AN EFFECTIVE GENERATION OF LAMB WAVES IN A THIN
PLATE USING LASER LINE ARRAY ILLUMINATION AND THEIR
PROPAGATION CHARACTERISTICS
T.S. Jang1, J.J. Lee1, and S.S. Lee2
'Department of Mechanical Engineering, Korea Advanced Institute of Science and
Technology, Daejeon 305-701, Korea
NDE Group, Korea Research Institute of Standards and Science, Daejeon 305-340, Korea
ABSTRACT. Symmetric and antisymmetric Lamb modes are excited in low-frequency-thickness
regime by illuminating a thin plate with an array of Q-switched Nd:YAG laser-generated line sources.
The propagation of laser-generated Lamb waves is detected by measuring the out-of-plane
displacements in a non-contact manner using the fiber optic Sagnac interferometer. The laser
generation and non-contact detection of narrowband Lamb waves at the selected operating points with
relatively small rate of change in group velocity is presented.
INTRODUCTION
The point-by-point inspection using conventional ultrasonic testing method is a
time-consuming process for nondestructive inspection of large structures because the
transducer should be scanned over the whole area to be inspected. Guided waves, however,
can carry information about the integrity of the material in their path by line-by-line and
offer a possible more efficient tool for nondestructive inspection of large plate-like
structures. Generation and detection of Lamb waves offer an effective NOT technique that
will detect defects quickly and reliably [1-3]. Lamb waves can propagate over several
meters through the entire thickness of the plate, and the NDT technique using Lamb waves
is widely used for the rapid and long-range inspection [2]. A high-powered pulsed laser
also can be used to generate all types of elastic waves including bulk waves, surface waves
and guided waves. A laser pulse can generate elastic waves in a sample and a laser
interferometer can detect the signal at a different position like a pitch-catch technique.
Laser-generated surface waves propagate as Lamb or plate waves providing the ultrasonic
wavelength is much greater than the plate thickness. Laser-generated Lamb waves also can
be utilized for the effective nondestructive inspection of plate-like structures. The major
advantage of laser ultrasound is that it is a non-contact technique and can therefore be used
for the situation inaccessible with conventional probing.
Lamb waves generated by a laser source, however, have broadband characteristics
as compared to conventional methods using piezoelectric or EMT transducers [4].
Generation of Lamb waves in non-dispersive region can facilitate the unambiguous signal
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/$20.00
311
interpretation. A specific mode and transducer selection for Lamb wave inspection was
discussed in detail in the literature [3]. In this study, narrowband Lamb waves in low
frequency regime in a thin plate are simply generated by line array illumination of
Nd:YAG pulsed laser, and the non-contact measurement of ultrasound is performed by the
flexible fiber probe of the fiber optic Sagnac interferometer. The wavelength of lasergenerated Lamb waves is adjusted by changing the spacing between each line illumination
of Nd:YAG pulsed laser. The bandwidth of the spatial frequency of Lamb waves can be
narrowed by a spatially periodic heating of sample surface with the laser line array of a Qswitched Nd:YAG pulsed laser. The laser generation and detection of narrowband Lamb
waves at the selected operating points with the small rate of change in group velocity is
presented.
LASER GENERATION OF NARROWBAND LAMB WAVES
Longitudinal and shear bulk waves and Rayleigh surface waves are generated
simultaneously by the pulsed laser source. As the plate thickness decreases, the transfer
from laser-generated Rayleigh to Lamb waves occurs. Classical Lamb waves are defined
as elastic waves of plane strain propagating in a traction free, homogeneous and isotropic
plate. Frequency equations for symmetric and antisymmetric waves are expressed as
following [5]
tan qh _
tanph
4pqk2
+1 = symmetric
-1 = antisymmetric
where 2h is the thickness of a plate, k is the wave number. If the longitudinal wave
velocity, the shear wave velocity and the angular frequency are denoted by CL, CT and CD,
respectively, then/? and q are related to the following Equation (2):
The ultrasonic velocity is dependent on the product of frequency and thickness of a
plate; therefore, the analysis of the detected output signal may be complicated according to
the frequency component of the excited Lamb modes. A high-powered laser pulse is
passed through a cylindrical lens and this line source is usually utilized to excite Lamb
modes in a plate. The propagation direction of laser-generated Lamb wave is normal to the
line source. The stainless steel plate with thickness of 1mm was used for the sample.
Nd: YAG laser pulse was used to generate the ultrasound, and the waveform was measured
by an out of plane sensitive laser interferometer. The typical laser-generated Lamb wave
for the stainless steel plate by a laser line source is shown in Figure l(a). Only the main
part of the signal with the large amplitude in part A shown in Figure l(a) was used for the
analysis of amplitude spectrum, because the late arrival signal includes the reflections at
the edges of the plate. The amplitude spectrum is dominant in low frequency regime, as
shown in Figure l(b). The rate of change of the group velocity of ao mode is considerable
in low frequency-thickness regime, thus frequency-dispersion in the waveform is evident,
with the higher frequencies arriving first, and the lower frequencies arriving late. This
phenomenon also results from the broadband wavelength spectrum of the ultrasound
generated by a line source. As a result, the analysis of waveform may be difficult owing to
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the superposition of several modes and the frequency-dispersion characteristics. If we
consider the normalized Gaussian beam intensity, as an example, the spatial profile of
single line illumination produces a broadband wavelength distribution, as shown in Figure
2(c). The periodic heating of sample surface by laser line array illumination, however,
makes the wavelength spectrum narrow, as shown in Figure 2(d). In this study, the
spatially periodic illumination for narrowband Lamb wave generation is performed by a
combination of a beam expander, a cylindrical lens and multiple slits with various spacing,
as shown in Figure 3. The wavelength of Lamb waves in a plate is adjusted by changing
the distance between the sample and the lens. The Fraunhoffer diffraction is assumed to be
negligible because the slit width is so much greater than the wavelength of 1064nm
Nd:YAG laser. The wavelength change is observed from the beam marks on burn paper as
shown in Figure 3, and is used for the selection of operating point with relatively small rate
of change in the group velocity of Lamb waves.
0
20
40
60
(b)
80 100 120 140 160 180 200
Time (usec)
i.u-
n sz
T3
0.6-
"cl 0.4-
fr
0.2:
/
^^
"v^--——
0.000
05
15
10
2.
Frequency (MHz)
FIGURE 1. Lamb waves generated by single line illumination; (a) typical waveform for stainless steel plate
of 1mm thickness; (b) normalized amplitude spectrum of part A in waveform.
Normalized Gaussian beam intensity
Normalized Gaussian beam intensity
0.80.6:
0.40.2nn.
(a)
single line
illumination
0.8:
0.6:
0.40.2-
(b)
line array
illumination
rm10
15
20
25
30
Spatial distribution (mm)
15
20
25
30
Spatial distribution (mm)
200
(c)
*r
0
(d)
loos' 504
5
6
Wavelengh (mm)
0.2
0.4
0.6
0.8
1.0
1.2
1.4 1.6 1.8
Wavelength (mm)
FIGURE 2. (a) and (b) are spatial profiles of normalized Gaussian beam intensity of single line illumination
and line array illumination, respectively; (c) is wavelength spectrum of single line illumination; (d) is
wavelength spectrum of line array illumination near fundamental wavelength component.
v
Multiple
„ ,. , . , Probing
]^1Cal \fib.
Cyl
Plano-convex
cylindrical lens
Multiple
slit
FIGURE 3. Experimental setup for laser generation of narrowband Lamb waves; (a) shows beam marks
produced by spatially periodic illumination, where probing fiber is used for non-contact measurement of
ultrasound; (b) represents principle of wavelength adjustment, where A, is wavelength of periodic heating of
Nd:YAG laser pulse, f() is focal length of cylindrical lens, and x is distance between plate and lens.
CONFIGURATION OF FIBER OPTIC SAGNAC INTERFEROMETER FOR
NONCONTACT DETECTION OF ULTRASOUND
Fiber optic interferometers generally have the considerable advantage in the case of
parts of complex geometry and in harsh environments, because they transmit the light
through the flexible optical waveguide and do not require the precise alignment of
sensitive optics or an ideal measurement environment for the detection of ultrasound. In
this study, the fiber optic Sagnac interferometer was configured for the detection of lasergenerated Lamb waves in a non-contact manner. Jang et al. [6] reported an alternative fiber
optic Sagnac interferometer that is suitable for the out-of-plane measurement of ultrasound
in a non-contact manner. Figure 4 shows the configured fiber optic system consisting of
ordinary single-mode fibers, fiber polarization controllers, a PZT ring phase modulator, a
fiber delay, a focuser and fiber couplers with the splitting ratio of 0.5. A fiber polarization
controller (PCI) is used to maximize the visibility of the interferometer. Both a PZT ring
phase modulator and a fiber polarization controller (PC2) are installed in the Sagnac loop.
Only the fiber polarization controller PC2 is used to control of phase bias and the fiberwrapped PZT modulator is used for the confirmation of proper phase bias.
Ultrasonic waves: u(t) = ^4cos(coa/L)
Fiber
dejayline
PZTPhas ^
Dead port
FIGURE 4. Configuration of fiber optic Sagnac interferometer for ultrasound detection; PCI and PC2 are
fiber polarization controllers, and DC1, DC2 are fiber couplers with splitting ratio of 0.5.
314
If the visibility is denoted by F, and the input intensity /0 is normalized to unity,
then the interference intensity /' resulting from only clockwise (CW) and counterclockwise (CCW) beams may be simplified such that [6]
1
(3)
where fa is the phase bias between CW and CCW beams, A^ is the phase change due to
ultrasonic signal, and ac is the optical loss at the focuser that is assumed to be dominant
over any other loss in optical path. When the phase bias fa is equal to ;r/2, the best
sensitivity of the interferometer is obtained for the detection of ultrasound with small
amplitude.
The optical phase delay of the light passing through a fiber is generally given by
nkl, where n is the refractive index, k is the laser wave number, and / is the physical length
of the fiber. In the Sagnac interferometer, CW and CCW beam paths have the same
physical length of the fiber; however, a conventional low-birefringence single-mode
optical fiber may have different refractive indices between the stressed and non-stressed
axes by bending [7]. As a result, an arbitrary optical phase delay of the light can be
obtained between CW and CCW beams. There also exists the desired birefringence
making nil phase bias between CW and CCW beams for arbitrary incident polarization.
This birefringence can be achieved by controlling a 3-coil fiber polarization controller
installed in the Sagnac loop. The operating principle of configured fiber optic Sagnac
interferometer was described in detail in reference [6]. Out-of-plane harmonic motion
produced by a PZT disk was monitored in a non-contact manner; as an example, some
results in low frequency regime are presented in Figure 5(b) and 5(d). Ultrasonic
(a)
> o/
/\
'\
\
2
^o 3> 0.4
V
/
/
* 0.2(b)
> 0.0 /*S w
-0.2
-0.4
\
/
^v\ J /
/
\
/N
/
\ // \\
V,
I
/
\J
f\
1r\
\
\
\
\
/
\J
^xALy / =v /*\ V, /^ /~\
\\uS
\s
S
20
40
100
60
Time (jisec)
40
i
lLj^_J
Y»
&
o
60
Time (usec)
(e)
!
!
/~N
/N
\y
Vx/
^
->/
*
V
Time (usec)
FIGURE 5. (a) and (c) represent input voltages applied across PZT disk at 56kHz, 420kHz, respectively; (b)
and (d) are detection signals of out-of-plane harmonic motion of PZT disk corresponding to inputs (a), (c),
respectively; (e) represents detection signal and its normalized frequency spectrum of ultrasonic pulse
produced by conventional PZT transducer.
315
oscillation produced by a conventional PZT transducer also was successfully detected, as
shown in Figure 5(e), and the performance of the configured system was validated [6].
EXPERIMENTAL RESULTS AND DISCUSSIONS
Phase and group velocity dispersion curves were calculated, as shown in Figure 6,
from the measurement of the longitudinal and shear wave velocities for stainless steel.
Lamb waves were generated by the laser line array illumination for a stainless steel plate
of 0.5mm thickness. Laser-generated Lamb waves were detected by the fiber optic Sagnac
interferometer. The distance between the laser source and the non-contact detection point
is 115mm. The slope of straight line on the phase velocity dispersion curve of Figure 6(a)
denotes the constant wavelength A, of Lamb waves from the relation of A = c p h / f ; where
cph is the phase velocity and/is the frequency. The narrow-banded center wavelength is
adjusted experimentally by the control of the spacing of laser line array, as illustrated in
Figure 3. Lamb modes, thus, can be excited at the intersection points of the straight line
with different modes. The center frequency of laser-generated Lamb mode is varied
according to the adjustment of the center wavelength. The group velocity of ao mode in
low frequency regime was calculated from the measured wave packets; the rate of change
of group velocity was considerable. The group velocities at various center frequencies of
ao mode are represented as symbols in Figure 6(b). Results agree well with the calculated
group velocity dispersion curve; the center frequency of the measured ao mode is in good
agreement with the frequency of each intersection point of the wavelength line; the
measured group velocity at that frequency also agrees well with the ao curve in Figure 6(b).
The excitation point of ao mode is changed by adjusting the spacing of line sources in
spatially periodic heating of laser line array illumination; a0 mode, thus, can be generated
in the region of the small rate of change in group velocity.
Another experiment was performed to generate the narrow-banded ao mode with
relatively small dispersion. Figure 7(a) and 7(b) represent the phase velocity and group
velocity dispersion curves for stainless steel plate of 1mm thickness, respectively. The rate
of change of group velocity with respect to frequency is zero at the marked point on group
2
3
Frequency (MHz)
FIGURE 6. (a) Phase velocity dispersion curve; (b) group velocity dispersion curve for stainless steel plate
of 0.5mm thickness. Straight lines shown in (a) correspond to constant wavelength of Lamb mode. Solid
circle represents experimental measurement of group velocity of aQ mode at given wavelength.
316
(c)
Center freq.: 1.2MHz
Group vel.: 2973m/s
1
20
2
3
Frequency(MHz)
40
2.2MHz
1642m/s
60 80 100
Time (usec)
120
140
160
FIGURE 7. (a) Phase velocity; (b) group velocity dispersion curves for 1mm stainless steel plate; (c)
waveform produced by line array illumination.
velocity dispersion curve. At these regions, ultrasonic wave propagation can be nondispersive. The line on the phase velocity dispersion curve denotes the constant
wavelength of 2mm and the intersection points of this line with a0 and s0 modes were
obtained. The intersection point with ao mode shows that the rate of change of group
velocity is nearly zero; thus the mode excitation at this point can produce a non-dispersive
ao mode. The spacing between each line source was set to 2mm by adjusting the distance
between the sample and the lens. Lamb wave with narrow spatial bandwidth was produced
by line array illumination and the detected signal is shown in Figure 7(c). The detected ao
mode has the center frequency of 1.2MHz and the group velocity of 2973m/s. This result
corresponds to the intersection of wavelength line of 2mm with ao mode curve in Figure
7(b). In addition to ao mode obtained in Figure 7 (c), so mode is also observed. The
detected so signal has the center frequency of 2.2MHz and the group velocity 1642m/s; it
has higher frequency and lower group velocity than the obtained ao signal. This results
from the fact that the frequency at ao intersection point P is lower than that of so
intersection points Q and the corresponding group velocity is higher at the point P than Q,
as shown in Figure 7(b). At the intersection point Q, however, so mode does not show the
small rate of change in group velocity. The asymmetric a0 mode generally has the
dominant out-of-plane displacement and the ordinary laser interferometers detect the outof-plane displacement more easily; thus it is considered that the ao mode obtained in small
dispersion region is effective for the inspection of a plate. A narrowband asymmetric ao
mode can be simply generated in non-dispersive region by the laser line array illumination
and the proper wavelength control. Simple laser line array illumination and the non-contact
detection by the alternative fiber optic sensor can be applied as the laser-based NDT
technique using Lamb waves for plate structures.
CONCLUSIONS
The laser generation and detection of narrowband Lamb waves were performed. A
narrowband asymmetric aO mode with the small rate of change in group velocity can be
317
simply generated by the laser line array illumination and the proper wavelength control.
The center wavelength of Lamb wave can be selected by the adjustment of the spacing of
the illuminating line sources. This scheme is very simple to generate the spatially narrowbanded Lamb waves. The configured fiber optic Sagnac interferometer is very simple and
is effective for non-contact detection of ultrasonic waves and can be applied for any other
ultrasonic measurements. Laser line array illumination and alternative fiber optic Sagnac
interferometer can be applied as the laser-based ultrasonic technique for the inspection of
plate-like structures.
ACKNOWLEDGEMENTS
This study was supported by the MOST (Ministry of Science and Technology)
research fund of Korea under contract No. 2000-N-NL-01-C-091. The authors would like
to thank MOST for the financial support.
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5. Achenbach, J.D., Wave Propagation in Elastic Solids, North-Holland Publishing
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