1

TEL AVIV UNIVERSITYThe Iby and Aladar Fleischman Faculty of Engineering

The Zandman-Slaner School of Graduate Studies

Measuring Ultrasonic Lamb Waves Using Fiber Bragg Grating Sensors

By

Eyal Arad (Dery)

Under the supervision of

Prof. Moshe Tur

2

This study…

Deals with the detection of propagating ultrasonic waves in plates, used for damage detection.

The detection is performed using a fiber optic sensor (specifically, a Fiber Bragg Grating sensor) bonded to or embedded in the plate.

3

Contents• General Introduction:

– Structural Health Monitoring and Non-Destructive Testing– Lamb Waves in NDT– Fiber Bragg Grating Sensors

• The goals of this work• Analysis and results

– Analytical solutions – Numerical solutions and comparison – Tangentially bonded FBG – Setup and Experimental Results

• Effects and implications – Angular Dependence – Rosette Calculations

• Summary of Findings • Future Work

4

General Introduction

Structural Health Monitoring (SHM) and Non-Destructive Testing (NDT)

• SHM- the process of damage identification (detection, location, classification and severity of damage) and prognosis

• SHM Goal- increase reliability, improve safety, enable light weight design and reduce maintenance costs

• NDT- an active approach of SHM

• Several NDT techniques exist, among them is Ultrasonic Testing

• Many Ultrasonic Testing techniques for plates utilizes Lamb Waves in a Pulse- Echo method (damage= another source)

• Usually, both transducer and sensor are piezoelectric elements

5

Lamb Waves Implementations in NDT• Lamb waves are Ultrasonic (mechanic) waves propagating in a thin

plate (thickness<<wavelength)

• Important characteristics for NDT:

– Low attenuation over long distances

– Velocity depends on the frequency (could be dispersive)

– Creates strain changes that can be detected

6

Lamb Waves Implementations in NDT

• Some examples for suggested implementationsin the aerospace field:– Qing (Smart Materials and Structures, v.14 2005)

– Kojima (Hitachi Cable Review, v. 23, 2004)

7

Lamb Waves Propagation

• In infinite material 3 independent modes of displacement exist

• In thin plates the x and y displacements are coupled (boundary conditions) and move together

• Two types of modes exist:

– Symmetric waves(around x)

– Antisymmetric waves

8

Lamb Waves Propagation

• Plane wave (infinite plate)– Symmetric waves (displacement)

Where ξ is the wave number ω/vph, and α,β are proportional to the material’s constants

– Antisymmetric waves

txiy

txix

eyCyBu

eyCyBiu

sinsin

coscos

txiy

txix

eyDyAu

eyDyAiu

coscos

sinsin

2

222

4tan

tan

b

b

222

24

tan

tan

b

b

α,β

9

Lamb Waves Propagation• Cylindrical Lamb wave

– In the area close to the transducer

– Symmetric case

• H0 and H1 are Hankel Function of zero and first kind.

– For the antisymmetric solution it is only necessary to interchange sinh and cosh

tiz

tir

ezb

bzrAHu

ezb

bzrAHu

'sinh'sinh

'sinh

'

2'sinh

''

'

'cosh'cosh

'cosh

2

''cosh

''

22

2

220

2

22

221

Y XZ

r

10

Lamb Waves Propagation

• Dispersion relations (Vph(f)):• Lamb wave modes

222

24

tan

tan

b

b

2

222

4tan

tan

b

b

• The selected working mode is A0

11

Fiber Bragg Grating (FBG) Sensors• Permanent, periodic perturbation of the refractive index

• λB=2neffΛ

• Reflection curve

• Measuring Ultrasound according to:

R

RR B0

)R( P)(P optin,optr,

BB 79.0

1549.0 1549.2 1549.4 1549.6 1549.8 1550.00

4

8

12

16

Ref

lect

ion

Wavelength , nm

Pout,opt

λB

ΔλB

R0

ΔR

neutral

with strain

12

FBG’s advantages for NDT:– Directional Sensitivity– Small Size– Fast Response – up to several MHz– Ability to Embed inside Composites– EMI, RFI Immunity– Ability to Multiplex (several sensors on the

same fiber)

13

Summary of Introduction

SHM & NDT concept and goal

Lamb waves and their importance to NDT

FBG principle and advantages in NDT

14

Purpose of This Study• To build an analytical model for a pulse

of propagating Lamb wave, in order to validate a Finite Element (numerical) model, for applying on complex cases which cannot be solved analytically.

• To analyze the behavior of the detected ultrasonic signal at close range to the transducer, where the wave is cylindrical.

• Extending published plane wave analysis, to analyze the effect of close range sensing on the angular dependence of FBGs and on angle-to-source calculations.

FBG

wavefront

PZT

FBG

ε1

Incident wave

x,εxx

y,εyy

εA

arbitrary direction

ε2

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Analysis and Results Lamb Wave Solutions for a Pulse Input• Input: single period sine function pulse

• Plane wave A0:

– x=0

Using inverse Fourier transformto convert to the time domain

bDbAisignalFbyxu

signaltbyxu

x

x

sinsin)(,,0~,,0

bGbi

signalFA

sinsin

)(

A0 plane wave displacements ux (blue) and uy (green) vs. time at x=0

and y=b

yGyAbyxu y coscos),0(~

1.5 2 2.5 3 3.5 4

x 104-

-1

0

1

2

3

4

5

t

Dis

plac

emen

t

2.3 2.4 2.5 2.6 2.7 2.8

x 10-4

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

time

Am

plitu

de

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Lamb Wave Solutions for a Pulse Input

• For all x (Plane wave A0)

– Dispersion relation- A0 is dispersive

uy displacements of A0 at distances of 0 (blue), 10(green), 20 (red) and 30cm (cyan) ux displacements of A0 at distances of 0 (blue), 10(green), 20 (red) and 30cm (cyan)

xiyy

xixx

ebyxubyxu

ebyxubyxu

),,0(~),,(~),,0(~),,(~

2.5 3 3.5 4 4.5 5 5.5 6

x 10-4

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

t

Dis

pla

cem

en

t

2 3 4 5 6

x 10-4

-2

-1

0

1

2

3

4

5

t

Dis

pla

cem

en

t

watch

0.5 1 1.5 2 2.5 3 3.5 4 4.5

x 105

1000

2000

3000

4000

5000

6000

f[Hz]

Vp

h[m

/s]

Dispersion relation for A0 (blue) and S0 (black)

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Lamb Wave Solutions for a Pulse Input• Cylindrical Lamb wave

)(_),,(~_),,(

0

0

signalFsignalinputFbzrru

signalinputtbzrru

r

r

b

bb

brH

signalFA

'sinh'sinh'sinh

2'

'sinh''

)(

2

22

2201

bbrH

zbb

zrHsignalF

zrur'sinh

2'

'sinh

'sinh'sinh'sinh

2'

'sinh)(

,,~

2

22

01

2

22

1

bbrH

zbb

zrH

zruz'sinh

2'

'sinh''

'cosh'cosh'cosh

'2

'cosh''

'

),,(~

2

22

2201

22

2

220

uz displacements of A0 at r= PZT edge (blue), 5 (green), 10 (red) and 20cm (cyan)

ur displacements of A0 at r= PZT edge (blue), 5 (green), 10 (red) and 20cm (cyan)

2.5 3 3.5 4 4.5

x 10-4

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

t

Dis

pla

cem

en

t

2 2.5 3 3.5 4 4.5 5

x 10-4

-1

0

1

2

3

4

t

Dis

pla

cem

en

t

watch

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• Finite Element Method (FEM)A computer simulation which divides the plate into small elements and solves the energy relations between them.

– The analytical solutions Were crucial in choosing the parameters for the FE Models in order to receive the correct model

– The FEM enables solving even more complex cases (e.g. plate with a damage)

Courtesy of Iddo Kressel of IAI ltd.

x

y

z

r

z

2.4 2.6 2.8 3 3.2 3.4 3.6

x 10-4

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

time

Dis

pla

cem

en

t

analytical Ur at r0 (5mm)

analytical Ur at 11cmFEM Ur at r

0 (5mm)

FEM Ur at 11cm

Numerical solutions and comparison

2.5 3 3.5 4 4.5

x 10-4

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

t

Dis

pla

cem

en

t

Analytical Uz at r

0 (5mm)

Analytical Uz at 11 cm

Analytical Uz at 31 cm

FEM Uz at r

0 (5mm)

FEM Uz at 11 cm

FEM Uz at 31 cm

Analytical model

Numerical model

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• What is the analytical influence of cylindrical waves in Lamb wave detection by a FBG?

• The FBG signal is angular dependent (as opposed to PZT sensor)

• FBG parallel to the Plane wavefront- No Signal in the tangential FBG

• Cylindrical wave- Signal (strain) Exists

• The tangential strain is:– Different in its shape than the radial strain

– It can not be neglected at close distance

– Decays faster

2.2 2.4 2.6 2.8 3 3.2

x 10-4

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

time

an

lytic

al s

tra

in (

no

rma

lize

d)

radial (blue) and tangential (green) strains at 21mm

r

ur

u

r

rr

Tangentially bonded FBG

FBG

wavefront

FBG

wavefront

PZT

20

Purpose- to measure an ultrasonic Lamb wave via FBG sensor and validate analytical and numerical models

Basic measurement setup: • Function Generator produces an input

signal. • The PZT transforms the electrical

signal to an ultrasonic wave that propagates through the plate.

• The sound vibrations affect the FBG which is bonded to the plate.

• The FBG transforms the mechanical vibrations to an optical Bragg reflection shift.

• This shift is identified by the optical interrogation system.

Laser source

Detector

Function Generator +Amplifier

Signal Processing

PZT Exciter

FBG sensor

x

y

x

r

θ

setup

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Experimental Results

• These figures reinforce two claims:– The tangential strain, though smaller and decaying faster than the

radial strain, exists

– Experimental and analytical results match

2.4 2.6 2.8 3 3.2 3.4 3.6 3.8

x 10-4

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

time

stra

in

εr strains of measured (red) vs. analytic (blue) at 7cm, with analytic S0 included

2.6 2.7 2.8 2.9 3 3.1 3.2 3.3

x 10-4

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

time

tan

ge

ntia

l str

ain

(n

orm

aliz

ed

)

measured (red) and analytic (blue) strains for tangential FBG at 7cm

Tangential strain Radial strain

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• Plane wave:

• Cylindrical wave:For θ=0 (PZT-FBG angle) the principal strains are in the x,y directions:

22max coscos xxFBG

r

ur

u

ryy

rrxx

Angular Dependence

)cos( 2max FBG

FBG

wavefront

PZT

βx

Goal: to show the different angular dependence of FBGs for plane and cylindrical waves

PZT Exciter

FBG sensor

x

y

r

2222 sincossincosr

u

r

u rryyxxFBG

0 15 30 45 60 75 90 105 120 135 150 165 180-0.2

0

0.2

0.4

0.6

0.8

1

1.2

angle

no

rma

lize

d s

tra

in a

mp

litu

de

Analytical angular dependence for plane wave assumption (cos2(β), green line) and cylindrical assumption (blue line) at 21mm from the source

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Cylindrical wave (cont.):When ignoring the tangential effect, the error could be large. For example, at β=75 degrees:

2.5 2.6 2.7 2.8 2.9 3 3.1 3.2

x 10-4

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

time

stra

in (

no

rma

lize

d)

75 degrees comparison of general analytic strain (blue) measured signal (green) and analytic without tangential strain

(red)

Angular Dependence

PZT Exciter

FBG sensor

x

y

r

Conclusion: The tangential strain affects the angular dependence and cannot be ignored at small distances from the source.

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• Rosettes are used for damage location in NDT

• Prior work uses only plane wave rosettes Our work intends to:

Enable accurate location of damages in a close range Present different calculation for each wave (planar/

cylindrical)

What is a rosette?

Rosette Calculations

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• For a Plane wave: – Only 2 FBGs are required!

– Signals are in-phase.

– Max. values can be used

3.5 4 4.5 5 5.5

x 10-4

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

time

norm

aize

d st

rain

Signals of 2 FBGs oriented at different angles in the plane wave case

2max cosFBG

Rosette Calculations

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• For a cylindrical wave:– 3 FBGs are required!

– Signals are not necessarily in phase and differ from each other!!!

– Signal values should be taken at a specific time!

2.4 2.6 2.8 3 3.2 3.4

x 10-4

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

time

no

rma

lize

d s

tra

in

Measured strains for angles: 0 (blue), 45 (green) and 90 (red) degrees

C

B

A

y

xA

B

C

A0°B45°C90°

FBG

C

FBG A

Rosette Calculations

27

• Cylindrical wave (cont.)Angle to the source:– Analytically (θ is 0).

2.6 2.65 2.7 2.75 2.8 2.85 2.9 2.95 3

x 10-4

-80

-60

-40

-20

0

20

40

60

80

time

ap

pro

xim

ate

d a

ng

le (

an

aly

tica

l)

anglestrain 0 deg.strain 45 deg.strain 90 deg.

Estimated angle to the source (bold blue line), using analytical strain solutions (also added for time reference)

900

090452)2tan(

Rosette Calculations

PZT Exciter

FBG sensor

x

y

r

C

B

A

y

xA

B

C

A0°B45°C90°

FBG

C

FBG A

28

• Cylindrical wave (cont.)Angle to the source:

– Angle from measured signal was not as expected!!!

– Applying a 1mm shift to one of the FBGs in the analytical calculation shows a similar effect ☺

2.65 2.7 2.75 2.8

x 10-4

-40

-30

-20

-10

0

10

20

30

40

time

ap

pro

xim

ate

d a

ng

le (

shift

ed

an

aly

tic)

anglestrain 0 deg.strain 45 deg.strain 90 deg.

2.6 2.65 2.7 2.75 2.8

x 10-4

-40

-30

-20

-10

0

10

20

30

40

time

ap

pro

xim

ate

d a

ng

le

anglestrain 0 deg.strain 45 deg.strain 90 deg.

The effect of 8*10-7 [sec] time shift (~1 mm) of one of the analytical strain solutions on the angle estimation capability

Estimated angle to the source (bold blue line), using measured strain signals (also added for time reference)

Rosette Calculations

900

090452)2tan(

29

• Conclusions and Implications– Realistically, the estimated angle will

never be constant

– Improved analysis method for cylindrical rosettes:

• Perform analysis for each time step

• Choose the angle for which the denominator is maximal

– In plane wave rosettes this problem does not exist since it is possible to assume signals are in phase

Golden Rule: For long distance use plane wave rosette, For short distance- cylindrical wave rosette

2.6 2.65 2.7 2.75 2.8

x 10-4

-40

-30

-20

-10

0

10

20

30

40

time

ap

pro

xim

ate

d a

ng

le

anglestrain 0 deg.strain 45 deg.strain 90 deg.

Estimated angle to the source (bold blue line), using measured strain signals (also added for time reference)

Rosette Calculations

900

090452)2tan(

30

Summary of FindingsExact analytical solutions for a pulse of plane and cylindrical Lamb waves was calculated.Parameters for a Finite Element Model were determined.The angular dependence of FBGs at close range to the transducer, where the wave is cylindrical, was analyzed and measured.Three FBG rosette calculations were performed and the effect of the tangential strain on the angle finding was analyzed.The effect of co-location error was demonstrated.

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Future Work

Applying FBGs to NDT system for damage detection Real time monitoring

High accuracy at all distances

AnisotropyComposite plates, which are common in the industry, are usually anisotropic

Ability to embed optical fibers

Phase and group velocities are angle dependent

0.00

0.05

0.10

0.15

0.20

0

30

60

90

120

150

180

210

240270

300

330

0.00

0.05

0.10

0.15

0.20

Slo

wn

ess

Su

rfa

ce,

z/x1

03

S0 Slowness Curve

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Acknowledgements• Prof. Moshe Tur• Lab colleagues, and especially:

– Yakov Botsev – Dr. Nahum Gorbatov

• Iddo Kressel• Shoham