colors

on the gra(h corres(ond to the areas >here the velocity is highest DredE and lo>est

DblueE2 $ote that these measurements are ta4en as a steady state Di2e2 the velocity (rofile

is the absolute value of the velocityE as o((osed to Figure 7 >hich is the instantaneous

modal distribution of the (late2 With this in mind- Figure 10 can be directly com(ared to

the modal (atterns in Figure 7 De2g2 1st mode in the u((er left of each figure should sho>

the same (atternE2 !he e


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, 17 ,

Fi+ure '7( P$ Mode Sha.es 9'st to :

th Modes from $..er Left to Lower %i+ht;

6hke, :oction

9odl :ines

hke, :oction

9odl :ines

hke, :oction

9odl :ines

hke, :oction

9odl :ines

hke, :oction

9odl :ines

hke, :oction

9odl :ines


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8( Conclusions

!he icroflo>n measurement system has sho>n the ca(ability to accurately measure

the dynamic res(onse of a structure2 !able 7 sho>s the com(arison of each of the three

methods outlined in this (roject2 !he test >as sho>n to be >ithin 7X of either (redictionmethod for each of the first 8 modes2 !he icroflo>n measurements >ere also sho>n to

generally follo> the mode sha(es that >ere (redicted from both the analytical and finite

element methods2 Im(rovements u(on the test setu( could (otentially have sho>n a

cleaner measurement for the higher modes Das >ell as the modes above the 8th

E2

Ta0le 8 Com.arison of Calculated and Measured Natural Fre3uencies

!hree different ty(es of modal analyses >ere used in this (roject) analytical- finite

element and test methods2 .e(ending on the a((lication- any>here from one to all three

of these methods may need to be used to fully understand the structure2 "ach of the

analyses has their o>n strengths and >ea4nesses2 !he icroflo>n (article velocity

sensor has advanced measurement technology2 !he results of this (roject have im(lica,

tions in any of the many industries that currently (erform vibratory analysis2 $on contact

velocity measurements can be used to define the dynamics of a structure- (rovide insight

to (ro(er accelerometer (lacement and6or (rovide im(ortant in(ut into analytical or

finite element models2

Analytical FEA TestMode

i()*

,e-uenc#

/

,e-uenc#

/

,e-uenc#

/

1 2(2* 680.1 678.1 684.8

2 3(1* 72.8 722.3 726.3

3 3(2* 1$76.2 1$63.0 1$0$.0

4 1(3* 16.2 1680.8 1682.0

$ 4(1* 166.4 143.7 113.0

6 2(3* 2280.3 22$8.7 2207.0


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, 1; ,

:( %eferences

@1 She(herd- L %onlon- S2 YStructural Intensity odeling and Simulations for

.amage .etection2 AS" Zournal of Cibration and Acoustics2 #ctober /01/2

Colume 15: Issue 7@/ Allam- SL YA $e> !y(e of uffler 3ased on icro(erforated !ubes2 AS"

Zournal of Cibration and Acoustics2 Zune /0112 Colume 155 Issue 5

@5 de 3ree- &,"2 Y!he icroflo>n- ",3oo42

[htt()6>>>2microflo>n2com6library6boo4s\2 icroflo>n !echnologies2 Arn,

hem- !he $etherlands2 /01/2

@: !ijs- "L $ejade- AL de 3ree- &,"2 YCerification of P,B Intensity %alculation2

icroflo>n !echnologies

@7 !ijs- "L de 3ree- &,"2 YRecent .evelo(ments Free Field PB Im(edance !ech,

nique2 icroflo>n !echnologies2

@8 Wind- ZL de 3ree- &,"2 YSound Source 'ocali+ation and Sound a((ing Bsing a

PB Sensor Array2 icroflo>n !echnologies2

@; Yicroflo>n !echnologies = PB Regular Probe anual2 C120 /00?,05

@9 de 3ree- &,"2 Y!he Cery $ear Field !heory- Simulations and easurements of

Sound Pressure and Particle Celocity in the Cery $ear Field2 Bniversity of

!>ente2 International %onference on Sound and Cibration2 Zune /00:

@? 3levins- R2 YFormulas for $atural Frequency and ode Sha(e2 Krieger Publish,

ing %om(any2 %o(yright 1?;?

@10 Waller- 2 YCibration of Free Rectangular Plates2 Proc2 Phys2 Soc2 D'ondonE-

ser2 3- vol2 8/- no2 575- 1?:?- ((2 /;;,/97

@11 3a+ley- $2 W2L Fo


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, 19 ,

!..endi@ ! A !nalytical Prediction S.readsheet

Ta0le !' Values of Lam0da S3uared $sed in !nalytical !nalysis 91>2;

lm


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!..endi@ " A Microflown Scan and Paint n.uts

Fi+ure "' Parameters $sed in Microflown !nalysis

Parameter Value

m=le !te m=les%econd $0000

9um Points 812

;?e,l= @ $0

9um#=e /nning

9um

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