REGULAR PAPER

Japanese Journal of Applied Physics 54, 07HE16 (2015)
http://dx.doi.org/10.7567/JJAP.54.07HE16

Linear array transducer for high-power airborne ultrasound using ﬂextensional structure
Jun Yamamoto, Yosuke Mizuno, Marie Tabaru, and Kentaro Nakamura
Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503, Japan
Received December 12, 2014; revised March 2, 2015; accepted April 6, 2015; published online June 29, 2015
To change the direction of ultrasonic irradiation without moving a transducer, a high-power airborne ultrasonic transducer for a one-dimensional
phased array system was designed and tested. A ﬂextensional element transducer with higher-mode bending vibration was fabricated to obtain ahigh vibration amplitude over a wide aperture, where a phase-compensating stepped structure was employed. The width of the main lobe at half
maximum and the sidelobe level were measured to be 14.3 deg and 0.78, respectively. The maximal sound pressure of 132 dB (0 dB re. 0.02 mPa)
was obtained under the applied voltage of 4.0 V. The beam steering characteristics of a phased array using eight elements were compared with thesimple theory. © 2015 The Japan Society of Applied Physics

1.

Introduction

There are many application ﬁelds of high-power airborne
ultrasound, such as noncontact levitation,1–7) nondestructive
testing,8–11) removal of solid or liquid particles,12–15) anddefoaming.16,17) In such ﬁelds, the frequency range from 20
to 40 kHz is practically used, and the sound pressure level
sometimes exceeds 160 dB. It is required that the direction ofradiation be changed quickly through an electrical signal for
precise control and increase in the eﬃciency of the target
process. For levitation applications, for example, it isrequired that the position of small objects or droplets beshifted in a linear direction by changing the direction ofultrasonic irradiation.1,3,5) High-power airborne ultrasound isusually generated by using a ﬂexural vibrating plate excitedby a Langevin transducer with a horn, the directivity of which
is ﬁxed.16–21) To change the direction of ultrasonic irradiation
linearly without moving the transducer, a one-dimensional
phased array system should be used.
Several studies have already been reported on a phasedarray for high-power airborne ultrasound, where conventionalcommercial ultrasonic sensors were integrated.7,22–27) However, the sound pressure of a commercial transducer islimited.23) The diameter of a sensor, usually approximately
10 mm, is larger than the wavelength in air, 8.5 mm at a
driving frequency of 40 kHz.28) Thus, it is diﬃcult to havea smaller spacing between two adjacent transducers, andunwanted grating lobes are generated. A conventional
airborne transducer is composed of a very thin aluminum
corn and a bending piezoelectric disc. The resonancefrequency is largely changed or the vibration displacement
is easily lowered, even if a droplet, for example, is attached to
the radiator corn. This structure is too fragile to be used forhandling liquid or for a harsh environment.
The objective of this study is to develop a high-power
ultrasonic transducer applicable for a one-dimensional phasedarray with a water-proof and dust-proof capability byeliminating any fragile structure. In this paper, we report
the ﬁrst prototype of the transducer, the fundamental
characteristics of the element transducer, and the test of thebeam steering operation for an eight-element array system,
introducing ﬂextensional and stepped structures.
2.

Structure of the linear array transducer

Figure 1 shows the conceptual structure of a one-dimensional
phased array system, which is composed of linearly arrayed

Fig. 1. (Color online) Conceptual conﬁguration of one-dimensional arrayand the coordinate system.

element transducers. The radiation surface of each element
has a long narrow rectangular shape.28) In this ﬁgure, the xaxis is the longer direction of the radiation surface, the y-axis
the arrayed direction, and the z-axis the radiation direction.
Beam steering is performed in the yz-plane through phaseddrive, and a small beam width is obtained in the xz-planeowing to the large beam width in the x-direction. The xlength of the radiation surface should be four or ﬁve times
the wavelength in air for the small beam width,29) while they-width of the radiation surface should be less than the
wavelength to inhibit the generation of grating lobes.28) In
this study, the working frequency is set at 30 kHz for the trial.
The thickness of the radiation surface for one element shouldbe less than the wavelength to inhibit the generation ofgrating lobes in phased-array operation. The width of theradiation surface is designed to be larger than ﬁve times the
wavelength to induce irradiation at angles conﬁned within
20–30 deg. Thus, the radiation surface was determined to be
70 × 5 mm2 in the prototyping. The thin rectangular radiation
surface is required to vibrate uniformly at a high vibration
amplitude to radiate the main beam in the z-direction.
However, it is generally diﬃcult to have a uniform vibration
over a large surface. On the other hand, higher-mode bending
vibrations in a ﬂextensional structure can be easily generated
on a bar at a high vibration amplitude;30) such vibrations havean out-of-phase amplitude and result in a split radiation
pattern. Thus, the stepped surface to compensate the phase
inverse was introduced; this method has already been usedin conventional ﬂexural vibrating plates.18–22) The detailed
structure based on this concept has been explored as follows.
The four structures shown in Fig. 2 were investigatedthrough ﬁnite element analysis (FEA). Figure 2(a) shows the07HE16-1© 2015 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 54, 07HE16 (2015)

J. Yamamoto et al.

Fig. 3. (Color online) Vibration modes for each transducer model
calculated using FEA. The color indicates the magnitude of the vibration
displacement normalized by the maximum value.

ZZexpðjkrÞ
dS;
uðx; yÞ
PðR; Þ ¼ jfr
S
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
r ¼ ðx  R sin Þ2 þ y2 þ ðR cos Þ2 ;Fig. 2. (Color online) Structures of element transducers.

fundamental conﬁguration including a ﬂextensional structure,
where a multilayered piezoelectric cermics element of
5 × 5 × 18 mm3 (PI P885T0001) is inserted in a duralumin(A7075P) frame. The duralumin frame and piezoelectricelement are bonded to each other with epoxy. The uppersurface indicated by a blue line in Fig. 2 is the radiating
surface. Figure 3(a) shows the calculated vibration mode,
whose eigenfrequency is 33.3 kHz. A one-and-a-half-wavelength bending vibration is generated on the radiation
surface, and the vibration in the central part is out of phaseto the rest of the radiation surface. The calculated curve in
Fig. 4(a) shows the far ﬁeld directivities calculated from thevibration velocity distribution uðx; yÞ obtained in Fig. 3(a)
using

ð1Þ

where PðR; Þ is the sound pressure at the distance of R(= 1.0 m) and the angle θ, j is the imaginary unit, ρ is thedensity of air (= 1.225 kg=m3), f is the frequency, k is thewave number, and c is the sound speed (= 340 m=s).31) The
integral is carried out over the radiation surface S. The result
is normalized with the maximum value. The highest radiation
appears in the angled directions as shown in Fig. 4(a). Thisis due to the vibration distribution with both positive andnegative displacements on the surface as mentioned previously. The fundamental bending mode, which has an inphase displacement all over the surface, can be excited atonly a lower frequency. If the thickness of the bending part isincreased, the resonance frequency will increase, but theexcited vibration amplitude will decrease.
Thus, the steps of 5.3 mm in the central part of theradiation surface were introduced as shown in Fig. 2(b). The
step size is adjusted to half the wavelength in air to cancel thenegative phase in the vibration as illustrated in Fig. 5, andthen a uniform wave front is obtained in air. Figure 3(b)shows the vibration modes calculated by FEA. This method
was originally employed in the previous study using a plate
and a Langevin transducer.17) The thickness of the side of the

07HE16-2© 2015 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 54, 07HE16 (2015)

J. Yamamoto et al.

Fig. 6. (Color online) Measurements of the radiation parts.

Fig. 7. Resonance frequency and vibration velocity ratio vs s.
Fig. 4. Directivity patterns calculated using the vibration distribution
given in Fig. 3.

Fig. 5. (Color online) Phase compensation mechanism using the stepped
structure.

radiation surface is reduced to 2.4 mm to increase thevibration with smaller mass and to keep the resonancefrequency at approximately 30 kHz. The vibration in thecentral part of the radiation surface is much smaller than thaton the side because of its weight, and the sidelobe level ishigher than half the main lobe level, as shown in Fig. 4(b).
Next, to increase the vibration amplitude in the central partof the radiation surface, a hole is created in the stepped part,as shown in Fig. 2(c). Against our expectations, the central
part has a smaller vibration that is in phase with the otherparts, as shown in Fig. 3(c). The sidelobe level increases,
as shown in Fig. 4(c). This distribution pattern was not
suﬃciently changed by alternating the thickness of theradiation part.
To generate the vibration in the central part, the steps are
installed on the bottom side, as well as on the top, with thehole introduced, as shown in Fig. 2(d). The rectangular holein the stepped part is enlarged to resonate in the expansion
mode, as demonstrated in Fig. 3(d). Figure 6 illustrates
essential parameters of the radiation part: s is the height of thebottom step, vc is the maximum vibration velocity in thecentral part of the radiation surface, vs is the velocity on theside, and vb the velocity at the bottom. The ratio vs=vc shouldbe less than 1.0 to decrease the sidelobe level of thedirectivity in the xz-plane, while the ratio vb=vc should be
as low as possible to prevent the bottom step from aﬀecting
the directivity. Figure 7 shows the resonance frequency andthe vibration velocity ratios vs=vc and vb=vc as functions of s.
The ratio vs=vc is always higher than 1.0 for the given rangeof s, although the ratio vb=vc becomes minimum at s =6.1 mm. In this prototype, although the ratio vs=vc did notmeet the requirement, s = 6.1 was employed for the elementtransducer, because the resonance frequency becomes closer
to 30.0 kHz and the ratio vb=vc is minimum. The sidelobe
level is expected to be less than half the main lobe level, as
shown in Fig. 4(d).
3.

Characteristics of the element transducer

3.1

Vibration velocity distribution
The vibration velocity distribution along the x-axis on theradiation surface of the model in Fig. 2(d) was measured
with a laser Doppler velocimeter (LDV) at a frequency of
30.0 kHz when a peak-to-peak voltage of 1.0 V was applied
to the piezoelectric element. Figure 8 shows the results,
where the vertical dotted lines indicate the positions of thesteps.
Directional characteristics of the radiated ﬁeld
The directivities in the xz-plane and yz-plane were measured
1.0 m away from the radiation surface with a 1=8-in.
condenser microphone (ACO 7118). In the experiment, themicrophone was ﬁxed and the element under test was rotatedaround the axis of the coordinate system presented inFig. 2(d). The side of the transducer was surrounded by aurethane sponge to minimize the radiation from unwanted
parts. The results are shown in Fig. 9 with red dots and3.2

07HE16-3© 2015 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 54, 07HE16 (2015)

J. Yamamoto et al.
Table I. Comparison of the directivity characteristics at 30.0 kHz(FWHM, full width at half maximum; SL, sidelobe level).
FWHM
(deg)

SL

Measured

14.3

0.78

Estimated

14.0

0.44

Piston11.4

0.22

Fig. 8. Vibration velocity distribution measured at 30 kHz.

Fig. 10.

Sound pressure in free ﬁeld as a function of the distance.

Fig. 11. Sound pressure level as a function of the voltage.

3.3
Fig. 9. (Color online) Directivity patterns at 30 kHz.

curves. The blue curve is the sound pressure PðR; Þcalculated from Eq. (1), where the measured vibration
distribution of Fig. 8 was used for uðx; yÞ. The measured
and estimated values were normalized with each maximum.
In the xz-plane, the green dotted line represents the directivityof the piston vibrator with the same aperture calculated
from29)DðÞ ¼sinðka sin Þ;ka sin 

ð2Þwhere a is half the larger width of the radiation surface.28)
Table I shows the full width at half maximum (FWHM) andthe sidelobe level (SL) of each directivity in Fig. 9(a). The
measured FWHM is almost the same as the estimated andpiston value, while the sidelobe level is higher than thecalculations. It is thought that this discrepancy is caused by
the radiation leaked from other vibrating surfaces such as theside of the step and other surfaces. In the directivity measured
in the yz-plane, the measured value is almost in agreementwith the estimated value, as shown in Fig. 9(b).

Measurement at high vibration amplitude
Figure 10 shows the distance characteristics of the prototypetransducer measured along the z-axis as well as a ﬁtted curve.
It was conﬁrmed that the sound pressure of the prototypetransducer is almost inversely proportional to the distance inthis range. The measurement of sound pressure at a highvibration amplitude was performed at a distance of 300 mm.
To prevent the piezoelectric element from breaking down due
to thermal stress, a burst signal was employed as the input.
Figure 11 shows the results. The output sound pressure level
increased proportionally to the input voltage up to 132 dB(0 dB = 0.02 mPa). When the input voltage exceeded 4.0 V,
the sound pressure level dropped. This sudden decrease wascaused by the weakening of the bonding part between theduralumin frame and the piezoelectric element, and the soundpressure level never recovered to the original value.
4.

Eight-element phased array characteristics

4.1

Experimental setup
Figure 12 shows a photograph of the eight-element linear
array using the prototype transducers. The width of theelement transducer is 5 mm and the spacing between theelements is 2 mm, and then the interval between the elements
is 7 mm, which is smaller than the wavelength at 30 kHz. The
total aperture of the array is 70 × 54 mm2. The elements are

07HE16-4© 2015 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 54, 07HE16 (2015)

J. Yamamoto et al.
Table II.

Fig. 12. (Color online) Photograph of the eight-element array.

Resonance characteristics of the eight element transducers.
Resonance frequency(kHz)

Admittance
(mS)

CH1

30.29

329

79

CH2

30.13

476

133

CH3
CH4

30.20
29.75

321
458

97
159

CH5

30.09

465

154

CH6

30.25

576

133

CH7

29.78

606

94

CH8

30.01

368

160

Table III.
element.

QualityfactorErrors in the vibration velocity amplitude and the phase of eachVibration velocity
(m=s)

Phase
(deg)

CH1

0.116

0

CH2

0.140

−4

CH3

0.101

−2

CH4

0.110

+2

CH5

0.122

−7

CH6

0.116

−5

CH7

0.104

−3

CH8

0.091

−5

4.2

Fig. 13.

(Color online) Driving electronics.

ﬁxed together using tapes at the positions exhibiting small
vibration displacements found in Fig. 3(d).
Figure 13 illustrates driving electronics for the array. A
digital-to-analog (D=A) converter board (National Instruments PCI-7831R) is controlled by a PC generated eightphase sinusoidal signals, which are fed to the elementtransducers via linear power ampliﬁers (National Semiconductor LM380N). Each element (CH1–CH8) has aslightly diﬀerent resonance frequency owing to uncertainly
in fabrication, and thus velocities and phases deviate between
the transducers for the same driving frequency. The
resonance characteristics of each transducer are summarizedin Table II. The driving frequency is set at 30.3 kHz, whichis slightly higher than all the resonance frequencies. The
amplitudes and phases of the driving voltages were socompensated that the amplitudes and phases of the vibration
velocities would be the same. Table III shows the resultant
amplitudes and phases of the vibration velocities measured
using the LDV. Phase diﬀerences could not be completely
corrected, because the minimum pitch in the phase diﬀerence
controlled by the D=A converter used in the experiment was
14.7 deg at this frequency.

Beam steering characteristics
The directivities in the yz-plane were measured 1.0 m awayfrom the array at the phase diﬀerences of −66, −36.6, 0, 29.4,
and 58.8 deg. In the experiment, the microphone was ﬁxed
and the array was rotated around the axis set at the centerof the radiation surface, as presented in Fig. 13. Figure 14
shows the directivity pattern for each phase diﬀerence. The
red dots and curves indicate the measured sound pressure.
The blue solid and black dotted curves indicate the values
calculated using Eq. (1) with and without the variations in
the amplitude and phase shown in Table III, respectively.
The directivity is normalized at each peak sound pressure.
Figure 14 shows the angles of the main lobe for the phase
diﬀerences Δφ given between the transducers. The ideal
value in Fig. 15 is calculated from28)
180 1 ’ c
sin
¼
;
ð3Þ

360 d  fwhere θ is the radiation angle and the interval of the sourced is 7 mm. It was conﬁrmed that the radiation angle was
successfully controlled by changing the phase diﬀerence.
The maximum values of the sound pressure level were
118 dB for the phase −66.0 deg, 121 dB for −36.6 deg,
123 dB for 0 deg, 122 dB for 29.4 deg, and 120 dB for
58.8 deg. The maximum output sound pressure for the eightelement phased array is expected to be 150 dB, if it is simply
calculated by multiplying the sound pressure of a single
element eight times. It was diﬃcult to obtain such a highoutput, because the resonance frequencies of the elements
were not identical in the prototype transducers.
5.

Conclusions

The trial manufacture of a high-power airborne ultrasonictransducer for a one-dimensional phased array was per-

07HE16-5© 2015 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 54, 07HE16 (2015)

J. Yamamoto et al.

Fig. 15. (Color online) Beam steering characteristics.

the phase diﬀerence, the radiation angle can be controlled
as we expected. The fabrication process is required to be
improved to minimize the resonance frequency variation.

Fig. 14. (Color online) Directivity of the phased array.

formed. A radiation surface with steps was designed to have auniform wave front in air, and the structure was modiﬁed tohave a higher vibration amplitude. The directivity at 30.0 kHz
showed the FWHM of 14.3 deg and the sidelobe level of
0.78. The sound pressure of 132 dB was obtained at the
distance of 300 mm. It is necessary to optimize the shape ofthe transducer to obtain a higher vibration amplitude at thecenter of the radiation surface than in the side parts.
Multilayered piezoelectric elements should be replaced byother low-loss elements for higher-amplitude operation.
The phased array characteristics obtained using eighttransducers were tested. It was conﬁrmed that, by changing

1) D. Koyama and K. Nakamura, IEEE Trans. Ultrason. Ferroelectr. Freq.
Control 57, 1152 (2010).
2) D. Koyama and K. Nakamura, IEEE Trans. Ultrason. Ferroelectr. Freq.
Control 57, 1434 (2010).
3) Y. Ito, D. Koyama, and K. Nakamura, Acoust. Sci. Technol. 31, 420 (2010).
4) R. Kashima, S. Murakami, D. Koyama, K. Nakamura, and M. Matsukawa,IEEE Trans. Ultrason. Ferroelectr. Freq. Control 61, 1024 (2014).
5) M. Ding, D. Koyama, and K. Nakamura, Appl. Phys. Express 5, 097301(2012).
6) R. Nakamura, Y. Mizuno, and K. Nakamura, Jpn. J. Appl. Phys. 52,
07HE02 (2013).
7) T. Hoshi, Y. Ochiai, and J. Rekimoto, Jpn. J. Appl. Phys. 53, 07KE07(2014).
8) A. Osumi and Y. Ito, J. Acoust. Soc. Am. 133, 3499 (2013).
9) A. Osumi and Y. Ito, Proc. IEEE Int. Ultrasonics Symp., 2010, p. 2376.
10) A. Osumi, K. Doi, and Y. Ito, Jpn. J. Appl. Phys. 50, 07HE30 (2011).
11) A. Osumi, M. Enomoto, and Y. Ito, Jpn. J. Appl. Phys. 53, 07KC16 (2014).
12) G. J. Brereton and B. A. Bruno, J. Sound Vib. 173, 683 (1994).
13) Y. Ito and M. Kotani, Jpn. J. Appl. Phys. 43, 2840 (2004).
14) Y. Ito, S. Nakayama, and R. Miwa, Jpn. J. Appl. Phys. 38, 3312 (1999).
15) Y. Ito, R. Kato, and A. Osumi, Jpn. J. Appl. Phys. 52, 07HE12 (2013).
16) J. A. Gallego-Juarez, Proc. IEEE Int. Ultrasonics Symp., 1994, p. 1343.
17) J. A. Gallego-Juárez, G. Rodriguez, V. Acosta, and E. Riera, Ultrason.
Sonochem. 17, 953 (2010).
18) A. Barone and J. A. Gallego Juarez, J. Acoust. Soc. Am. 51, 953 (1972).
19) J. A. Gallego Juárez, J. Sound Vib. 26, 411 (1973).
20) J. A. Gallego-Juarez, G. Rodriguez-Corral, and L. Gaete-Garreton,
Ultrasonics 16, 267 (1978).
21) H. Okada, M. Kurosawa, S. Ueha, and M. Masuda, Jpn. J. Appl. Phys. 33,3040 (1994).
22) T. Hoshi, T. Iwamoto, and H. Shinoda, 3rd Joint Eurohaptics Conf. Symp.
Haptic Interfaces for Virtual Environment and Teleperator Systems, 2009,p. 256.
23) T. Hoshi, D. Abe, and H. Shinoda, IEEE 18th Int. Symp. Robot and Human
Interactive Communication, 2009, p. 7.
24) T. Hoshi, M. Takahashi, and T. Iwamoto, IEEE Trans. Haptics 3, 155(2010).
25) T. Hoshi, IEEE World Haptics Conf., 2011, p. 569.
26) T. Hoshi, IEEE Haptics Sym., 2012, p. 399.
27) S. Takeoka and Y. Yamasaki, Int. Congr. Acoustics, 2010.
28) S. C. Wooh and Y. Shi, Wave Motion 29, 245 (1999).
29) C. T. Molloy, J. Acoust. Soc. Am. 20, 387 (1948).
30) T. Inoue, T. Nada, T. Miyama, K. Sugiuchi, and S. Takahashi, Proc. IEEE
Ultrasonics Symp, 1987, p. 765.
31) K. B. Ocheltree and L. A. Frizzell, IEEE Trans. Ultrason. Ferroelectr. Freq.
Control 36, 242 (1989).

07HE16-6© 2015 The Japan Society of Applied Physics