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Wireless frequency-tuned generation and measurement of torsional waves using magnetostrictive nickel gratings in cylinders
Sensors and Actuators A 126 (2006) 73–77
Wireless frequency-tuned generation and measurement of torsional waves using magnetostrictive nickel gratings in cylinders Ik Kyu Kim, Yoon Young Kim ∗ School of Mechanical and Aerospace Engineering and Multiscale Design Center of the Institute of Advanced Machinery Design, Seoul National University, Sillim-Dong San 56-1, Kwanak-Gu, Seoul 151-742, Korea Received 12 January 2005; received in revised form 16 August 2005; accepted 20 September 2005 Available online 3 November 2005
Abstract The objective of this work is to experimentally investigate the possibility of using a magnetostrictive nickel grating for frequency-tuned wireless generation/measurement of elastic torsional waves in a non-ferromagnetic aluminum cylinder. In doing so, the effects of the grating size and distance on the frequency-tuning characteristics are studied. Although the employed transduction principle is the magnetostrictive principle used in the existing surface acoustic wave devices which are magnetostrictively transduced, the magnetostrictive nickel grating in our transducer configuration served not as electrical conductors but as deforming elements. The transduction frequency was controlled by the grating distance and the wireless wave generation/measurement was carried out employing solenoid coils encircling a nickel-grated cylinder. In addition, two small permanent magnets were installed to adjust the wave propagation direction. © 2005 Elsevier B.V. All rights reserved. Keywords: Nickel grating; Magnetostriction; Frequency-tuned; Torsional wave; Transducer
1. Introduction The magnetostrictive generation of guided elastic waves [1–4] and surface acoustic waves [5–8] has been studied as an alternative to piezoelectric generation [9]. For the generation of the magnetostrictively transduced surface waves, an alternating current is passed through conducting meander lines or gratings that are placed on the top of a magnetic base plate, such as an yttrium iron garnet (YIG) base plate. These plates are deformed by the magnetic field developed in the conductors [10,11]. The spacing of the meander lines and the grating distance can tune the generated elastic waves to a given frequency. In most magnetostrictive elastic wave generation devices, the gratings and meander lines are used as the conducting elements, and not as deforming elements, so they are directly wired to the electrical supply. To avoid the need for direct wiring and to investigate the possibility of wireless frequency-tuned wave generation and measurement, we must consider to use a grating as the deform-
∗
Corresponding author. E-mail address: [email protected] (Y.Y. Kim).
0924-4247/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2005.09.027
ing elements, and not only as conducting elements. This means that the gratings are required to be made of a magnetic material, and not just of a conducting one, and that the elastic waves generated in the base plate arise from the elastic deformation of the gratings. In this work, we selected nickel as the grating material, and non-ferromagnetic aluminum as the base material. Solenoid coils encircling the nickel grating supply a magnetic field to them. If our wireless generation and measurement are successful, elastic waves propagating in plates submerged in a liquid can be measured. Furthermore, solenoid coils can be made on a much larger scale, even if the grated plates are fabricated on a micro scale. In consideration of this long-term research goal, we investigated an initial simple case: wireless elastic torsional wave generation and measurement in an aluminum cylinder in the frequency range of a few kilohertz to several hundred kilohertz. 2. Experiments A photograph of the nickel strip-grated aluminum cylinder and the configuration of the nickel gratings are shown in Fig. 1. The schematic diagram of the experimental setup is also shown in Fig. 2. The wave generation and measurement
74
I.K. Kim, Y.Y. Kim / Sensors and Actuators A 126 (2006) 73–77
Fig. 1. Experimental setup: nickel gratings attached to a hollow aluminum cylinder (outer radius a = 12.5 mm, inner radius b = 11.5 mm).
Fig. 2. A schematic diagram of the experimental setup and the transducer locations.
setup shown in Fig. 2 can be used for the nondestructive evaluation of pipes, but the experiment depicted in Figs. 1 and 2 will be viewed as a low-frequency counterpart to a high-frequency surface wave generation experiment. In our investigation, the grating was bonded to the aluminum cylinder using epoxy resin. Two Nd–Fe–B permanent magnets, attached at the side of the cylinder (Fig. 1), were used to provide a circumferential uniform static magnetic field. The superposition of the axial alternating magnetic field from the solenoid coils and the circumferential field from the magnets generates torsional waves in the axial direction. The related mechanics is briefly illustrated in Fig. 3. The main advantage of using torsional waves is that the first
branch of the dispersion curve of the torsional waves is nondispersive. This superposition technique has been used in pipe inspection applications, where a nickel strip that was almost as long as the cylinder’s circumference was bonded circumferentially and pre-magnetized in the circumferential direction by directional rubbing with a permanent magnet [12]. The solenoid coils encircling the nickel grating are shown in Fig. 2, and these could be used as both wave transmitting and wave receiving coils. However, we used two sets of the same nickel grating to facilitate the experimental measurements. In our experiments, narrow-band Gabor pulses were sent through the coils at Point A, and were measured by the coils at Point B. The definition of the Gabor pulse, s(t), as a function of time, t,
Fig. 3. Generation of torsional waves: The superposition of the axial alternating magnetic field from the solenoid coils and the circumferential field from the magnets generates torsional waves in the axial direction.
I.K. Kim, Y.Y. Kim / Sensors and Actuators A 126 (2006) 73–77
75
is given by s(t) =
1 1/4
(σ 2 π)
t2 exp − 2 eiηt 2σ
(1)
where η is the center frequency of the pulse. The pulse shaping parameter, σ, was selected as σ = 5.0/η, as this value enables a good balance between the time and frequency localizations to be achieved [13]. 3. Results and discussion Several experiments were conducted using the nickel gratings, but an investigation into the frequency-tuning capability of the wireless nickel-grating technique was the main research aim. Fig. 4 shows a typical signal (voltage output) measured by the solenoid coils at Point B. The signal in Fig. 4 was obtained for the width of each grating strip, w = 4 mm, grating distance, d = 6 mm, η = 490 kHz, and the number of strips, n = 3. Pulse 1 is the torsional wave propagated over distance AB, and Pulse 2 is the reflected pulse from the end of the cylinder, C. exp The experimentally estimated torsional wave speed, cT , was exp cT = 3150 m/s, which agrees well with the theoretical wave theory speed, cT = 3180 m/s [14,15], of the first branch of torsional waves in the hollow aluminum cylinder. This figure may be sufficient to show the successful generation and measurement of torsional waves using our proposed wireless method. Signals measured at other frequencies resembled those shown in Fig. 4. To investigate the frequency-tuning characteristics of the nickel gratings, two sets of experiments were conducted: one set for a single strip with various strip widths (w), and another set using a grating (with the number of strips equal to three) with various grating distances (d). Fig. 5 shows the frequency response of the proposed transducer configuration for a single strip. To facilitate the comparison of the frequency characteristics of each transducer for different grating distances, the measured voltage, V, at Point B was normalized to its peak value, Vpeak . It is clear that for a given strip width, there are certain tuning frequencies at which the response is at a maximum. By using
Fig. 5. The frequency response of single-strip transducers with strip widths equal to 25, 10, and 5 mm.
the well-known frequency–wavelength relationship of f = cT /λ, where f = frequency, and λ = wavelength, and the experimentally exp determined torsional wave speed of cT = 3150 m/s, the data in Fig. 5 show that λ/2w = 1.36, 1.12, and 1.05 for w = 5, 10, and 25 mm, respectively, at the tuned frequencies. Namely, the wavelength (λ) corresponding to the tuning frequency (f) approaches a value of twice the width of the single strip unless the width is very small. Obviously, the signal output and the tuning frequency concentration can be improved if more than one strip are used. Fig. 6 shows the frequency responses for three-strip grating transducer. The same voltage normalization used for Fig. 5 was also employed in this case. The grating distance (d) was varied from 6 to 12 mm. As expected, the grating distance affects the tuning frequency. More specifically, the relationship between the grating distance (d) and the tuning frequency (ftune ), which is the frequency giving the maximum response, was well predicted by pred using ftune ≈ cT /d. A comparison between the experimentally exp identified tuning frequency, ftune , and the predicted tuning frepred quency, ftune , is shown in Table 1. Note that the data presented in Table 1 were obtained for w = d/2. To estimate the effect of the strip width adjustment on the frequency response of the three-strip grating transducer, experiments were conducted for a fixed strip width of w = 4 mm (i.e., with various values of d, but with fixed w). The results are plotted in Fig. 6. The strip width affects the frequency characteristics of the three-strip grating transducer, but the effect is not significant, unless the difference between w and d/2 is very large. Table 1 A comparison between the theoretical and experimental results
Fig. 4. A typical signal measured at the Point B for a grating distance d = 6 mm, with a center frequency of η = 490 kHz.
pred
exp
d (mm)
ftune (kHz)
ftune (kHz)
6 8 10 12
520 390 310 260
490 380 300 250
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Fig. 6. The frequency characteristics of the proposed grating-type transducers for various grating distances, d (in mm). The strip widths in the grating were either fixed at w = 4 mm, or varied as w = d/2: (a) d = 6 mm, (b) d = 8 mm, (c) d = 10 mm, and (d) d = 12 mm.
4. Conclusions The results of this investigation are as follows. First, wireless frequency-tuned generation and measurement of elastic waves is possible in a nickel-grated aluminum cylinder. With a transducer configuration consisting of a magnetostrictive nickel grating, permanent magnets, and solenoid coils, torsional waves were successfully generated and measured. The width of a single strip affects the frequency-tuning characteristics of the transducer, but the key tuning parameter is the grating distance. These results agree with those observed for wired magnetostrictive surface acoustic generation devices. It is expected that the technique here investigated may be also used for developing surface acoustic filters in a much higher frequency range, and work in this area is in progress.
Acknowledgement This work is supported by the Creative Research Initiatives Program of the Korea Ministry of Science and Technology.
References [1] D.C. Jiles, Theory of the magnetomechanical effect, J. Phys. D 28 (1995) 1537–1546. [2] H.C. Lee, Y.Y. Kim, Wave selection using a magnetomechanical sensor in a solid cylinder, J. Acoust. Soc. Am. 112 (3) (2002) 953– 960. [3] H. Kwun, C.M. Teller, Magnetostrictive generation and detection of longitudinal, torsional, and flexural waves in a steel rod, J. Acoust. Soc. Am. 96 (2) (1994) 1202–1204. [4] H. Kwun, K.A. Bartels, Magnetostrictive sensor technology and its applications, Ultrasonics 36 (1998) 171–178. [5] K.A. Ellis, R.B. van Dover, T.J. Klemmer, G.B. Alers, Magnetically transduced surface acoustic wave devices, J. Appl. Phys. 87 (9) (2000) 6304–6306. [6] F.W. Voltmer, R.M. White, C.W. Turner, Magnetostrictive generation of surface elastic waves, Appl. Phys. Lett. 15 (1969) 153–154. [7] T.-L. Tsai, S.D. Wu, G. Thomas, H.S. Tuan, Excitation of magnetoacoustic surface waves by meander lines, J. Appl. Phys. 48 (1977) 4687– 4693. [8] W.P. Robbins, J. Bowers, Comparison of the grating and meander-line transducers for magnetoelastic surface-wave excitation, J. Appl. Phys. 50 (1979) 78–80. [9] J.W. Gardner, V.K. Varadan, O.O. Awadelkarim, Microsensors, MEMS and Smart Devices, Wiley, New York, 2001.
I.K. Kim, Y.Y. Kim / Sensors and Actuators A 126 (2006) 73–77 [10] R. Murayama, K. Mizutani, Conventional electromagnetic acoustic transducer development for optimum lamb wave modes, Ultrasonics 40 (2002) 491–495. [11] M. Hirao, H. Ogi, EMATs for Science and Industry: Noncontacting Ultrasonic Measurements, Kluwer Academic Publishers, London, 2003. [12] H. Kwun, US Patent 6,429,650 B1 (2002). [13] J.-C. Hong, K.H. Sun, Y.Y. Kim, The matching pursuit approach based on the modulated-Gaussian pulse for efficient guided-wave damage inspection, Smart Mater. Struct. 14 (2005) 548–560. [14] K.F. Graff, Wave Motion in Elastic Solids, Ohio State Univesity Press, 1975. [15] J.L. Rose, Ultrasonic Waves in Solid Media, Cambridge University Press, New York, 1999.
Biographies Ik Kyu Kim received his BS degree from Seoul National University, Department of Biosystems and Biomaterials Science and Engineering and
77
his MS degree from Seoul National University, School of Mechanical and Aerospace Engineering in 2002. He has been on the PhD candidate in Seoul National University since 2002. He is also the researcher of the national creative research initiatives center for multiscale design designated by the Korea Ministry of Science and Technology. His scientific interests are magnetostriction, ultrasonic waves, and sensor/transducer technology. Yoon Young Kim received his BS and MS degrees from Seoul National University and his PhD degree from Stanford University, Department of Mechanical Engineering, 1989. He has been on the faculty of School of Mechanical and Aerospace Engineering, Seoul National University since 1991. He is also the director of the national creative research initiatives center for multiscale design designated by the Korea Ministry of Science and Technology. His research areas include multiphysics system design and sensor/transducer technology.
Wireless frequency-tuned generation and measurement of torsional waves using magnetostrictive nickel gratings in cylinders Ik Kyu Kim, Yoon Young Kim ∗ School of Mechanical and Aerospace Engineering and Multiscale Design Center of the Institute of Advanced Machinery Design, Seoul National University, Sillim-Dong San 56-1, Kwanak-Gu, Seoul 151-742, Korea Received 12 January 2005; received in revised form 16 August 2005; accepted 20 September 2005 Available online 3 November 2005
Abstract The objective of this work is to experimentally investigate the possibility of using a magnetostrictive nickel grating for frequency-tuned wireless generation/measurement of elastic torsional waves in a non-ferromagnetic aluminum cylinder. In doing so, the effects of the grating size and distance on the frequency-tuning characteristics are studied. Although the employed transduction principle is the magnetostrictive principle used in the existing surface acoustic wave devices which are magnetostrictively transduced, the magnetostrictive nickel grating in our transducer configuration served not as electrical conductors but as deforming elements. The transduction frequency was controlled by the grating distance and the wireless wave generation/measurement was carried out employing solenoid coils encircling a nickel-grated cylinder. In addition, two small permanent magnets were installed to adjust the wave propagation direction. © 2005 Elsevier B.V. All rights reserved. Keywords: Nickel grating; Magnetostriction; Frequency-tuned; Torsional wave; Transducer
1. Introduction The magnetostrictive generation of guided elastic waves [1–4] and surface acoustic waves [5–8] has been studied as an alternative to piezoelectric generation [9]. For the generation of the magnetostrictively transduced surface waves, an alternating current is passed through conducting meander lines or gratings that are placed on the top of a magnetic base plate, such as an yttrium iron garnet (YIG) base plate. These plates are deformed by the magnetic field developed in the conductors [10,11]. The spacing of the meander lines and the grating distance can tune the generated elastic waves to a given frequency. In most magnetostrictive elastic wave generation devices, the gratings and meander lines are used as the conducting elements, and not as deforming elements, so they are directly wired to the electrical supply. To avoid the need for direct wiring and to investigate the possibility of wireless frequency-tuned wave generation and measurement, we must consider to use a grating as the deform-
∗
Corresponding author. E-mail address: [email protected] (Y.Y. Kim).
0924-4247/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2005.09.027
ing elements, and not only as conducting elements. This means that the gratings are required to be made of a magnetic material, and not just of a conducting one, and that the elastic waves generated in the base plate arise from the elastic deformation of the gratings. In this work, we selected nickel as the grating material, and non-ferromagnetic aluminum as the base material. Solenoid coils encircling the nickel grating supply a magnetic field to them. If our wireless generation and measurement are successful, elastic waves propagating in plates submerged in a liquid can be measured. Furthermore, solenoid coils can be made on a much larger scale, even if the grated plates are fabricated on a micro scale. In consideration of this long-term research goal, we investigated an initial simple case: wireless elastic torsional wave generation and measurement in an aluminum cylinder in the frequency range of a few kilohertz to several hundred kilohertz. 2. Experiments A photograph of the nickel strip-grated aluminum cylinder and the configuration of the nickel gratings are shown in Fig. 1. The schematic diagram of the experimental setup is also shown in Fig. 2. The wave generation and measurement
74
I.K. Kim, Y.Y. Kim / Sensors and Actuators A 126 (2006) 73–77
Fig. 1. Experimental setup: nickel gratings attached to a hollow aluminum cylinder (outer radius a = 12.5 mm, inner radius b = 11.5 mm).
Fig. 2. A schematic diagram of the experimental setup and the transducer locations.
setup shown in Fig. 2 can be used for the nondestructive evaluation of pipes, but the experiment depicted in Figs. 1 and 2 will be viewed as a low-frequency counterpart to a high-frequency surface wave generation experiment. In our investigation, the grating was bonded to the aluminum cylinder using epoxy resin. Two Nd–Fe–B permanent magnets, attached at the side of the cylinder (Fig. 1), were used to provide a circumferential uniform static magnetic field. The superposition of the axial alternating magnetic field from the solenoid coils and the circumferential field from the magnets generates torsional waves in the axial direction. The related mechanics is briefly illustrated in Fig. 3. The main advantage of using torsional waves is that the first
branch of the dispersion curve of the torsional waves is nondispersive. This superposition technique has been used in pipe inspection applications, where a nickel strip that was almost as long as the cylinder’s circumference was bonded circumferentially and pre-magnetized in the circumferential direction by directional rubbing with a permanent magnet [12]. The solenoid coils encircling the nickel grating are shown in Fig. 2, and these could be used as both wave transmitting and wave receiving coils. However, we used two sets of the same nickel grating to facilitate the experimental measurements. In our experiments, narrow-band Gabor pulses were sent through the coils at Point A, and were measured by the coils at Point B. The definition of the Gabor pulse, s(t), as a function of time, t,
Fig. 3. Generation of torsional waves: The superposition of the axial alternating magnetic field from the solenoid coils and the circumferential field from the magnets generates torsional waves in the axial direction.
I.K. Kim, Y.Y. Kim / Sensors and Actuators A 126 (2006) 73–77
75
is given by s(t) =
1 1/4
(σ 2 π)
t2 exp − 2 eiηt 2σ
(1)
where η is the center frequency of the pulse. The pulse shaping parameter, σ, was selected as σ = 5.0/η, as this value enables a good balance between the time and frequency localizations to be achieved [13]. 3. Results and discussion Several experiments were conducted using the nickel gratings, but an investigation into the frequency-tuning capability of the wireless nickel-grating technique was the main research aim. Fig. 4 shows a typical signal (voltage output) measured by the solenoid coils at Point B. The signal in Fig. 4 was obtained for the width of each grating strip, w = 4 mm, grating distance, d = 6 mm, η = 490 kHz, and the number of strips, n = 3. Pulse 1 is the torsional wave propagated over distance AB, and Pulse 2 is the reflected pulse from the end of the cylinder, C. exp The experimentally estimated torsional wave speed, cT , was exp cT = 3150 m/s, which agrees well with the theoretical wave theory speed, cT = 3180 m/s [14,15], of the first branch of torsional waves in the hollow aluminum cylinder. This figure may be sufficient to show the successful generation and measurement of torsional waves using our proposed wireless method. Signals measured at other frequencies resembled those shown in Fig. 4. To investigate the frequency-tuning characteristics of the nickel gratings, two sets of experiments were conducted: one set for a single strip with various strip widths (w), and another set using a grating (with the number of strips equal to three) with various grating distances (d). Fig. 5 shows the frequency response of the proposed transducer configuration for a single strip. To facilitate the comparison of the frequency characteristics of each transducer for different grating distances, the measured voltage, V, at Point B was normalized to its peak value, Vpeak . It is clear that for a given strip width, there are certain tuning frequencies at which the response is at a maximum. By using
Fig. 5. The frequency response of single-strip transducers with strip widths equal to 25, 10, and 5 mm.
the well-known frequency–wavelength relationship of f = cT /λ, where f = frequency, and λ = wavelength, and the experimentally exp determined torsional wave speed of cT = 3150 m/s, the data in Fig. 5 show that λ/2w = 1.36, 1.12, and 1.05 for w = 5, 10, and 25 mm, respectively, at the tuned frequencies. Namely, the wavelength (λ) corresponding to the tuning frequency (f) approaches a value of twice the width of the single strip unless the width is very small. Obviously, the signal output and the tuning frequency concentration can be improved if more than one strip are used. Fig. 6 shows the frequency responses for three-strip grating transducer. The same voltage normalization used for Fig. 5 was also employed in this case. The grating distance (d) was varied from 6 to 12 mm. As expected, the grating distance affects the tuning frequency. More specifically, the relationship between the grating distance (d) and the tuning frequency (ftune ), which is the frequency giving the maximum response, was well predicted by pred using ftune ≈ cT /d. A comparison between the experimentally exp identified tuning frequency, ftune , and the predicted tuning frepred quency, ftune , is shown in Table 1. Note that the data presented in Table 1 were obtained for w = d/2. To estimate the effect of the strip width adjustment on the frequency response of the three-strip grating transducer, experiments were conducted for a fixed strip width of w = 4 mm (i.e., with various values of d, but with fixed w). The results are plotted in Fig. 6. The strip width affects the frequency characteristics of the three-strip grating transducer, but the effect is not significant, unless the difference between w and d/2 is very large. Table 1 A comparison between the theoretical and experimental results
Fig. 4. A typical signal measured at the Point B for a grating distance d = 6 mm, with a center frequency of η = 490 kHz.
pred
exp
d (mm)
ftune (kHz)
ftune (kHz)
6 8 10 12
520 390 310 260
490 380 300 250
76
I.K. Kim, Y.Y. Kim / Sensors and Actuators A 126 (2006) 73–77
Fig. 6. The frequency characteristics of the proposed grating-type transducers for various grating distances, d (in mm). The strip widths in the grating were either fixed at w = 4 mm, or varied as w = d/2: (a) d = 6 mm, (b) d = 8 mm, (c) d = 10 mm, and (d) d = 12 mm.
4. Conclusions The results of this investigation are as follows. First, wireless frequency-tuned generation and measurement of elastic waves is possible in a nickel-grated aluminum cylinder. With a transducer configuration consisting of a magnetostrictive nickel grating, permanent magnets, and solenoid coils, torsional waves were successfully generated and measured. The width of a single strip affects the frequency-tuning characteristics of the transducer, but the key tuning parameter is the grating distance. These results agree with those observed for wired magnetostrictive surface acoustic generation devices. It is expected that the technique here investigated may be also used for developing surface acoustic filters in a much higher frequency range, and work in this area is in progress.
Acknowledgement This work is supported by the Creative Research Initiatives Program of the Korea Ministry of Science and Technology.
References [1] D.C. Jiles, Theory of the magnetomechanical effect, J. Phys. D 28 (1995) 1537–1546. [2] H.C. Lee, Y.Y. Kim, Wave selection using a magnetomechanical sensor in a solid cylinder, J. Acoust. Soc. Am. 112 (3) (2002) 953– 960. [3] H. Kwun, C.M. Teller, Magnetostrictive generation and detection of longitudinal, torsional, and flexural waves in a steel rod, J. Acoust. Soc. Am. 96 (2) (1994) 1202–1204. [4] H. Kwun, K.A. Bartels, Magnetostrictive sensor technology and its applications, Ultrasonics 36 (1998) 171–178. [5] K.A. Ellis, R.B. van Dover, T.J. Klemmer, G.B. Alers, Magnetically transduced surface acoustic wave devices, J. Appl. Phys. 87 (9) (2000) 6304–6306. [6] F.W. Voltmer, R.M. White, C.W. Turner, Magnetostrictive generation of surface elastic waves, Appl. Phys. Lett. 15 (1969) 153–154. [7] T.-L. Tsai, S.D. Wu, G. Thomas, H.S. Tuan, Excitation of magnetoacoustic surface waves by meander lines, J. Appl. Phys. 48 (1977) 4687– 4693. [8] W.P. Robbins, J. Bowers, Comparison of the grating and meander-line transducers for magnetoelastic surface-wave excitation, J. Appl. Phys. 50 (1979) 78–80. [9] J.W. Gardner, V.K. Varadan, O.O. Awadelkarim, Microsensors, MEMS and Smart Devices, Wiley, New York, 2001.
I.K. Kim, Y.Y. Kim / Sensors and Actuators A 126 (2006) 73–77 [10] R. Murayama, K. Mizutani, Conventional electromagnetic acoustic transducer development for optimum lamb wave modes, Ultrasonics 40 (2002) 491–495. [11] M. Hirao, H. Ogi, EMATs for Science and Industry: Noncontacting Ultrasonic Measurements, Kluwer Academic Publishers, London, 2003. [12] H. Kwun, US Patent 6,429,650 B1 (2002). [13] J.-C. Hong, K.H. Sun, Y.Y. Kim, The matching pursuit approach based on the modulated-Gaussian pulse for efficient guided-wave damage inspection, Smart Mater. Struct. 14 (2005) 548–560. [14] K.F. Graff, Wave Motion in Elastic Solids, Ohio State Univesity Press, 1975. [15] J.L. Rose, Ultrasonic Waves in Solid Media, Cambridge University Press, New York, 1999.
Biographies Ik Kyu Kim received his BS degree from Seoul National University, Department of Biosystems and Biomaterials Science and Engineering and
77
his MS degree from Seoul National University, School of Mechanical and Aerospace Engineering in 2002. He has been on the PhD candidate in Seoul National University since 2002. He is also the researcher of the national creative research initiatives center for multiscale design designated by the Korea Ministry of Science and Technology. His scientific interests are magnetostriction, ultrasonic waves, and sensor/transducer technology. Yoon Young Kim received his BS and MS degrees from Seoul National University and his PhD degree from Stanford University, Department of Mechanical Engineering, 1989. He has been on the faculty of School of Mechanical and Aerospace Engineering, Seoul National University since 1991. He is also the director of the national creative research initiatives center for multiscale design designated by the Korea Ministry of Science and Technology. His research areas include multiphysics system design and sensor/transducer technology.