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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
15
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
16
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)
17
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
18
• 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
19
• 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
21
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
22
• 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
23
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.
24
• 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
25
• 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
26
• 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.
31
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
32
Acknowledgements• Prof. Moshe Tur• Lab colleagues, and especially:
– Yakov Botsev – Dr. Nahum Gorbatov
• Iddo Kressel• Shoham