E-Journal of Advanced Maintenance Vol.2 (2010/2011) 34-42
Japan Society of Maintenology

Monitoring System for Pipe Wall Thinning Management using
Electromagnetic Acoustic Transducer
Daigo KOSAKA1, Fumio KOJIMA2,*, Hiroshi YAMAGUCHI2,, and Kosuke UMETANI3
1

Graduate School of Engineering, Kobe University, 1-1 Rokkodai-cho, Nada-ku,Kobe 657-8501,
Japan
2
Organization of Advanced Science and Technology, Kobe University, 1-1 Rokkodai-cho,Nada-ku,Kobe 657-8501, Japan
3
Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku,Kobe
657-8501, Japan.

(Received; April 25th, 2010)

Abstract. This paper demonstrates the effectiveness and feasibility of monitoring system for pipe wall thinning
using electromagnetic acoustic transducer (EMAT). The proposed EMAT system provides no contact, highresolution measurement, and remote capability of inspection procedures. First, a simulation based analysis isperformed to study the measurement sensitivities with respect to pipe wall thinning. Secondly, taking into
account that FAC damage is extended into the downstream of orifice, verification tests are implemented basedon thickness measurements at grid points on the outer surface of pipe. Various type of test pipes with FAC
damage model were provided for our laboratory experiments. Finally, the validity and the feasibility of our
proposed method are demonstrated through the practical test at the real plant.
KEYWORDS: nondestructive test, condition monitoring, on-line monitoring, flow accelerated corrosion,cavitation and erosion

1.

Introduction

Pipe wall thinning management in nuclear power plants is aimed at providing a life
management process ensuring replacement or repair prior to in-service failure. The inspection
techniques for pipe wall thinning management are ultrasonic testing (UT), radiographic testing(RT), and pulse-eddy current testing (PEC), etc. Among them, UT technique provides the accurate
resolution for the pipe wall thickness measurement. The main objective of UT inspection is to
identify the location of maximum thinning, to ascertain the extent and depth of the thinning, andto evaluate the wear rate. Figure 1 illustrates the flow chart of JSME rules on pipe wall thinning
management for PWR power plants [1]. As depicted in Fig. 1, the recommended inspection
process consists of marking a grid pattern on the components and using the appropriate ultrasonictransducer and data acquisition equipment to take wall thickness measurements at the grid
inspection points. Those inspection procedures are performed during a unit outage with insulation
removed from the piping area. There also exist so many inaccessible locations for the in-situ
inspection by surveyors in practical plants. Electromagnetic acoustic transducer (EMAT) has several
advantages on inspection techniques compared with UT approach [2-6]. EMAT is an economical andsimple inspection device that is composed of electrical coils and permanent magnets. Since EMAT
is equipped with permanent magnets, it is possible to allocate self-holding sensors on carbon steel
pipes during operations. Moreover, various kinds of testing signal can be automatically reproduced
by electrical circuits without human experts unlike conventional ultrasonic non-destructive testing.
Those advantages allow the remote capabilities of inspection performance and, as a result, theinspection technique using EMAT is feasible for continuous surveillance of pipe wall thinning.
*

Corresponding author, E-mail: kojima@koala.kobe-u.ac.jp

ISSN – 1883 – 9894/10/11 © 2010/2011 – JSM and the authors. All rights reserved.

34

D. KOSAKA et al./ Monitoring System for Pipe Wall Thinning Management
using Electromagnetic Acoustic Transducer

Eight-point measurements for large
diameter pipe (A150 or larger)

Normal measurement policy
Threshold thickness

t m = t sr +Standard CA-2310 survey

tn: minimum thickness
tsr: safety requirementYestmeasure > tm

52
(t n − t sr )
3

4

6

3

7

2

1

8

Detailed CA-2320 survey
No
Thinning rate

CA-3000 Evaluation framework

Measurement pitch with 20[mm]Fig.1. JSME rules on pipe wall thinning management for PWR power plants

Taking into account those effects, we propose an on-line monitoring of pipe wall thinning using
EMAT. This paper is organized as follows. First, a simulation based analysis is performed to study themeasurement sensitivities with respect to pipe wall thinning. Secondly, taking into account that FAC
damage is extended into the downstream of orifice, verification tests are implemented based on
thickness measurements at grid points on the outer surface of pipe. Test pipes with FAC damage
model were provided for our laboratory experiments. Finally, the validity and the feasibility of our
proposed method are demonstrated through the practical test at the real plant.
2.

Analysis of pipe wall thickness measurement

Let us assume that the electromagnetic fields are two-dimensional spatial domain. The vector
potential and the applied current are approximated as A = (0,0, Az ) J = (0,0, J z ) . Our inspection
procedure is governed by an electromagnetic-acoustic coupling equations. Let Ω and Ωc be theinspection area and a sample specimen and let⎧ Ac in Ωc × T
Az = ⎨ air zin (Ω − Ωc ) × T
⎩ Az

(1)

be the z-component of the electromagnetic vector potential. Then the transmitted signal is generated
by the following the initial boundary value problem:− ∇ ⋅ν (B )∇Az + σ∂Az= 0 in Ωc × T
∂t

−

1

μ0

∇ 2 Az = J z

in (Ω − Ωc ) × T(2)

together with the initial and boundary conditions. Then the corresponding ultrasonic testing wave isgoverned by the following linear elastic problem:ρ∂ 2u− (2G + λ )∇(∇ ⋅ u ) + G∇ × (∇ × u ) = f
∂t 2

35

in (Ω − Ωc ) × T(3)

D. KOSAKA et al./ Monitoring System for Pipe Wall Thinning Management
using Electromagnetic Acoustic Transducer

The excitation of ultrasonic testing signal is mainly governed by three force mechanisms (See[2] for more details) :f = f L + f M + f MS = J e × B e + (∇ × B ) ⋅ M e + ∇ ⋅ TMS

in (Ω − Ωc ) × T(4)where f L , f M and f MS denote Lorentz force in conductors, a direct interaction between themagnetization of the material and the applied field, and the magnetostrictive mechanism. Moreprecisely, J e , B e , M e and TMS imply the eddy current generated by the coil, the magnetic flux density
driven by EMAT, the bias magnetization of the material, and the magnetostrictive stress tensor,
respectively. The reflected and transmitted waves produce the eddy current nearby sub-surface given by− ∇ ⋅ν (B )∇Aez + σ
−

1

μ0

∂Aez
⎛ ∂u
⎞
= σ ⎜ × Be ⎟k in Ωc × T
∂t
⎝ ∂t
⎠

(5)

∇ Az = 0 in (Ω − Ωc ) × T
2

Thus the detecting voltage of EMAT is characterized by
L

L

(

)

V = −∑ ∫ (∇ × A ) ⋅ ds = −∑ Azair (t , ri ) − Azair (t , li ) di .
i =1

Ci

i =1

(6)

For convenience of discussions, the numerical treatment of wave propagation behavior of piping
system (1-5) is restricted to austenitic stainless steel (SUS304). Since this material is non magnetic
material, the ultrasound source (4) is mainly governed by the Lorentz force:f ≅ f L = J e × Be

in (Ω − Ωc ) × T .

(7)and the magnetic resistivity in (2) and (5) becomes ν (B ) = 1 μ0 . As illustrated in Fig. 2, thecorrosion model is given by a polar coordinate function with piecewise linear splines:Mc(θ ,q ) = ∑ qiM BiM (θ ) q0L ≤ θ ≤ qoR .

(8)

i =1

To discretize the system model (1-5) by a finite element method, the reference domain Ω isdivided into a finite number of elements as shown in Fig. 3. The number of finite elements and nodes
in the numerical experiments reported on here were set as 252384 and 253680, respectively. The
method of mapping technique is adopted for solving the system model [7, 8]. Consequently, thenumerical solution of wave front analysis can be implemented by solving a set of the ordinary{ }M

differential equations with defect parameter set q = qiM i =1 . Figure 4 shows sample animations ofwave propagation behavior inside pipe wall. As shown in Fig. 4(a), if the excitation of the ultrasoundsource is applied to the outer surface of no wall thinning area, the raypath of upgoing and downgoingwaves can take the radius direction of pipe. However, in the case where the excitation is applied to theouter surface of the corrosion area as shown in Fig. 4(b), the raypath becomes scattered to thecircumferential direction as well as radius one. Figure 5 depicts the test pipe sample fabricated tosimulate corrosion shape. The corrosion model is characterized by ellipsoidal shape with two radiusparameters (a, b ) . Figure 6 demonstrates a numerical result and synthetic measurement signal using
pulse-echo method corresponding to Fig. 5(b) with a =40 [mm] and b = 3 [mm]. The sensor was
allocated at the center of corrosion. Two test pipes were examined in our experiments. The nominal

36

D. KOSAKA et al./ Monitoring System for Pipe Wall Thinning Management
using Electromagnetic Acoustic Transducer

wall thickness of each sample was chosen as 17 [mm] and 20 [mm], respectively. The time of flight(TOF) related to the sound speed of signal propagation for downstream and upstream of flow can bederived from the time interval of peak-to-peak voltages. As shown in Fig. 6, the simulation result
demonstrates good agreement with the experimental data. Since the existence of corrosion affects thepulse-echo signal, the geometrical shape of corrosion can be found by profiling the collection ofpeak-to-peak voltages included in measurement signals. We have proposed the scanning method for
detecting pipe wall thinning area in [9]. Moreover, the inverse analysis using the measurement model
as stated in this section has been proposed in [10]. Although received EMAT signals from back-wallecho are distinguishing high in amplitude, pulse-echo method becomes quite crucial in case of thinpipe. Due to the limitation of sensor structure, it is noted that the use of pulse-echo method in EMAT
is limited to on-site inspections. In the next section, we consider an alternative thickness measurement
strategy using electromagnetic acoustic resonance method (EMAR) [11, 12].

Fig.2. Corrosion model of pipe wall thinning

Fig. 3. The decomposition of the finite elements(a) wave propagation with respect to(b) wave propagation with respect tothe excitation outside corrosion
the corrosion area
Fig. 4. Wave propagation behaviorab(a) SUS304 test pipe fabricated(b) Corrosion model with two
to simulate corrosions
Parameters (a, b)
Fig. 5. Test pipe used in the experiments

37

D. KOSAKA et al./ Monitoring System for Pipe Wall Thinning Management
using Electromagnetic Acoustic Transducer

0.5

0.5
20mm

0.4

17mm

0.3

0.2

0.2
Signal (V) .

Signal (V) .

20mm

0.4

17mm

0.3
0.1
0
-0.1

0.1
0
-0.1

-0.2

-0.2

-0.3

-0.3

-0.4

-0.4

-0.5

-0.5
0

10

20

Time (μs)

30

40

50

0

(a) experimental results

10

20Time (μs)

30

40

50

(b) simulation results

Fig. 6. Comparative results between measurement and simulation experiments(a = 40[mm], b=3[mm], wall thickness 17 [mm], 2-[mm])3.

Thickness Measurements of Pipe Wall

3.1 Experimental Set-up
The whole experimental apparatus for thickness measuring is shown in Fig. 7. It is composed ofan EMAT, a pulsar receiver (RPR-4000 RITEC Inc.), an oscilloscope, and a computer for dataacquisition. The sensor is added to 800 [Vpp] by the pulser. The reflective waveforms are recorded by
a computer coupled to an oscilloscope. Figure 8 shows the photograph of EMAT used in our
experiments. The coil of EMAT is 80 turns embedded in a flexible substrate with 10[mm] diameter.
Two Neodymium magnets are used in the sensor. Magnetic flux density at the front surface is 0.5 [T].
3.2 Measurement Method by EMAR
Pulse-echo method is a fundamental technique in the conventional ultrasonic inspection byhuman experts. In order to apply EMAT to pipe wall thickness measurement, we require the remotecapability of inspection, reproducing the desired test signals, and the high resolution of thickness
measurements. Thickness measurement by pulse-echo method can be evaluated by

T=

vΔt
2

(9)

where T , v , and Δt denote thickness, sound velocity and TOF. As indicated in the previous
section, it is difficult to recognize TOF Δt for the case of thin pipe. Electromagnetic acoustic
resonance method (EMAR) is an alternative thickness measurement method based on frequency
domain. This can be derived from

T=

ν

(10)

2Δf

where Δf denotes a peak interval with respect to the frequency. It is very clear that, if T is smaller,
then Δt becomes smaller interval while Δf becomes larger interval. This implies that EMAR
method is more accurate measurement technique than pulse-echo method. Figure 9 illustrates
thickness measurements by EMAR. In our preliminary experiments, the resolution is up to 0.1 [mm]for carbon steel samples (SS400) with 3 to 5 [mm] thickness.

38

D. KOSAKA et al./ Monitoring System for Pipe Wall Thinning Management
using Electromagnetic Acoustic Transducer

Oscilloscope

Burst power supply

Diplexer

Aｍｐ.

input outpu

input outpu

BP
input

outp

EMAT
Test sample

Fig. 8. EMAT sensor

0.3

0.3

0.2

0.2

Sensor output (V)Sensor output (V)Fig. 7. Experimental setup

0.1
0
-0.1
-0.2
-0.3

0.1
0
-0.1
-0.2
-0.3

0

50

100
150
Time (µs)

200

250

0

(a) resonance signal

50

100
150
Time (µs)

200

250

(b) non resonance signal

0.02

Sensor output

4.7mm
0.015

0.343MHz

0.324MHz

5mm

0.01
0.005
0
0

0.5

1

1.5

2

2.5

3

Freq. (MHz)(c) resonance spectrum
Fig. 9. An illustration of thickness measurements by EMAR

3.3 Measurement experiments
In the series of experiments, carbon steel pipes (2B-SS400) were used and each sample wasfabricated to simulate FAC (10% and 50% notch samples) as illustrated in Fig. 11. The recommended
UT inspection process consists of marking a grid pattern on the components and using the appropriate
transducer and data acquisition equipment to take wall thickness measurements at the grid inspection
points. Those grid points can be usually determined by the dimension of pipe. In our experiments,
eight measurement points (a to h) were chosen with respect to the circumferential direction of pipeand sixteen circle sections (1 to 16) were set with respect to the axial direction of pipe. Totally, one
hundred twenty eight grid points were selected for measurements as indicated in Fig. 10. Table 1
summarizes measurement results. Thickness measurements by conventional UT technique were also
implemented for the comparative discussions. Figure 11 shows sizing results of pipe wall thinning by
EMAT. To date, we have used 6B-SS400 test pipes with three thinning models (0.5, 1.0, 2.0 [mm])and 2B-SS400 pipe samples with three thinning models (0.4, 0.5, 0.6 [mm]). Taking into account ofreal FAC manner, the geometry of those thinning models was given by ellipsoid shape with respect toaxial direction of pipe. In all case, the measurements performed as well as or better than it did in the
results listed here.

39

D. KOSAKA et al./ Monitoring System for Pipe Wall Thinning Management
using Electromagnetic Acoustic Transducer(a) Dimension of test pipe with wall thinning (2B-SS400, 10 % notch)(b) Laboratory experiments

Fig. 10. Experimental condition of thickness measurements by EMAR
Table 1. Results of thickness measurements by EMAT and UT(a) measurement section at one to eight
a
b
c
d
e
f
g

1

2

3

4

5

6

7

EMAT

4.88

4.88

4.30

4.29

4.91

4.91

4.94

8
4.95

UT

4.90

4.90

4.30

4.30

4.80

4.90

4.90

5.00

EMAT

4.88

4.87

4.33

4.34

4.90

4.92

4.92

4.95

UT

4.90

4.90

4.40

4.30

5.00

4.90

4.90

5.00

EMAT

4.89

UT
EMAT

4.84

UT
EMAT

4.95

UT
EMAT

5.07

UT
EMAT

4.83

UT

4.95

4.49

4.51

4.51

5.00

4.90

5.03

4.90

4.50

4.50

4.50

5.00

4.90

5.00

4.84

4.25

4.26

4.83

4.83

4.85

4.85

4.80

4.20

4.20

4.80

4.80

4.80

4.80

4.98

4.38

4.36

4.96

4.98

4.99

4.97

5.00

4.30

4.40

4.90

5.00

5.00

5.00

5.03

4.48

4.49

5.03

5.04

5.04

5.04

5.00

4.40

4.40

5.00

5.00

5.00

5.00

4.85

4.42

4.40

4.39

4.83

4.86

4.85

4.80

4.30

4.30

4.20

4.40

4.80

4.70

EMAT

4.86

4.88

4.46

4.45

4.90

4.91

4.91

4.94

UT

4.80

4.80

4.40

4.40

4.80

4.80

4.80

4.80

Design Value

5.00

5.00

4.50

4.50

4.50/5.00

5.00

5.00

5.00

h

(b) measurement section at nine to sixteen
9
a
b
c
d
e
f
g

10

11

12

13

14

15

16

EMAT

4.96

4.96

4.95

4.94

4.95

4.97

4.98

4.98

UT

5.00

4.90

5.00

4.90

4.90

5.00

5.00

5.00

EMAT

4.97

4.95

4.95

4.92

4.94

4.97

5.00

5.00

UT

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

EMAT

5.01

5.00

4.99

4.95

4.92

4.92

4.95

4.97

UT

5.00

5.00

5.00

4.90

4.90

4.90

5.00

5.00

EMAT

4.85

4.85

4.84

4.81

4.83

4.84

4.85

4.87

UT

4.80

4.80

4.80

4.80

4.80

4.80

4.80

4.90

EMAT

4.94

4.99

4.98

4.96

4.97

4.96

4.96

4.92

UT

4.90

4.90

5.00

4.90

5.00

5.00

5.00

4.90

EMAT

5.03

5.04

5.02

5.04

5.07

5.08

5.05

5.07

UT

5.00

5.00

5.00

4.90

5.00

5.00

5.00

5.00

EMAT

4.87

4.85

4.85

5.00

4.88

4.88

4.85

4.85

UT

4.80

4.70

4.80

4.90

4.90

4.90

4.90

4.90

EMAT

4.93

4.94

4.92

4.94

4.96

4.97

4.97

4.97

UT

4.90

4.80

4.80

4.80

4.90

4.90

4.90

4.90

Design Value

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

h

40

D. KOSAKA et al./ Monitoring System for Pipe Wall Thinning Management
using Electromagnetic Acoustic Transducer
5.50
5.00
Wall thickness (mm)

4.50
4.00

EMAT-a3.50

EMAT-b

3.00

EMAT-c

2.50

EMAT-d

2.00

EMAT-e1.50

EMAT-f

1.00

EMAT-g0.50

EMAT-h0.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Axial potision

Fig. 11. Sizing results of pipe wall thinning by EMAT

4.

Feasibility Studies

The feasibility studies of pipe wall thickness measurements by EMAR method were carried out inthe real plant of Fossil Power Engineering Center, Kansai Electric Power Co. Inc (KEPCO). The
evaluation of data from a large number of power inspections shows that FAC can extend into thepiping downstream of orifices. The prescribed fifty-six grid points were selected using JSME
management standard of pipe wall thinning [1] as indicated in Fig. 12. Table 2 summarizes themeasurement results by the conventional UT and by the proposed EMAT method. UT inspections
were performed by human experts of the plant and EMAT measurements were carried out by using
the exact same equipments at our laboratory. Compared with UT sizing results, maximum difference
between UT and EMAT measurements became 0.28 [mm], average difference was 0.08 [mm], andmedian was 0.07 [mm], respectively.

(a) experimental condition(b) measurement points

Fig. 12. Sizing methodology in the real plant at orifice downstream
Table 2. Measurement results in the real plant
1
a
b
c
d
e
f
g

2

3

4

5

6

7

8

EMAT

8.7

8.5

8.6

8.6

8.7

8.9

8.7

9.0

UT

8.8

8.7

8.6

8.6

8.7

8.8

8.8

8.9

EMAT

8.5

8.6

8.7

8.8

8.5

8.7

8.6

8.8

UT

8.6

8.7

8.5

8.8

8.7

8.5

8.7

8.8

EMAT

8.5

8.8

8.6

8.8

8.7

8.7

8.6

8.7

UT

8.5

8.8

8.7

8.8

8.9

8.8

8.7

8.8

EMAT

11.0

10.9

10.8

11.1

10.9

10.8

10.7

10.9

UT

11.0

11.0

10.9

11.0

10.7

10.9

10.9

11.1

EMAT

10.9

10.8

10.9

11.0

10.9

10.8

10.8

11.0

UT

10.9

10.9

10.9

11.0

11.1

11.0

10.9

11.0

EMAT

10.4

10.8

11.0

11.0

11.3

11.1

10.7

11.1

UT

10.7

10.9

11.0

11.1

11.4

11.0

10.9

11.0

EMAT

10.7

10.9

11.0

11.0

11.0

10.9

10.7

10.8

UT

11.0

11.0

11.0

11.1

11.1

10.9

10.8

11.0

41

D. KOSAKA et al./ Monitoring System for Pipe Wall Thinning Management
using Electromagnetic Acoustic Transducer

5.

Conclusions

The effectiveness and feasibility of monitoring system for pipe wall thinning using electromagnetic
acoustic transducer are discussed. Simulation based analysis were performed to study the measurement
sensitivities with respect to pipe wall thinning. The variety of computational results shows good agreementwith laboratory experimental results. Furthermore, numerical analysis for carbon steel pipe with wall
thinning has been successively tested using EMAR measurement method. The essential role of developing
simulator is to construct signal processor for recovering pipe wall thinning profiles. Our current research
direction is directed to the inverse analysis for implementing continuous surveillance of real power
plants. Taking into account that FAC damage is extended into the downstream of orifice, verification
tests were implemented based on thickness measurements at grid points on the outer surface of pipe.
Various type of test pipes with FAC damage model were provided for our laboratory experiments. The
validity and the feasibility of our proposed method were demonstrated through the practical test at thereal plant. Throughout the experimental results, we believe these provide rather conclusive evidence thatsizing methodology of pipe wall thickness can be successfully performed by our proposed method. We
are currently pursuing experimental investigations to further refine our methods as well as to test othertypes of piping structures (elbow, reducer, etc) and more realistic flaw types (FAC, LDI) with regard toease and accuracy in detection and characterization of pipe wall thinning using EMAT based methods.
Acknowledgement
This work has been performed as a part of the National Research Project for Enhancement of Measuresagainst the Ageing of Nuclear Power Plants sponsored by the Nuclear and Industrial Safety Agency (NISA).
The authors also gratefully acknowledge the Institute of Nuclear Safety System Inc (INSS) and the Fossil
Power Engineering Center, KEPCO for their assistance in the experimental works described in this paper.
References[1] The Japan Society for Mechanical Engineers, Codes for nuclear power generation facilities: Ruleson pipe wall thinning management for PWR power plants, Vol. JSME S NG-1 2006 (in Japanese).
[2] H.M. Fros, Electromagnetic-ultrasonic transducer: Principles, practice and applications, in: PhysicalAcoustics, Vol. 14, W.P. Mason and R.N. Thurston eds., Academic Press, New York, 1979, pp. 179-275.
[3] R.B. Thompson, Physical principles of measurements with EMAT transducers, in: PhysicalAcoustics, Vol.19, Academic Press, New York, 1990, pp. 157-200.
[4] B.W. Maxfield and C.M. Fortunko, The design and use of electromagnetic acoustic wave
transducers, in: Material Evaluation, Vol.41, 1983, pp. 1399-1408.
[5] K. Mirkhani et al. Optimal design of EMAT transmitters, in: NDT&E International, Vol. 37, 2004,
pp. 181–193.
[6] D. MacLauchlan, S. Clark, B. Cox, T. Doyle, and B. Grimmett, Recent advancements in theapplication of EMATs to NDE, in: Proc. of the 16th WCNDT 2004, Montreal, Canada.
[7] H.T. Banks, F. Kojima, and W.P. Winfree, Boundary estimation problems arising in thermal
tomography, Inverse Problems, 6(4), (1990), 897-921.
[8] H.T. Banks and F. Kojima, dentification of material damage in two dimensional domains using
SQUID based NDE System, Inverse Problems, 18(6) (2002), 1831-1855.
[9] D. Kosaka, F. Kojima, and H. Yamaguchi, Quantitative evaluation of wall thinning in pipe wallusing electromagnetic acoustic transducer, International Journal of Applied Electromagnetics andMecjhanics, to appear in 2010.
[10] D. T. Nguyen and F. Kojima, Identification of sub-surface defect parameters in plates using
electromagnetic acoustic interaction, International Journal of Applied Electromagnetics andMecjhanics, to appear in 2010.
[11] K. Kawashima, Very high frequency EMAT for resonant measurement, in: Proc IEEE UltrasonicSymposium, No. 2, 1994, pp.1111-1119.
[12] H. Ogi, “Field dependence of coupling efficiency between electromagnetic field and ultrasonicbulk waves”, J. Appl. Phys. 82 (8), 15, pp. 3940-3949, 1997.

42