·Table of Contents ·Methods and Instrumentation | Laser-Ultrasonic generation of Single-Mode Lamb wave in Thin PlateSeung Seok Lee, Sang Whoe Dho, Young Gil Kim, Bong Young Ahn, Se-kyoung LeeNondestructive Testing Group, Korea Research Institute of Standards and Science, P.O.BOX 102, Yusong, Taejon 305-600, Korea Contact |
Lamb waves[1,3-6] are the elastic wave motions that can propagate in a solid such as a thin plate, and have two basic mode types, symmetrical and anti-symmetrical, according to whether the displacements on both surfaces of a plate are in phase or in anti-phase. The lowest symmetric( s_{0} ) Lamb wave(LSL wave) propagates with only a little dispersion at low frequency-thickness product( f . d ) values. Because of this characteristic of the LSL wave, we commonly use it to measure the elastic properties of a plate or to detect defects in a thin plate.
Specially, when the LSL wave is used to measure the reflection from sides of a plate or defects in a plate, the superposition[2] of the reflection waves from edges or defects on anti-symmetric Lamb waves makes a serious difficulty in data analysis. That is the reason to develop a technique to suppress the undesired anti-symmetric Lamb waves.
Degertekin and Khuri-Yakub[4] present a technique to excite selectively the lowest order symmetric or anti-symmetric Lamb wave modes using Hertzian contacts in thin solid plates.
In this study, we present a technique to generate the LSL wave by the symmetric laser beam technique without special contacts[4] in a thin plate. This technique is very simple, but very effective.
Fig 1: Schematic diagram to measure Lamb waveform with an EMAT when the laser beam II is moved from symmetric point(zero point) to x-direction |
Consider the situation of Fig. 1 as the propagation of Lamb waves generated by laser-ultrasonics in a thin plate. Solutions are required for the wave equation[1]
(1) |
subject to the boundary condition
(2) |
The wave solutions may be found by the method of separation of variables for x, y in the 2-dimensional solution. From the wave propagation theory[1] in a thin plate, we can easily predict the form of the wave solution as the linear combination of symmetric and anti-symmetric modes[1].
(3) |
This solution is induced by the laser beam I. The laser beam II also makes equal waves except the reverse in y direction.
The total wave solution propagating in x direction by the laser beam I and II is the superposition[2] of f_{I}(y1,x1)
and f_{II}(y2,x2)
(4) |
If the laser beam I is equal to the laser beam II in power, beam size, and distribution of energy the amplitudes of the waves of f_{I}(y1,x1) and f_{II}(y2,x2) are equal each other.
Symmetric and anti-symmetric Lamb wave modes[1,5,6] generated by the laser beam I and II at y1 = d/2 , y2 = -d/2 have the next characteristics
(5) |
Using this results, we find Eq. 6 from Eq. 4 by disregarding initial phase at x1 = x2 = x,
(6) |
This result implies that all anti-symmetric Lamb wave modes are suppressed.
Fig. 2 shows a schematic diagram of the experimental setup for generation and detection of the LSL wave. The laser generation and non-contact detection of the LSL wave is studied in brass plate of 100mm thickness, 20cm´40cm size. The generating laser is a non-focused Q-switched Nd:YAG laser system with a pulse width of 6ns. Generation of the Lamb wave is accomplished by a single shot mode in the ablation regime with a laser pulse of 650mJ. Original one beam is divided into two equal beams by 1:1 beam splitter.
Fig 2: Experimental setup for laser-ultrasonic generation of the single mode |
Lamb wave in a thin plate of 100mmthickness, 20cm´40cm size
Two equal beams quasi-simultaneously arrive at the target points of the thin plate within delay time less than 2ns. The waveform of the Lamb wave is detected by Electro-Magnetic Acoustic Transducer (EMAT) fixed at the position as seen in Fig. 1. The EMAT is designed to vibrate both in symmetric mode and in anti-symmetric mode. The waveform averaged 30 pulses is captured by a Lecroy 9310 digital oscilloscope and is stored for subsequent analysis on a notebook computer by GPIB interface.
Fig. 3 shows the waveforms received by the EMAT when the laser beam II is moved from symmetric point (zero point) to x-direction. As be shown in Fig. 3.a, a LSL wave and reflection waves from edges are only observed at the symmetric point by the suppression of the anti-symmetric Lamb wave mode. The symmetric mode (s_{0}) and the anti-symmetric mode(a_{o}) are observed in Fig. 3.b-3.d when the symmetric characteristic of two laser beam is broken.
Fig 3: Lamb wave and reflection waves from edges measured by an EMAT |
Figure 4 shows peak amplitudes of LSL waves at each distance. The peak amplitude of the LSL wave at the symmetric point (x=0mm) is about three times bigger than the peak amplitude at maximum distance(near x=10mm) where a LSL wave is divided into two LSL waves. We see that the LSL wave is at the situation of constructive superposition at x=0mm and destructive superposition at near x=10mm. The distance which makes destructive superposition is about half of wavelength of the LSL wave(with velocity ~ 3835 m/sec and center frequency ~ 200 kHz) measured by the EMAT in the specimen.
Fig 4: Change of peak amplitudes of LSL waves at each distance |
In summary, we present a new laser-ultrasonic technique to generate the lowest symmetric (s_{0}) Lamb wave in thin plates. Using this technique, in which two symmetric laser beams quasi-simultaneously hit at the same point on both sides of the plate, we absolutely suppressed the anti-symmetric Lamb wave mode. This technique is applicable to any situation that requires symmetric Lamb wave mode operation and does not need additional contacts or special equipment.
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