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Laser-Ultrasonic generation of Single-Mode Lamb wave in Thin Plate Seung Seok Lee, Sang Whoe Dho, Young Gil Kim, Bong Young Ahn, Se-kyoung Lee Nondestructive Testing Group, Korea Research Institute of Standards and Science, P.O.BOX 102, Yusong, Taejon 305-600, Korea Contact

Abstract

We present a laser-ultrasonic technique to generate the lowest symmetric( s₀ ) Lamb wave in thin plate. Using this special technique, in which two symmetric laser beams quasi-simultaneously hit at the same point on both sides of the plate, we absolutely suppress anti-symmetric Lamb wave modes. This technique is applicable to any situation that requires symmetric Lamb wave mode operation and does not need additional contacts or special equipment.

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( s₀ ) 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)

where f is the displacement potential and p_res is the resultant pressure at the boundary.

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 (s₀) 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 (s₀) 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.

References

1. H.F. Pollard, Sound Waves in Solids(Pion Limited, London, 1977).
2. E. Hecht and A. Jajac, Optics(Addison-Wesley Publishing Company, 1979)
3. C. B. Scruby and L. E. Drain, Laser Ultrasonics : Techniques and Applications (Adam Hilger, 1990)
4. F.L. Degertekin and B. T. Khuri-Yakub, Appl. Phys. Lett. 69, 146(1996)
5. A.C. Bushell, C. Edwards and S.B. Palmer, British. J. NDT, 33, 177(1991)
6. D.A. Hutchins and K. Lundgren, J. Acoust. Soc. Am. 85, 1441(1989)

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