research article interdigital piezopolymer transducers for...

Research ArticleInterdigital Piezopolymer Transducers for Time ofFlight Measurements with Ultrasonic Lamb Waves onCarbon-Epoxy Composites under Pure Bending Stress

Andrea Bulletti and Lorenzo Capineri

Dipartimento Ingegneria dellrsquoInformazione Universita degli Studi di Firenze Via S Marta 3 50139 Firenze Italy

Correspondence should be addressed to Lorenzo Capineri lorenzocapineriunifiit

Received 10 May 2015 Revised 23 July 2015 Accepted 9 August 2015

Academic Editor Chengkuo Lee

Copyright copy 2015 A Bulletti and L Capineri This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Interdigital transducers fabricated with piezopolymer film have been realized to excite ultrasonic Lamb waves in a compositelaminate subjected to pure bending stresses Lamb waves were generated and detected in a cross-ply [0∘90∘] 4mm thick carbon-fiber composite by using two interdigital transducers in pitch-catch configuration We demonstrate that the choice of thepiezopolymer transducer technology is suitable for this type of investigation and the advantages of the proposed transducerassembly and bonding are described A full set-up is described to determine the relationship between the time of flight of therecorded signals and the applied bendingmoment Interdigital transducerswere designed according to simulations of the dispersioncurves in order to operate at a central frequency of 450 kHz This frequency corresponds to a central wavelength of 16mm andto a group velocity of about 6000ms for the first symmetric guided wave mode The variations in the time of flight of ultrasonicrecorded signals were measured as a function of the variations in the bending moment The static and dynamic load tests were ingood agreement with strain gage measurements performed in the micro deformation range (0ndash1400120583mm)

1 Introduction

Recent developments in the technology of materials have ledto an increase in the use of composite laminates which areemployed in aircraft space vehicles boats bridges buildingrestorations and many other engineering applications Thekey features of both carbon-fiber-reinforced (CFRP) andglass-fiber-reinforced (GFRP) plastic composite laminatesare their strength and stiffness properties which can betailored to meet the design requirements of CAD tools Inmany applications composites are employed to build partsof complex structures and are subjected to bending andortensile stresses Normal tensile stresses can be monitored bymeans of strain measurements Overstresses can lead to theinitiation of damage and to the growth of existing voids andsmall cracks to the point of forming a macroscopic crackThe damage initiation processes are due to local stresses inthe fibers and in the reinforcement matrix interface Henceit is important to develop monitoring methods for in situ

strain and stress measurements of the status of compositematerials including bending stress For tensile stresses twonondestructive testing techniques exist that are suitable forexperimental investigations ultrasonic methods [1 2] andfiber Bragg grating [3 4] Bothmethods can also be comparedwith standard strain gage methods for sensitivity accuracyand applicability to large composite material structuresor components The transducers technology for generatingLamb waves and their relative advantages are reported in [5]

The generation of selected guided wave modes is ofparticular importance for enhancing the sensitivity of themeasurements with particular mechanical stress conditionsIn our experience the flexible transducers made of piezopoly-mer film with interdigital electrodes are an effective solutionfor damage and impact detection on aircraft reusable com-ponents [6 7] For this application we investigated anotherimportant feature of flexible transducers that is the acousticcoupling with removable adhesive tapes With these typesof transducers we studied this particular mechanical loading

Hindawi Publishing CorporationJournal of SensorsVolume 2015 Article ID 259621 11 pageshttpdxdoiorg1011552015259621

2 Journal of Sensors

condition because it has not yet been fully investigated inthe literature The experimental set-up was arranged (seeSection 2) in order to obtain a good approximation of purebending loading conditions

In a previous paper [2] we demonstrated that Youngrsquosdynamic modulus of a unidirectional carbon fiber measuredwith ultrasonic methods increased significantly with thetensile stress The experimental measurements of time offlight (TOF) performed under tensile load were used toderive a relationship between strain and the TOF of theleading symmetric Lamb wave mode 119878

0 Stiffening effects

were observed by means of TOF observations for bothunidirectional and multidirectional CFRP laminates

The use of ultrasonic Lamb waves for the characteri-zation of a bending stress has significant potential for theNondestructive Evaluation (NDE) of large-area compositelaminates because they can propagate across a vast distancewith acceptable signal attenuation However the problemof estimating the bending stress by means of TOF mea-surements needs to be carefully analyzed because eachcomposite laminate can sustain multiple Lamb wave modesthe phase velocity of which in turn depends on the transduceroperating frequencies and on the laminate-thickness productInterdigital transducers (IDT) are usually employed becausethey make it possible to select specific propagation modesthat can propagate efficiently in the composite laminate Thefrequency tuning range for Lamb wave modes that we chosewas obtained by suitably designing the finger width and pitch[8]

In this study a 4mm thick symmetric cross-ply [0∘90∘]CFRP laminate was adopted The phase and group velocitydispersion curves of the Lamb wave modes were estimatedIn Section 2 we report the conditions for obtaining purebending stress The modeling of the composite laminate andthe calculations of the phase and group velocity diagramsin the frequency domain for the transducer design arereported in Section 3Themodel thatwe developedwas basedon the transfer matrix method proposed by Adler [9] InSection 4 we describe the experimental set-up realized forthe characterization of the CFRP sample with interdigitalpiezopolymer transducers and in Section 5 we compare theresults obtained with strain gage measurements mounted onthe same sample

2 Underlying Theory of Pure BendingStress in Composite Laminates

In our work we assumed a composite laminate that wassubjected to pure bending on four points ideally withoutfriction This condition made it possible to have a portionof the laminate with a constant deformation in order todetermine the relationship between the applied bendingmoment and both the TOF and the strain We assumed thefollowing

(i) The laminate thickness was ℎ and the front and backsides were identified by the coordinates 119911 = ℎ2 and119911 = minusℎ2 respectively

(ii) The thickness (ℎ) was the smallest dimension

F C

D

B

ALT

LM

yz

x

minush2

+h2

h

(a)x

Mx 120576x

(b)

Figure 1 (a) Pure bending on 4 points (A B C and D) applied toa thin plate 119871

119879

= 500mm 119871119872

= 265mm and ℎ = 4mm and119865 is the applied force in 119911 direction (b) bending moment119872

119909

andlongitudinal deformation 120576

119909

We assumed 120576119909

as being proportionalto119872119909

(iii) No stress and strain existed along 119911 direction(iv) 119872

119911and 119872

119910bending moments along 119911 and 119910 direc-

tions respectively were equal to zero

By considering the theory of the propagation of planar wavesin a thin laminate we could define three leading equationsreferring to the three Cartesian orthogonal directions (seeFigure 1(a))

120597120590119909

120597119909+120597120591119910119909

120597119910+120597120591119911119909

120597119911+ 120588 sdot 119891

119909= 120588 sdot

1205972

119906

1205971199052

120597120591119909119910

120597119909+120597120590119910

120597119910+120597120591119911119910

120597119911+ 120588 sdot 119891

119910= 120588 sdot

1205972V1205971199052

120597120591119909119911

120597119909+120597120591119910119911

120597119910+120597120590119911

120597119911+ 120588 sdot 119891

119911= 120588 sdot

1205972

119908

1205971199052

(1)

where 120588 was the density of the laminate 119891119909 119891119910 and 119891

119911were

the forces applied in 119909 119910 119911 directions 119906 V and119908 were thedisplacement vectors and 120591

119894119895and 120590

119896were the shear and the

longitudinal stresses respectivelyThe force considered was only applied in 119911 direction

indicated as 119865 (see Figure 1(a)) The resulting forces appliedin two points (B and C) on the laminate were equal to 1198652and the only bendingmoment119872

119909 was along 119909-axis with the

distribution reported in Figure 1(b)Conditions (i) (ii) and (iii) led to the following condi-

tions in the stress components

120591119909119911= 120591119911119909= 120591119910119911= 120591119911119910= 120590119911= 0 (2)

Based on previous assumptions the shear strains 120574119909119910

andthe longitudinal strain 120576

119910could be considered zero and the

resulting strain 120576119909was only in the longitudinal direction

Within a small deformations range 120576119909was proportional to

the bending moment 119872119909 It was observed that the bending

Journal of Sensors 3

h

z (direction 3)

x (direction 1)

y (direction 2)

CFRP

Figure 2 Reference system adopted for guidedmode analysis of theCFRP cross-ply [0∘90∘] laminate

moment 119872119909and the longitudinal strain 120576

119909were constant

between the two load application points B and C (within119871119872

segment) Within this region by considering 119871119879

asthe distance between A and D points the ideally bendingmoment119872

119909was constant and equal to (119871

119879minus119871119872)times1198654 Based

on these assumptions (four points bending without friction)our experiments were carried out on pure bending stressmeasurements with ultrasonic TOF and strain gage methodsusing only one direction for the measurements

3 Interdigital Transducer Design byGroup Velocity Analysis for a CFRPCross-Ply [0∘90∘] Laminate

A4mm thickCFRP cross-ply [0∘90∘] samplewas consideredin order to calculate phase and group velocity dispersioncurves of ultrasonic guided waves The reference system formodes calculation is shown in Figure 2

We calculated phase and group velocity dispersion curvesfor the longitudinal guided wave propagation in our cross-ply [0∘90∘] CFRP laminate (see Figures 3(a) and 3(b))by developing a dispersive modes calculation program inMATLAB The shear horizontal (SH) and vertical (SV)modes were not considered in the computation for theconfiguration adopted in the TOF measurements To verifythe accuracy of the developed model we first compared theanalytical solutions of phase and group velocity dispersioncurves of the homogeneousmaterials aluminum copper andnickel Afterwards we compared the dispersion curves ofboth unidirectional and cross-ply [0∘90∘] compositematerialsobtained with our model as compared to those reported inthe literature for a similar composite material [10]

Theuse of TOFmeasurements in order to characterize thepure bending stress of composite material led us to considergroup velocity measurements of the received signals incorrespondence with different bending conditions Analysisof the TOF measurements can be carried out by using thecross-correlation method or by means of an estimate ofthe delays in the signals at 50 of the maximum of theirenvelope maximum amplitudes Preliminary measurementsperformed on the composite material sample in stress-freeconditions showed that the cross-correlation method wasmuch more sensitive to the TOF variations

Table 1 IDTs design parameters width (119882) length (119871) fingersseparation (119878 = 120582IDT2) number of fingers (119873) 120576IDTmin = 120582IDT minus119882and 120582IDTmax = 120582IDT +119882

119882 [mm] 119871 [mm] 120582IDT [mm] 120582IDTmin [mm] 120582IDTmax [mm] 1198733 275 16 12 18 6

31 Mode Excitation by means of an Interdigital TransducerWe used a pair of interdigital transducers in pitch-catchconfiguration in order to transmit and receive the Lambwavemodes [11]

Considering interdigital transducers we can define thefollowing relationship

V119901

119891119888times ℎ=120582IDTℎ (3)

where V119901is the phase velocity of the ultrasonic wave 119891

119888is

the central frequency for the driving signal ℎ is the thicknessof the CFRP cross-ply [0∘90∘] sample and 120582IDT is thewavelength of the interdigital transducer In our case study120582IDT = 16mm (see Table 1) the operating frequency 119891

119888is

450 kHz and ℎ = 4mm (see Figure 3(a))Furthermore the dimension of the transducer finger can

be chosen to cover a range of wavelengths that in our caseare 120582IDTmin = 390 kHz and 120582IDTmax = 550 kHz The designedtransducer will operate in the range of corresponding fre-quencies between these two values with the advantage ofthe selection of two quasi-non-dispersive modes 119860

1and 119878

1

In particular considering Figure 3(b) the central frequencyfor the driving signal 119891

119888= 450 kHz corresponds to a group

velocity of about 6000ms The group velocity of these twomodes is very close and so we have verified this characteristicexperimentally by applying the cross-correlation methodbetween two signals acquired at two different distances fromthe IDT received for the calculation of the group velocityThe measurements were carried out on the same compositematerial in stress-free conditions and using the preliminaryset-up reported in [12] The number of cycles of the burstdriving signal at central frequency 119891

119888was experimentally

evaluated A similar approach is reported in [13]Figure 4 shows a typical signal detected in a stress-free

path on the 4mm thick CFRP composite in correspondencewith a distance of 160mm between the transmitting and thereceiving IDTsWe can observe that the twomodes119860

1and 1198781

overlap and are not distinguishable in thewaveletThedrivingsignal which is characterized by four cycles of sine wave at119891119888= 450 kHz is also shown in the same figure

32 Piezopolymer IDTs Coupling on CFRP Laminate Animportant phase of the experimental set-up preparation isthe coupling of the piezopolymer transducers on the CFRPlaminate The standard solution for piezoceramic ultrasonictransducers with a rigid case is the acoustic coupling gelthis method has been tested also with our flexible IDTsbut does not guarantee repeatable measurements because ofthe inhomogeneous layer underneath the large transducersurface (25mmtimes 40mm) and the lack of keeping the positiondue to the change of adhesion force due to temperature


A0

S0

A1 S1 A2 S2 A3 S3

120582IDT

120582IDTmin

120582IDTmax

450kHz390kHz 550kHz

2

18

16

14

12

1

08

06

04

02

0

Phas

e velo

city

(ms

)

times104

1 2 3 4 5 6 7 8 9 10

Frequency (Hz) times105

(a)

A0

S0

A1

S1

A2S2 A3

S3

450kHz

410kHz

390kHz

550kHz

7000

6000

5000

4000

3000

2000

1000

0

Gro

up v

eloci

ty (m

s)

2 3 4 5 6 7 8 9 10


(b)

Figure 3 (a) Phase velocity dispersion curves for a 4mm thick CFRP cross-ply [0∘90∘] laminate with superimposing our interdigitaltransducer characteristics and operating frequency (b) group velocity dispersion curves for a 4mm thick CFRP cross-ply [0∘90∘] laminate

Driving signalReceived signal

Time (s)0 01 02 03 04 05 06 07 08 09 1

times10minus4

minus4

minus3

minus2

minus1

0

1

2

3

4

Am

plitu

de (V

)

Figure 4 Driving signal (light grey) and received signal (black)detected in a stress-free path on the 4mm thick CFRP compositewhen considering a distance of 160mm between the transmittingand the receiving IDT

variation of the acoustic coupling gel and drying Then amore repeatable and acoustically efficient solution is thepermanent fixing by bonding the transducer to the CFRP byselecting a suitable epoxy adhesive The bonding procedurewith a standard epoxy adhesive has been carried out atenvironmental conditions (the curing takes 12 hours) becausethe curing process at higher temperatures (gt80∘C) maylose the piezoelectric effect on piezopolymer transducersThis method has been compared to an alternative method

presented in this work based on a removable solution withbonding with adhesive tape This novel method has a greatadvantage that does not affect permanently the surface ofthe sample under test and makes the eventual transducersreplacement easy moreover during experimentation thetransducers orientation and positioning can be changed toobtain optimized characteristics of the ultrasonic guidedwave propagation However the removable solution requiresthe insertion of an additional layer between the piezopolymerfilm and the surface that can alter the acoustic coupling of thelength extensional deformation of the piezopolymermaterialA comparison of these two solutions has been carried out anddescribed in this section

The first solution has been implemented by carefullydeploying the epoxy on a layer with thickness similar to thatof the piezopolymer film (100 120583m)

In Figures 5(a)-5(b) and 6(a)-6(b) are shown the twophases of the bonding on a unidirectional CFRP sample ofan IDT The solution adopted for the connections of the IDTto the coaxial cable is the use of PCB technologywith pressurethat ensures low contact resistance between copper pad of thePCBs and gold metallization of the electrodes the pressureis obtained by micro rivets The IDT is aligned along thecarbon-fiber direction

The bonding of the IDTs biadhesive tape is carried out byselecting different types and choosing the one that has lowercompliance and large temperature range for maintainingadhesion force

In practice we select the biadhesive tape model Eurocellwith thickness 28120583m with acoustic impedance that bestmatches the coupling between the piezopolymer film and theCFRP This technological study demonstrates that couplingwith biadhesivemakes IDTs reusable with respect to standardepoxy adhesive [12]


(a) (b)

Figure 5 (a) Phase one of the bonding on a unidirectional CFRP sample of an IDT (b) Phase two of the bonding on a unidirectional CFRPsample of an IDT

(a) (b)

Figure 6 (a) Particular of the IDT bonded on a unidirectional CFRP (b) Particular of the IDT bonded on a unidirectional CFRP with cable

Fiber direction

270 mm

Figure 7 Two pairs of piezopolymer IDTs at the same distance of270mm in pitch-catch configuration

These two transducers have been also sealed with a thinwhite adhesive patch to be protected from the environmentThis soft patch does not change the acoustic response of thetransducers

For the comparison of the two solutions we mounted twopairs of piezopolymer IDTs at the same distance of 270mmin pitch-catch configuration as shown in Figure 7

The front-end electronics drives the two transmittingtransducers with a burst of 4 cycles at the frequency of180 kHz through anH bridge power amplifier with amplitude96Vpp The low noise amplifier has a gain of 60 dB and minus3 dBbandwidth of 500 kHz At this frequency 119860

0mode is also

propagatedIn Figure 8 are reported the two received signals propa-

gated along paths A-A and B-B shown in Figure 7The comparison points out that the permanent bonding

with epoxy provides a better acoustic coupling of about +6 dBand the removable solution does not alter the frequencycontent of the ultrasonic signal and guarantees an adequatesignal-to-noise ratioThe small delay between the two signalsis due to the different length of paths A-A and B-B

4 Experimental Set-Up

For our experiments we devised an experimental set-upconsisting of five main items

(i) A CFRP sample

(ii) A mechanical set-up for pure bending stress applica-tion


IDTs A-AIDTs B-B

minus01

minus005

0

005

01

Am

plitu

de (V

)

17 18 19 2 2116Time (s) times10minus4

Figure 8 The two received signals propagated along the paths A-Aand B-B shown in Figure 7

(iii) An electronic set-up for the IDTsrsquo signal excita-tionacquisition and signal processing

(iv) A pair of piezopolymer IDTs(v) A strain gage meter

The CFRP sample was a 4mm thick cross-ply [0∘90∘] lami-nateThe area of the CFRP sample (176 times 500mm2) was largeenough to place the IDTs in pitch and catch configurationwith a direct path length 119871

0= 160mm Two gages were

placed outside the ultrasonic waversquos transmission path inorder to measure the longitudinal and traversal surface strain(see Figure 5) The transversal gage was included in order toverify that the actual deformation along this direction wasnegligible as was assumed in Section 2 Moreover a gage forcompensating the temperature gradients was mounted on asmall piece of the same CFRP material and was placed closeto the other gage bonded on the CFRP sample surface

The experimental set-up for the application of purebending stress is reported in Figure 9

Themechanical set-up for generating pure bending stressshown in Figure 10 consisted of a metallic structure contain-ing two rigid aluminum bars placed at a relative distance119871119879= 500mm for holding the CFRP laminate which was

suspended at a certain height ℎ119872= 60mm from the bench

plane Force was applied to the CFRP laminate by means oftwo steel cylinders assumed to be perfectly rigid each witha diameter of 15mm The two cylinders were placed at adistance 119871

119872= 265mm Force 119865 was applied perpendicular

to the plane of the laminate in the central part of the areadelimited by 119871

119872(see Figure 10) To approximate a point-like

application we employed a bolt with a pin-ball terminationBy screwing the bolt the force was progressively appliedcausing the CFRP sample being tested to bend This bendingdeveloped mainly along x-z cross section of the laminate andled to an almost constant deformation on the CFRP samplewithin 119871

119872

IDT-Tx IDT-Rx

12

3 4

L0y

xz

(a)

IDT-Tx IDT-Rx2

34

6

1

5

F

y x

z

Arbitraryfunctiongenerator

Strain gagemeter Oscilloscope

(b)

Figure 9 Experimental set-up (a) bottom view of sample withthe sensors (b) cross section of sample 1 longitudinal gage 2transversal gage 3 gage used to compensate the thermal drift4 CFRP stress-free sample 5 power amplifier and 6 low noiseamplifier

xz

yF

Steel cylinder

hM

LMLT

Figure 10 Picture of the mechanicalexperimental set-up for purebending stress application on 4 points ℎ

119872

= 60mm 119871119872

= 265mmand 119871

119879

= 500mm

For the signals acquisition we used a TEKTRONIXmodel TDS 3013b digital oscilloscope with a 9-bit resolutionand 2 ns sampling time The driving burst was generatedby an AGILENT model 33220-20MHz arbitrary functiongenerator which was connected to a customized linear poweramplifier (gain 45 dB minus3 dB bandwidth 80 kHzndash1MHz) fordriving the transmitting transducer The excitation signalwas a burst with four sine cycles with amplitude 15 Vppand frequency 450 kHz which resulted in a peak-to-peakvoltage of 267V applied to the transmitting transducer


L

S

W

1 N

GNDt

PVDF

Metallizedgold

electrodes

x

y

z

120582 = 2S

V+Vminus

Figure 11 Geometry of interdigital transducers of gold metallizedelectrodes on a piezopolymer film (drawing not in scale) withcharacteristics reported in Table 1

The receiving transducer was connected to a low noiseinstrumentation amplifier with minus3 dB bandwidth of 1MHzand voltage gain of 56 dB This preamplifier was designed tomatch the piezopolymer electrical impedance for obtaininga high signal-to-noise ratio The digitized signals were thentransferred to a PC and processed offline

Two piezopolymer IDTs with design parameters reportedin Table 1 were used in a pitch-catch configuration placedon the CFRP as shown in Figure 10 The material used forthe sensor design was a commercial copolymer P(VDF-TrFE) film (PiezoTech SA St Louis France) with thicknesst = 100 120583m and a gold metallization with an approximatethickness of 01 120583m mass density 120588

119898= 1780 kgm and

longitudinal velocity 119881PVDF = 2200msThe IDT electrode geometry which is shown in Figure 11

was transferred onto the metallized piezopolymer film bymeans of a patented laser marking process [14]

An interlaced electrode configuration was adopted Thistransducer configuration was differential because the twoseries of electrodes (also called fingers) were driven withopposite phase signals (V+ and Vminus) and had the samereference ground electrode (GND) The basic transducerdesign parameters consisted of the width (119882) length (119871)piezopolymer film thickness (119905) separation of the fingers (119878)and the number of fingers (119873) The interlaced configurationrequires that finger separation 119878 should be half of thewavelength 120582IDT relative to the guided wave mode selectedParameter 119882 changes the effective IDT area and influencesthe acoustic response in the wave number domain Length119871 defines the directivity of the transducers according to theapproximated relationship for laminates [9]

12

34

7

65

L0

Figure 12 Zoom on sensors applied to sample of CFRP 1 longitudi-nal gage 2 transversal gage 3 gage used to compensate the thermaldrift of the other two 4 portion of the same CFRP sample usedfor compensation gage without mechanical stress 5 IDT for signaltransmission (Tx-IDT) 6 IDT for signal detection (Rx-IDT) and 7CFRP sample

The surface deformation was measured by a VISHAYmodel P-3500 strain gage meter that has the followingcharacteristics

(i) Resistance 24∘C 3500Ω plusmn 015(ii) Gage factor 24∘C 2095 plusmn 05(iii) Transversal sensitivity coefficient (119896

119905) +01 plusmn 02

Two strain gages bonded on theCFRP sample in longitudinaland transversal directions are shown in Figure 12 The thirdonewas used to compensate the thermal drift of the other twoThe longitudinal and transversal surface strains were read ona 5-digit display with 1 120583120576 = 1 120583mm resolution

With the longitudinal gage we measured deformationalong 119909 direction (120576

119909) instead with the transversal gage

we measured deformation along 119910 direction (120576119910) Since

preliminary measurements confirmed that the deformationalong 119910 directionwas two orders ofmagnitude lower than thedeformation in 119909 direction in the tests reported in Section 5we considered only the longitudinal deformation On thefront (119911 = minusℎ2) and back faces (119911 = +ℎ2) 120576

119909assumed

the valuesminus120576119861and+120576

119861 respectively For the longitudinal gage

shown in Figure 14 we considered +120576119861value 120576

119909values were

those usedwhenmeasuring the bending status of a compositelaminate by means of a gage bonded on the surface

5 Results with Static and Dynamic Loads

Using the set-up described in Section 4we carried out severaltests in different pure bending loading conditions Ourpreliminarymeasurements involved some signals acquired instress free bending conditions and inmedium andmaximumbending conditions Three acquired signals are shown inFigure 13 The time window was placed on the first sevenpeaks of the received signals The propagating signal wasa sine burst of four cycles at frequency 119891

119888= 450 kHz In

Figure 13 we show that the envelopes of the three signals wereequal in a time window of 20120583s

From the results of these preliminary tests we succeededin establishing the following measurement protocol in orderto have repeatable measurements

(i) Warm-up of the instruments at a constant roomtemperature for 30 minutes


Signal stress-free bending conditionsSignal medium bending conditionsSignal maximum bending conditions

02 04 06 08 1 12 14 16 18 20Time (s)

minus4

minus3

minus2

minus1

0

1

2

3

4

Am

plitu

de (V

)

times10minus5

Figure 13 Three signals acquired in medium and maximumbending conditions and in stress-free conditions The 20120583s timewindow was placed on the first seven peaks of the received signals

(ii) Calibration definition of the gage factor and balanc-ing the Wheatstone bridge of the strain gage meter

(iii) Loading and unloading the composite laminate for34 bending full cycles

(iv) Acquisition of the reference signal from Rx-IDT instress-free condition

(v) Acquisition of the first 7 peaks of the signals receivedin a time window of 20120583s at different bendingpositions such as those reported in Figure 13

The TOF variation (Δ119905) was calculated using the cross-correlation between pairs of acquired signals at differentloads using a script based on the MATLAB cross-correlationfunction ldquoxcorrrdquo In particular all received signals in a timewindow of 20120583s at different bending positions (see egsignals shown in Figure 13) were cross-correlated with thereference signal fromRx-IDT in stress-free condition and theresulting TOF variation values were recorded

51 Static Load Test with Assigned Values of Force In thisexperiment we applied known forces 119865 by means of cast-iron weights increased from 0 to 300N for each force valuethe surface strain 120576

119861and TOF variation (Δ119905) were collected in

static conditions after a rest period of 60 s Five data serieswere collected

The data plots for every series and for the correspondinglinear fitting are shown in Figure 14 The continuous linesrepresent the linear fitting expressed by

120576119861asymp 180 sdot 119865 + 59

Δ119905 asymp minus020 sdot 119865 + 08

(4)

0 100 200 3000

100

200

300

400

500

600

Applied load (N)

Data series 1

Data series 2

Data series 3

Data series 4

Data series 5

(120583m

m)

120576

F

B

(a)

Applied load (N)0 100 200 300

0

10

20

30

40

50

60minusΔt

Varia

tion

of ti

me o

f flig

ht (n

s)

Data series 1

Data series 2

Data series 3

Data series 4

Data series 5

F

(b)

Figure 14 Five series of data acquired with assigned loads in staticconditions The surface deformation versus applied load is reportedon (a) while the variation of TOF versus applied load is reported on(b)

The resulting standard deviations were 120590120576= 45 120583120576 and 120590

Δ119905=

25 ns

52 Dynamic Load Tests During these experiments weapplied an increasing bending load monotonically by slowlyscrewing the bolt in a continuous way We then measuredthe surface strain 120576

119861and TOF variation (Δ119905) simultaneously


Data series 1Data series 2

minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

Figure 15 Two series of data acquired in dynamic conditions Thecontinuous line indicates the quadratic fitting

The ultrasonic signals and strain gage measurements wererecorded for each load value The dynamic test for the fullload application lasted for 4 minutes The time lag betweenthe ultrasonic signal and the strain gage acquisitions whichwas due to the setting time of the strain gage meter displayoutput was less than 9 s

In these experimental conditions we plotted Δ119905 valuesversus the surface strain 120576

119861 The two data series and the

corresponding quadratic fits are reported in Figure 15The quadratic fitting curve which is expressed in [ns]

for Δ119905 and in [120583120576] for 120576119861 was evaluated on 120576

119861range which

extends from 0 to 1400 120583mm The continuous line is thequadratic fit of two data series It was found to be

Δ119905 asymp 2 sdot 10minus5

sdot 1205762

119861

minus 014 sdot 120576119861+ 29 (5)

with a standard deviation of 29 ns

53 Static Load Tests Similar to the previous experiments wemeasured the surface strain 120576

119861andΔ119905 in static load conditions

over 120576119861range extending from 0 to 1400 120583mm The relative

plotting of eight data series is reported in Figure 16The quadratic fit in [ns] for Δ119905 and in [120583120576] for 120576

119861is

reported in Figure 16 as a continuous line It was expressedas


sdot 1205762

119861

minus 012 sdot 120576119861+ 16 (6)

with an estimated standard deviation of 36 nsIn this case the standard deviation was greater than the

one obtained in the dynamic test probably due to the effectof a mechanical hysteresis that developed thanks to the effectof eight successive static load applications

54 Static LoadingUnloading Tests These tests were per-formed with a series of four repetitive loading and unloadingcycles of the laminate The measurement procedure was thesame as that of the previous tests

Data series 1Data series 2Data series 3Data series 4


minusΔt

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm) 120576B

Figure 16 Eight series of data acquired in static conditions Thecontinuous line indicates the quadratic fitting

The loading and unloading measurement results areshown respectively in Figures 17(a) and 17(b) Similar tothe previous tests we also found a good fit for this microdeformation in two quadratic regressions

Loading 997904rArr Δ119905 = 20 sdot 10minus5 sdot 1205762119861

minus 013 sdot 120576119861+ 07 (7)

Unloading 997904rArr Δ119905 = 23 sdot 10minus5 sdot 1205762119861

minus 014 sdot 120576119861+ 46 (8)

The estimated standard deviations were 31 ns and 37 ns for(7) and (8) respectively

6 Conclusions

The work has demonstrated that piezopolymer transducersare suitable to select guided waves mode for the measure-ments of TOF variation related to pure bending stress incomposite materials By experimental characterization orsimulation of Lamb waves in the composite laminate itis possible to design piezopolymer IDTs operating withtuned central frequency and bandwidth In the specific testsample we designed and fabricated piezopolymer interdigitaltransducers of 120582IDT = 16mm operating at 450 kHz for acorresponding symmetric mode group velocity of 6000msThe experimental tests provided an estimate of the relation-ship between the TOF variation and the micro deformationsmeasured with a strain as follows

(i) For 120576119861lt 1000 120583120576 there is a linear relationship

between the TOF variation (Δ119905) and the surface strain(120576119861)

(ii) For 1000 120583120576 lt 120576119861lt 1400 120583120576 the relationship

between the TOF variation and the surface strain iswell approximated by a quadratic fitting


Loading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(a)

Unloading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(b)

Figure 17 (a) Four series of data acquired in static conditions Themeasurements are relative to the loading phase of pure bendingstress The continuous line shows the quadratic fitting (b) Fourseries of data acquired in static conditions The measurements arerelative to the loading phase of pure bending stress The continuousline shows the quadratic fitting

From these measurements we were able to estimate thatthe bending load standard deviation for the ultrasonic TOFmethod was five times greater than that of the strain gageTheTOF variation (Δ119905) recordedwas all negative as observedalso in another published work We measured an increase ina single carbon fiber using Youngrsquos dynamicmodulus with anapplied tensile load and also bymeans of ultrasonic methodsThis nonlinear stress-strain response was also observed forCFRP laminates that had unidirectional andmultidirectionallayers

The advantage of the piezopolymer IDTs as compared tothe strain gage appeared when we investigated large stressed

areas of the composite laminate Moreover we developedand tested a simple and reliable method for the acousticalcoupling of piezopolymer IDTs on the sample surface basedon biadhesive tape that facilitates the transducers installationand removal on the item under test

Conflict of Interests

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

Acknowledgments

The authors wish to acknowledge the contributions of DrEdgardoRosi for providing theCFRP samples andDrMarinaMazzoni for the group velocity simulations

References

[1] M Duquennoy M Ouaftouh and M Ourak ldquoUltrasonicevaluation of stresses in orthotropic materials using Rayleighwavesrdquo NDT amp E International vol 32 no 4 pp 189ndash199 1999

[2] N Toyama and J Takatsubo ldquoAn investigation of non-linearelastic behavior of CFRP laminates and strain measurementusing Lamb wavesrdquo Composites Science and Technology vol 64no 16 pp 2509ndash2516 2004

[3] C K Y Leung Z Yang Y Xu P Tong and S K L Lee ldquoDelam-ination detection in laminate composites with an embeddedfiber optical interferometric sensorrdquo Sensors and Actuators APhysical vol 119 no 2 pp 336ndash344 2005

[4] Y Fan and M Kahrizi ldquoCharacterization of a FBG strain gagearray embedded in composite structurerdquo Sensors and ActuatorsA Physical vol 121 no 2 pp 297ndash305 2005

[5] Z Su L Ye and Y Lu ldquoGuided Lamb waves for identificationof damage in composite structures a reviewrdquo Journal of Soundand Vibration vol 295 no 3ndash5 pp 753ndash780 2006

[6] L Capineri A Bulletti M Calzolai and D Francesconi ldquoLambwave ultrasonic system for active mode damage detection incomposite materialsrdquo Chemical Engineering Transactions vol33 pp 577ndash582 2013

[7] L Capineri A Bulletti M Calzolai P Giannelli and DFrancesconi ldquoArrays of conformable ultrasonic Lamb wavetransducers for structural health monitoring with real-timeelectronicsrdquo in Proceedings of the 28th European Conferenceon Solid-State Transducers (EUROSENSORS rsquo14) Brescia ItalySeptember 2014

[8] M Veidt T Liu and S Kitipornchai ldquoModelling of Lambwaves in composite laminated plates excited by interdigitaltransducersrdquoNDT amp E International vol 35 no 7 pp 437ndash4472002

[9] E L Adler ldquoMatrix methods applied to acoustic waves inmultilayersrdquo IEEE Transactions on Ultrasonics Ferroelectricsand Frequency Control vol 37 no 6 pp 485ndash490 1990

[10] N Guo and P Cawley ldquoThe interaction of Lamb waves withdelaminations in composite laminatesrdquo Journal of the AcousticalSociety of America vol 94 no 4 pp 2240ndash2246 1993

[11] F Bellan A Bulletti L Capineri et al ldquoA new design andmanufacturing process for embedded Lamb waves interdigitaltransducers based on piezopolymer filmrdquo Sensors and ActuatorsA Physical vol 123-124 pp 379ndash387 2005


[12] A Bulletti L Capineri L Masotti O Occhiolini and E RosildquoStrain measurements on carbon-epoxy composites by Lambwaves piezopolymer interdigital transducersrdquo in Proceedings ofthe IEEEUltrasonics Symposium vol 1 pp 403ndash406 September2005

[13] S Grondel J Assaad C Delebarre and E Moulin ldquoHealthmonitoring of a composite wingbox structurerdquo Ultrasonics vol42 no 1ndash9 pp 819ndash824 2004

[14] L Capineri L Masotti G Masotti and M Mazzoni ldquoMatrix-type pyroelectric sensor method for its fabrication and devicefor characterizing laser beams comprising said sensorrdquo Euro-pean Patent no EP1380821 2004

International Journal of

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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



condition because it has not yet been fully investigated inthe literature The experimental set-up was arranged (seeSection 2) in order to obtain a good approximation of purebending loading conditions

In a previous paper [2] we demonstrated that Youngrsquosdynamic modulus of a unidirectional carbon fiber measuredwith ultrasonic methods increased significantly with thetensile stress The experimental measurements of time offlight (TOF) performed under tensile load were used toderive a relationship between strain and the TOF of theleading symmetric Lamb wave mode 119878

0 Stiffening effects

were observed by means of TOF observations for bothunidirectional and multidirectional CFRP laminates

The use of ultrasonic Lamb waves for the characteri-zation of a bending stress has significant potential for theNondestructive Evaluation (NDE) of large-area compositelaminates because they can propagate across a vast distancewith acceptable signal attenuation However the problemof estimating the bending stress by means of TOF mea-surements needs to be carefully analyzed because eachcomposite laminate can sustain multiple Lamb wave modesthe phase velocity of which in turn depends on the transduceroperating frequencies and on the laminate-thickness productInterdigital transducers (IDT) are usually employed becausethey make it possible to select specific propagation modesthat can propagate efficiently in the composite laminate Thefrequency tuning range for Lamb wave modes that we chosewas obtained by suitably designing the finger width and pitch[8]

In this study a 4mm thick symmetric cross-ply [0∘90∘]CFRP laminate was adopted The phase and group velocitydispersion curves of the Lamb wave modes were estimatedIn Section 2 we report the conditions for obtaining purebending stress The modeling of the composite laminate andthe calculations of the phase and group velocity diagramsin the frequency domain for the transducer design arereported in Section 3Themodel thatwe developedwas basedon the transfer matrix method proposed by Adler [9] InSection 4 we describe the experimental set-up realized forthe characterization of the CFRP sample with interdigitalpiezopolymer transducers and in Section 5 we compare theresults obtained with strain gage measurements mounted onthe same sample

2 Underlying Theory of Pure BendingStress in Composite Laminates

In our work we assumed a composite laminate that wassubjected to pure bending on four points ideally withoutfriction This condition made it possible to have a portionof the laminate with a constant deformation in order todetermine the relationship between the applied bendingmoment and both the TOF and the strain We assumed thefollowing

(i) The laminate thickness was ℎ and the front and backsides were identified by the coordinates 119911 = ℎ2 and119911 = minusℎ2 respectively

(ii) The thickness (ℎ) was the smallest dimension

F C

D

B

ALT

LM

yz

x

minush2

+h2

h

(a)x

Mx 120576x

(b)

Figure 1 (a) Pure bending on 4 points (A B C and D) applied toa thin plate 119871

119879

= 500mm 119871119872

= 265mm and ℎ = 4mm and119865 is the applied force in 119911 direction (b) bending moment119872

119909

andlongitudinal deformation 120576

119909

We assumed 120576119909

as being proportionalto119872119909

(iii) No stress and strain existed along 119911 direction(iv) 119872

119911and 119872

119910bending moments along 119911 and 119910 direc-

tions respectively were equal to zero

By considering the theory of the propagation of planar wavesin a thin laminate we could define three leading equationsreferring to the three Cartesian orthogonal directions (seeFigure 1(a))

120597120590119909

120597119909+120597120591119910119909

120597119910+120597120591119911119909

120597119911+ 120588 sdot 119891

119909= 120588 sdot

1205972

119906

1205971199052

120597120591119909119910

120597119909+120597120590119910

120597119910+120597120591119911119910

120597119911+ 120588 sdot 119891

119910= 120588 sdot

1205972V1205971199052

120597120591119909119911

120597119909+120597120591119910119911

120597119910+120597120590119911

120597119911+ 120588 sdot 119891

119911= 120588 sdot

1205972

119908

1205971199052

(1)

where 120588 was the density of the laminate 119891119909 119891119910 and 119891

119911were

the forces applied in 119909 119910 119911 directions 119906 V and119908 were thedisplacement vectors and 120591

119894119895and 120590

119896were the shear and the

longitudinal stresses respectivelyThe force considered was only applied in 119911 direction

indicated as 119865 (see Figure 1(a)) The resulting forces appliedin two points (B and C) on the laminate were equal to 1198652and the only bendingmoment119872

119909 was along 119909-axis with the

distribution reported in Figure 1(b)Conditions (i) (ii) and (iii) led to the following condi-

tions in the stress components

120591119909119911= 120591119911119909= 120591119910119911= 120591119911119910= 120590119911= 0 (2)

Based on previous assumptions the shear strains 120574119909119910

andthe longitudinal strain 120576

119910could be considered zero and the

resulting strain 120576119909was only in the longitudinal direction

Within a small deformations range 120576119909was proportional to

the bending moment 119872119909 It was observed that the bending


h

z (direction 3)

x (direction 1)

y (direction 2)

CFRP



119909were constant















V119901

119891119888times ℎ=120582IDTℎ (3)


119888is


119888is



1and 119878

1







1and 1198781




A0

S0

A1 S1 A2 S2 A3 S3

120582IDT

120582IDTmin

120582IDTmax

450kHz390kHz 550kHz

2

18

16

14

12

1

08

06

04

02

0

Phas

e velo

city

(ms

)

times104

1 2 3 4 5 6 7 8 9 10


(a)

A0

S0

A1

S1

A2S2 A3

S3

450kHz

410kHz

390kHz

550kHz

7000

6000

5000

4000

3000

2000

1000

0

Gro

up v

eloci

ty (m

s)

2 3 4 5 6 7 8 9 10


(b)



Time (s)0 01 02 03 04 05 06 07 08 09 1

times10minus4

minus4

minus3

minus2

minus1

0

1

2

3

4

Am

plitu

de (V

)









(a) (b)


(a) (b)


Fiber direction

270 mm





0mode is also






(i) A CFRP sample



IDTs A-AIDTs B-B

minus01

minus005

0

005

01

Am

plitu

de (V

)
















119872

IDT-Tx IDT-Rx

12

3 4

L0y

xz

(a)

IDT-Tx IDT-Rx2

34

6

1

5

F

y x

z



(b)


xz

yF

Steel cylinder

hM

LMLT


119872

= 60mm 119871119872

= 265mmand 119871

119879

= 500mm



L

S

W

1 N

GNDt

PVDF

Metallizedgold

electrodes

x

y

z

120582 = 2S

V+Vminus




119898= 1780 kgm and




12

34

7

65

L0




119905) +01 plusmn 02






119909assumed




119909values were




119888= 450 kHz In






02 04 06 08 1 12 14 16 18 20Time (s)

minus4

minus3

minus2

minus1

0

1

2

3

4

Am

plitu

de (V

)

times10minus5











120576119861asymp 180 sdot 119865 + 59


(4)

0 100 200 3000

100

200

300

400

500

600

Applied load (N)

Data series 1

Data series 2

Data series 3

Data series 4

Data series 5

(120583m

m)

120576

F

B

(a)


0

10

20

30

40

50

60minusΔt

Varia

tion

of ti

me o

f flig

ht (n

s)

Data series 1

Data series 2

Data series 3

Data series 4

Data series 5

F

(b)



Δ119905=

25 ns





minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)







119861range which



sdot 1205762

119861

minus 014 sdot 120576119861+ 29 (5)






119861is



sdot 1205762

119861

minus 012 sdot 120576119861+ 16 (6)






minusΔt

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm) 120576B




minus 013 sdot 120576119861+ 07 (7)


minus 014 sdot 120576119861+ 46 (8)


6 Conclusions







Loading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(a)

Unloading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(b)







Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










h

z (direction 3)

x (direction 1)

y (direction 2)

CFRP



119909were constant















V119901

119891119888times ℎ=120582IDTℎ (3)


119888is


119888is



1and 119878

1







1and 1198781




A0

S0

A1 S1 A2 S2 A3 S3

120582IDT

120582IDTmin

120582IDTmax

450kHz390kHz 550kHz

2

18

16

14

12

1

08

06

04

02

0

Phas

e velo

city

(ms

)

times104

1 2 3 4 5 6 7 8 9 10


(a)

A0

S0

A1

S1

A2S2 A3

S3

450kHz

410kHz

390kHz

550kHz

7000

6000

5000

4000

3000

2000

1000

0

Gro

up v

eloci

ty (m

s)

2 3 4 5 6 7 8 9 10


(b)



Time (s)0 01 02 03 04 05 06 07 08 09 1

times10minus4

minus4

minus3

minus2

minus1

0

1

2

3

4

Am

plitu

de (V

)









(a) (b)


(a) (b)


Fiber direction

270 mm





0mode is also






(i) A CFRP sample



IDTs A-AIDTs B-B

minus01

minus005

0

005

01

Am

plitu

de (V

)
















119872

IDT-Tx IDT-Rx

12

3 4

L0y

xz

(a)

IDT-Tx IDT-Rx2

34

6

1

5

F

y x

z



(b)


xz

yF

Steel cylinder

hM

LMLT


119872

= 60mm 119871119872

= 265mmand 119871

119879

= 500mm



L

S

W

1 N

GNDt

PVDF

Metallizedgold

electrodes

x

y

z

120582 = 2S

V+Vminus




119898= 1780 kgm and




12

34

7

65

L0




119905) +01 plusmn 02






119909assumed




119909values were




119888= 450 kHz In






02 04 06 08 1 12 14 16 18 20Time (s)

minus4

minus3

minus2

minus1

0

1

2

3

4

Am

plitu

de (V

)

times10minus5











120576119861asymp 180 sdot 119865 + 59


(4)

0 100 200 3000

100

200

300

400

500

600

Applied load (N)

Data series 1

Data series 2

Data series 3

Data series 4

Data series 5

(120583m

m)

120576

F

B

(a)


0

10

20

30

40

50

60minusΔt

Varia

tion

of ti

me o

f flig

ht (n

s)

Data series 1

Data series 2

Data series 3

Data series 4

Data series 5

F

(b)



Δ119905=

25 ns





minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)







119861range which



sdot 1205762

119861

minus 014 sdot 120576119861+ 29 (5)






119861is



sdot 1205762

119861

minus 012 sdot 120576119861+ 16 (6)






minusΔt

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm) 120576B




minus 013 sdot 120576119861+ 07 (7)


minus 014 sdot 120576119861+ 46 (8)


6 Conclusions







Loading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(a)

Unloading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(b)







Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










A0

S0

A1 S1 A2 S2 A3 S3

120582IDT

120582IDTmin

120582IDTmax

450kHz390kHz 550kHz

2

18

16

14

12

1

08

06

04

02

0

Phas

e velo

city

(ms

)

times104

1 2 3 4 5 6 7 8 9 10


(a)

A0

S0

A1

S1

A2S2 A3

S3

450kHz

410kHz

390kHz

550kHz

7000

6000

5000

4000

3000

2000

1000

0

Gro

up v

eloci

ty (m

s)

2 3 4 5 6 7 8 9 10


(b)



Time (s)0 01 02 03 04 05 06 07 08 09 1

times10minus4

minus4

minus3

minus2

minus1

0

1

2

3

4

Am

plitu

de (V

)









(a) (b)


(a) (b)


Fiber direction

270 mm





0mode is also






(i) A CFRP sample



IDTs A-AIDTs B-B

minus01

minus005

0

005

01

Am

plitu

de (V

)
















119872

IDT-Tx IDT-Rx

12

3 4

L0y

xz

(a)

IDT-Tx IDT-Rx2

34

6

1

5

F

y x

z



(b)


xz

yF

Steel cylinder

hM

LMLT


119872

= 60mm 119871119872

= 265mmand 119871

119879

= 500mm



L

S

W

1 N

GNDt

PVDF

Metallizedgold

electrodes

x

y

z

120582 = 2S

V+Vminus




119898= 1780 kgm and




12

34

7

65

L0




119905) +01 plusmn 02






119909assumed




119909values were




119888= 450 kHz In






02 04 06 08 1 12 14 16 18 20Time (s)

minus4

minus3

minus2

minus1

0

1

2

3

4

Am

plitu

de (V

)

times10minus5











120576119861asymp 180 sdot 119865 + 59


(4)

0 100 200 3000

100

200

300

400

500

600

Applied load (N)

Data series 1

Data series 2

Data series 3

Data series 4

Data series 5

(120583m

m)

120576

F

B

(a)


0

10

20

30

40

50

60minusΔt

Varia

tion

of ti

me o

f flig

ht (n

s)

Data series 1

Data series 2

Data series 3

Data series 4

Data series 5

F

(b)



Δ119905=

25 ns





minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)







119861range which



sdot 1205762

119861

minus 014 sdot 120576119861+ 29 (5)






119861is



sdot 1205762

119861

minus 012 sdot 120576119861+ 16 (6)






minusΔt

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm) 120576B




minus 013 sdot 120576119861+ 07 (7)


minus 014 sdot 120576119861+ 46 (8)


6 Conclusions







Loading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(a)

Unloading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(b)







Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)


(a) (b)


Fiber direction

270 mm





0mode is also






(i) A CFRP sample



IDTs A-AIDTs B-B

minus01

minus005

0

005

01

Am

plitu

de (V

)
















119872

IDT-Tx IDT-Rx

12

3 4

L0y

xz

(a)

IDT-Tx IDT-Rx2

34

6

1

5

F

y x

z



(b)


xz

yF

Steel cylinder

hM

LMLT


119872

= 60mm 119871119872

= 265mmand 119871

119879

= 500mm



L

S

W

1 N

GNDt

PVDF

Metallizedgold

electrodes

x

y

z

120582 = 2S

V+Vminus




119898= 1780 kgm and




12

34

7

65

L0




119905) +01 plusmn 02






119909assumed




119909values were




119888= 450 kHz In






02 04 06 08 1 12 14 16 18 20Time (s)

minus4

minus3

minus2

minus1

0

1

2

3

4

Am

plitu

de (V

)

times10minus5











120576119861asymp 180 sdot 119865 + 59


(4)

0 100 200 3000

100

200

300

400

500

600

Applied load (N)

Data series 1

Data series 2

Data series 3

Data series 4

Data series 5

(120583m

m)

120576

F

B

(a)


0

10

20

30

40

50

60minusΔt

Varia

tion

of ti

me o

f flig

ht (n

s)

Data series 1

Data series 2

Data series 3

Data series 4

Data series 5

F

(b)



Δ119905=

25 ns





minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)







119861range which



sdot 1205762

119861

minus 014 sdot 120576119861+ 29 (5)






119861is



sdot 1205762

119861

minus 012 sdot 120576119861+ 16 (6)






minusΔt

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm) 120576B




minus 013 sdot 120576119861+ 07 (7)


minus 014 sdot 120576119861+ 46 (8)


6 Conclusions







Loading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(a)

Unloading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(b)







Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










IDTs A-AIDTs B-B

minus01

minus005

0

005

01

Am

plitu

de (V

)
















119872

IDT-Tx IDT-Rx

12

3 4

L0y

xz

(a)

IDT-Tx IDT-Rx2

34

6

1

5

F

y x

z



(b)


xz

yF

Steel cylinder

hM

LMLT


119872

= 60mm 119871119872

= 265mmand 119871

119879

= 500mm



L

S

W

1 N

GNDt

PVDF

Metallizedgold

electrodes

x

y

z

120582 = 2S

V+Vminus




119898= 1780 kgm and




12

34

7

65

L0




119905) +01 plusmn 02






119909assumed




119909values were




119888= 450 kHz In






02 04 06 08 1 12 14 16 18 20Time (s)

minus4

minus3

minus2

minus1

0

1

2

3

4

Am

plitu

de (V

)

times10minus5











120576119861asymp 180 sdot 119865 + 59


(4)

0 100 200 3000

100

200

300

400

500

600

Applied load (N)

Data series 1

Data series 2

Data series 3

Data series 4

Data series 5

(120583m

m)

120576

F

B

(a)


0

10

20

30

40

50

60minusΔt

Varia

tion

of ti

me o

f flig

ht (n

s)

Data series 1

Data series 2

Data series 3

Data series 4

Data series 5

F

(b)



Δ119905=

25 ns





minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)







119861range which



sdot 1205762

119861

minus 014 sdot 120576119861+ 29 (5)






119861is



sdot 1205762

119861

minus 012 sdot 120576119861+ 16 (6)






minusΔt

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm) 120576B




minus 013 sdot 120576119861+ 07 (7)


minus 014 sdot 120576119861+ 46 (8)


6 Conclusions







Loading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(a)

Unloading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(b)







Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










L

S

W

1 N

GNDt

PVDF

Metallizedgold

electrodes

x

y

z

120582 = 2S

V+Vminus




119898= 1780 kgm and




12

34

7

65

L0




119905) +01 plusmn 02






119909assumed




119909values were




119888= 450 kHz In






02 04 06 08 1 12 14 16 18 20Time (s)

minus4

minus3

minus2

minus1

0

1

2

3

4

Am

plitu

de (V

)

times10minus5











120576119861asymp 180 sdot 119865 + 59


(4)

0 100 200 3000

100

200

300

400

500

600

Applied load (N)

Data series 1

Data series 2

Data series 3

Data series 4

Data series 5

(120583m

m)

120576

F

B

(a)


0

10

20

30

40

50

60minusΔt

Varia

tion

of ti

me o

f flig

ht (n

s)

Data series 1

Data series 2

Data series 3

Data series 4

Data series 5

F

(b)



Δ119905=

25 ns





minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)







119861range which



sdot 1205762

119861

minus 014 sdot 120576119861+ 29 (5)






119861is



sdot 1205762

119861

minus 012 sdot 120576119861+ 16 (6)






minusΔt

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm) 120576B




minus 013 sdot 120576119861+ 07 (7)


minus 014 sdot 120576119861+ 46 (8)


6 Conclusions







Loading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(a)

Unloading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(b)







Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











02 04 06 08 1 12 14 16 18 20Time (s)

minus4

minus3

minus2

minus1

0

1

2

3

4

Am

plitu

de (V

)

times10minus5











120576119861asymp 180 sdot 119865 + 59


(4)

0 100 200 3000

100

200

300

400

500

600

Applied load (N)

Data series 1

Data series 2

Data series 3

Data series 4

Data series 5

(120583m

m)

120576

F

B

(a)


0

10

20

30

40

50

60minusΔt

Varia

tion

of ti

me o

f flig

ht (n

s)

Data series 1

Data series 2

Data series 3

Data series 4

Data series 5

F

(b)



Δ119905=

25 ns





minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)







119861range which



sdot 1205762

119861

minus 014 sdot 120576119861+ 29 (5)






119861is



sdot 1205762

119861

minus 012 sdot 120576119861+ 16 (6)






minusΔt

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm) 120576B




minus 013 sdot 120576119861+ 07 (7)


minus 014 sdot 120576119861+ 46 (8)


6 Conclusions







Loading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(a)

Unloading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(b)







Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)







119861range which



sdot 1205762

119861

minus 014 sdot 120576119861+ 29 (5)






119861is



sdot 1205762

119861

minus 012 sdot 120576119861+ 16 (6)






minusΔt

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm) 120576B




minus 013 sdot 120576119861+ 07 (7)


minus 014 sdot 120576119861+ 46 (8)


6 Conclusions







Loading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(a)

Unloading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(b)







Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Loading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(a)

Unloading



minusΔt

120576B

0

50

100

150

TOF

varia

tion

(ns)

200 400 600 800 1000 1200 14000(120583mm)

(b)







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









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