Дослідження передачі енергії хвиль Лемба в електрично зв’язаних пластинах LiNbO₃
У роботi дослiджено передачу енергiї мiж хвилями Лемба в п’єзоелектричнiй шаруватiй структурi без акустичного контакту, в якiй зв’язок мiж окремими шарами вiдбувається через електричне поле. Дослiдження виявили ефективну передачу енергiї мiж прямими модами. Крiм того, в дiапазонi частот, де можуть i...
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| Cite this: | Дослідження передачі енергії хвиль Лемба в електрично зв’язаних пластинах LiNbO₃ / П.В. Бурлій, В.В. Козаченко, О.М. Жабітенко // Український фізичний журнал. — 2010. — Т. 55, № 6. — С. 712-715. — Бібліогр.: 7 назв. — укр. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860089807241216000 |
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| author | Бурлій, П.В. Козаченко, В.В. Жабітенко, О.М. |
| author_facet | Бурлій, П.В. Козаченко, В.В. Жабітенко, О.М. |
| citation_txt | Дослідження передачі енергії хвиль Лемба в електрично зв’язаних пластинах LiNbO₃ / П.В. Бурлій, В.В. Козаченко, О.М. Жабітенко // Український фізичний журнал. — 2010. — Т. 55, № 6. — С. 712-715. — Бібліогр.: 7 назв. — укр. |
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| container_title | Український фізичний журнал |
| description | У роботi дослiджено передачу енергiї мiж хвилями Лемба в п’єзоелектричнiй шаруватiй структурi без акустичного контакту, в якiй зв’язок мiж окремими шарами вiдбувається через електричне поле. Дослiдження виявили ефективну передачу енергiї мiж прямими модами. Крiм того, в дiапазонi частот, де можуть iснувати зворотнi хвилi при передачi енергiї з однiєї пластини в iншу спостерiгалось перетворення прямої моди у зворотню.
Energy transfer between Lamb waves in a layered piezoelectric structure without acoustic contact, in which separate layers are coupled by means of an electric field, has been studied. An effective energy transfer between direct modes has been found. In addition, a transformation of the direct mode into the backward one was observed at the energy transfer between the plates in the frequency range allowable for backward waves.
В работе исследовалась передача энергии между волнами Лемба в пьезоэлектрической слоистой структуре без акустического контакта, в которой связь между отдельными слоями происходит через электрическое поле. Исследования показали эффективную передачу энергии между прямыми модами. Кроме того, в диапазоне частот, где могут существовать обратные волны, при передаче энергии с одной пластины в другую наблюдалось превращение прямой моды в обратную.
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| first_indexed | 2025-12-07T17:22:22Z |
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P.V. BURLIY, V.V. KOZACHENKO, O.M. ZHABITENKO
ENERGY TRANSFER BETWEEN LAMB WAVES
IN ELECTRICALLY COUPLED LiNbO3 PLATES
P.V. BURLIY, V.V. KOZACHENKO, O.M. ZHABITENKO
Taras Shevchenko National University of Kyiv
(64, Volodymyrs’ka Str., Kyiv 03127, Ukraine; e-mail: victorc@ univ. kiev. ua )
PACS 43.20.E
c©2010
Energy transfer between Lamb waves in a layered piezoelectric
structure without acoustic contact, in which separate layers are
coupled by means of an electric field, has been studied. An ef-
fective energy transfer between direct modes has been found. In
addition, a transformation of the direct mode into the backward
one was observed at the energy transfer between the plates in the
frequency range allowable for backward waves.
Historically, it was volume elastic waves that were first
used in acoustoelectronics. With the development of
technologies, surface ultrasonic waves found their ap-
plication as well. Lamb waves are widely used for the
non-destructive examination of novel materials with lay-
ered structures [1, 2]. However, if the substance layer, in
which the Lamb waves propagate, possesses piezoelec-
tric properties, those waves demonstrate some specific
features. Recently, the researches on the application of
unique properties of waves in plates have been developed.
One of the interesting cases is the so-called backward
acoustic waves, i.e. the waves with the phase, vph, and
group, vg, velocities directed oppositely to each other,
unlike the case of ordinary direct waves, for which vph
and vg are directed identically. The existence of back-
ward waves was considered theoretically in detail and
proved experimentally in works [3–5].
In this work, an attempt is made to examine the en-
ergy transfer in a layered piezoelectric structure without
Fig. 1. Block diagram of the experimental setup
acoustic contact, in which separate layers are coupled by
means of an electric field. Namely, we intended to study
the features of the energy exchange between direct and
backward acoustic Lamb waves. The energy flows for
backward transverse normal waves were studied theo-
retically in work [6], whereas no such researches—neither
theoretical nor experimental – were carried out for Lamb
waves.
A system consisting of two Y Z-cut LiNbO3 plates is
studied. The plates 4× 1 cm2 in size were cut out from
the same crystal. However, they had different thick-
nesses equal to 640 (plate 1) and 650 µm (plate 2). A
small difference in thicknesses is convenient, because, as
will be shown further, there may occur a situation where
the direct mode is excited in one plate, and the backward
one in the other at the same frequency.
The block diagram of the experimental setup is shown
in Fig. 1. Making use of a pulse generator and a high-
frequency signal generator (HF generator), a radio pulse
2 to 10 µs in duration was formed in the modulator. Af-
ter amplification, it was applied to an exciting electrode
of the studied LiNbO3 plate (the experimental scheme
is depicted in Fig. 2). A metal plate 0.5 mm in width
was used as an exciting electrode. Owing to the inverse
piezoelectric effect, an acoustic wave was excited in the
plate. It was registered by the counter electrode which
could be shifted along the plate making use of a micro-
metric screw. The signal on the registering electrode was
applied to either of the two-channel oscillograph inputs.
The reference signal obtained from an HF-generator and
transmitted through a calibrated phase shifter was ap-
Fig. 2. Experimental scheme for measuring vph(f)
712 ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 6
ENERGY TRANSFER BETWEEN LAMB WAVES
plied to the other oscillograph input. The sum of both
signals was registered by an oscillograph. It allowed a
phase shift of the working signal with respect to the
reference one to be determined, which made it possi-
ble to measure the acoustic wavelength λ (two positions
of the registering electrode on the specimen were fixed,
for which the working signal had the same phase shift
with respect to the reference one). The phase velocity
was determined as vph = λf , where f is the frequency
of acoustic waves.
First, we theoretically evaluated the frequencies of
Lamb wave generation (the critical frequencies fcr.t.) for
individual plates, by analyzing thickness resonances. In
those calculations, the propagation velocities for corre-
sponding elastic waves were taken from the reference
book [7]. The values of fcr.t. for the first five modes are
quoted in Table 1 (for plate 1) and Table 2 (for plate 2),
where the notations QL and QT stand for waves that
are generated as quasilongitudinal and quasitransverse,
respectively, to the plate thickness.
Using the results of theoretical calculations for critical
generation frequencies, experimental researches of exci-
tation of corresponding modes have been carried out.
Every mode was excited in a definite narrow range of fre-
quencies close to fcr.t.. In order to associate every mode
with theoretical calculations, the experimental value of
critical frequency fcr.e., which was maximally close to
the theoretical value fcr.t. of the corresponding mode,
was selected. The experimental values for fcr.e. are also
quoted in Tables 1 and 2.
As is evident from the Tables, two modes, QL2 and
QT3, are generated in both plates in the vicinity of
10000 kHz. The generation frequencies of those modes,
owing to the coincidence of a number of parameters, lie
close to each other. As a rule, the mode of the pair,
which has a lower generation frequency, can also exist as
a backward one [5].
Mode QT1 was selected for studying the energy ex-
change between direct modes, whereas modes QL2 and
QT3 for studying the energy exchange between direct
and backward acoustic waves. First of all, the dispersion
dependences vph(f) for selected modes in each plates
were analyzed. The technique used for the determina-
tion of the phase velocity was described in work [4]. In
addition, a calibrated phase shifter was used in our ex-
T a b l e 1. Critical frequencies of Lamb waves in LiNbO3
plate 640 µm in thickness
QT1 QL1 QT2 QL2 QT3
fcr.t. 3508 5375 7016 10750 10524
fcr.e. 3750 5420 7630 10600 10270
3200 3600 9500 10000 10500 11000
-200
-100
0
100
200
7
6
5
43
2
1
f,kHz
�
p
h
,
*
1
0
3
m
/s
Fig. 3. Dispersion dependences vph(f) for Lamb waves in LiNbO3
plates: (1 ) mode QT1 in plate 1, (2 ) mode QT1 in plate 2;
(3 ) mode QL2 in plate 2; (4 ) mode QL2 in plate 1, (5 ) a sec-
tion of vph(f)-dependence for mode QT3 in plate 1 with a direct
Lamb wave, (6 ) a section of vph(f)-dependence for mode QT3 in
plate 2 with a backward Lamb wave, (7 ) a section of the vph(f)-
dependence for mode QT3 in plate 1 with a backward Lamb wave
perimental scheme (see Fig. 1) which allowed not only
the magnitude, but also the sign of the phase velocity to
be determined. For this purpose, the electrode register-
ing a signal was shifted with respect to the exciting one
by a quarter rather than a half wavelength. Depending
on whether the phase shift φ should be increased or de-
creased by 90◦ with the help of a phase shifter (in order
to compensate the phase shift of the signal induced by an
electrode displacement), the sign of vph was determined.
The two-channel input of an oscillograph gave an oppor-
tunity to compare the phases of signals obtained from
the specimen and from the phase shifter. The sign of
vph was “+” at φ = +90◦ and “−” at φ = −90◦. The
results of those experiments are presented in Fig. 3.
The data obtained definitively prove that only the
direct waves can expectedly be excited in both plates
in the vicinity of 3600 kHz, and both the direct and
backward ones in the vicinity of 10000 kHz. Owing to
the generation frequency difference between the corre-
sponding modes in both plates in the frequency range
9950−10350 kHz, which can be clearly observed by com-
paring the corresponding plots in Fig. 3, mode QT3 can
propagate in one of the plates. This mode, due to dif-
ferent group velocities, was simultaneously observed as
a direct (curve 5) and a backward one (curve 7). In
the other plate, only the direct QL2 mode was observed
T a b l e 2. Critical frequencies of Lamb waves in LiNbO3
plate 650 µm in thickness
QT1 QL1 QT2 QL2 QT3
fcr.t. 3450 5290 6900 10580 10350
fcr.e. 3535 5320 7246 9950 9900
ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 6 713
P.V. BURLIY, V.V. KOZACHENKO, O.M. ZHABITENKO
Fig. 4. Scheme of the experiment on the energy transfer between
LiNbO3 plates
(curve 3). All that provides a possibility to study – with-
out extra difficulties – the efficiency of energy transfer
between direct and backward waves.
A system of two plates was used for further researches.
The waves were excited in plate 1, and the signal was
read out from plate 2. The corresponding experimental
scheme is exhibited in Fig. 4.
Our researches found the effective energy transfer be-
tween direct modes at a frequency of 3650 kHz (the
transfer constant k = A2/A1 = 0.65, where A1 and A2
are the amplitudes of the output signal in the cases of one
and two plates, respectively). The excitation efficiency
for this mode in the system of electrically coupled waveg-
uides is almost the same as that for individual plates.
The energy transfer is no so effective at a frequency of
10230 kHz (the transfer constant k = 0.05). Moreover,
two separate signals with different time delays were pro-
nouncedly observed at this frequency. They could cor-
respond to a direct wave and a backward one, which are
excited simultaneously in plate 1. Since the group and
phase velocities for the backward wave are oppositely
directed, the signal, which corresponds to the backward
wave, should be directed toward the exciting electrode,
whereas the signal, which corresponds to the direct wave,
should be directed away from it.
To confirm that one of the signals corresponds to the
backward wave and the other to the direct one, addi-
tional studies of the dependence of the time delay τ of
those signals on the distance L between electrodes, which
can be varied by shifting one plate with respect to the
other, were carried out. The results of those experiments
are shown in Fig. 5, where curve 1 corresponds to the
backward wave and curve 2 to the direct one. From
Fig. 5, one can easily see that the time delay of signal 2
increases, if L grows, which is evident. But the time de-
lay of signal 1 decreases a little at that. Such a delay
of signal 1 can be explained by a complicated behav-
ior of this signal in the case where the acoustic wave in
plate 1 transforms from a direct wave into a backward
one. Then, the time delay in plate 2 will increase, but
it will decrease in the system of two plates. It can be
explained as follows.
3 4 5 6 7
15
20
25
30
35
40
2
τ
,
µ
s
L, cm
1
Fig. 5. Dependences of the output signal time delay on the dis-
tance between the Lamb-wave exciting and registering electrodes
in the system of electrically coupled plates at the energy transfer
(1 ) between direct modes and (2 ) between direct and backward
modes
Suppose that signal 1 in Fig. 5 corresponds to the
backward wave in plate 1. Then, its group velocity is
directed oppositely to the phase one. At the same time,
if the velocity vph preserves its direction, when the wave
transits from plate 1 into plate 2, the velocity vg is di-
rected away from the registering electrode. It results in
that the backward wave is registered as a mere reflec-
tion from the opposite (left) face of the plate. There-
fore, the paths for direct and backward waves in the
system are different. In the case where the plates have
the same length l and they are in either of two extreme
positions “one over the other”– 1) the upper plate almost
completely covers the lower one (L ≈ l) and 2) the up-
per plate is shifted almost to the edge of the lower one
(L ≈ 2l) – we can write down the following expression
for the time delays of the backward wave:
t2 = t1 −
l
2
(
1
vgb
− 1
vgd
)
. (1)
Here, t1 and t2 are the relevant quantities in the first and
second cases, respectively; and vgb and vgd are the group
velocities of backward and direct waves, respectively. As
a rule, vgb < vgd [3], and Eq. (1) testifies that t2 < t1.
This means that if the upper plate is shifted in such a
manner that the parameter L increases, the time delay
of signal 1 will gradually decrease. That is what was
observed in experiment.
1. L. Wang and F.G. Yuan, J. Phys. Chem. 67, 1370 (2007).
2. B.C. Lee and W.J. Staszewski, Smart Mater. Struct. 16,
249 (2007).
714 ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 6
ENERGY TRANSFER BETWEEN LAMB WAVES
3. P.V. Burliy and I.Ya. Kucherov, Pis’ma Zh. Eksp. Teor.
Fiz. 26, 644 (1977).
4. P.V. Burliy, P.P. Ilyin, and I.Ya. Kucherov, Zh. Tekhn.
Fiz. 51, 2196 (1981).
5. I.A. Borodina, B.D. Zaitseva, and I.E. Kuznetsova, Pis’ma
Zh. Tekh. Fiz. 34, 26 (2008).
6. D.A. Andrusenko, P.V. Burliy, and I.Ya. Kucherov, Ukr.
Fiz. Zh. 39, 10 (1994).
7. A.A. Blistanov, V.S. Bondarenko, V.V. Chkalova et
al., Acoustic Crystals: A Reference Book, edited by
M.P. Shaskolskaya (Nauka, Moscow, 1982) (in Russian).
Received 26.09.09.
Translated from Ukrainian by O.I. Voitenko
ДОСЛIДЖЕННЯ ПЕРЕДАЧI ЕНЕРГIЇ ХВИЛЬ ЛЕМБА
В ЕЛЕКТРИЧНО ЗВ’ЯЗАНИХ ПЛАСТИНАХ LiNbO3
П.В. Бурлiй, В.В. Козаченко, О.М. Жабiтенко
Р е з ю м е
У роботi дослiджено передачу енергiї мiж хвилями Лемба в
п’єзоелектричнiй шаруватiй структурi без акустичного конта-
кту, в якiй зв’язок мiж окремими шарами вiдбувається через
електричне поле. Дослiдження виявили ефективну передачу
енергiї мiж прямими модами. Крiм того, в дiапазонi частот, де
можуть iснувати зворотнi хвилi при передачi енергiї з однiєї
пластини в iншу спостерiгалось перетворення прямої моди у
зворотню.
ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 6 715
|
| id | nasplib_isofts_kiev_ua-123456789-56221 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 2071-0194 |
| language | Ukrainian |
| last_indexed | 2025-12-07T17:22:22Z |
| publishDate | 2010 |
| publisher | Відділення фізики і астрономії НАН України |
| record_format | dspace |
| spelling | Бурлій, П.В. Козаченко, В.В. Жабітенко, О.М. 2014-02-14T19:04:44Z 2014-02-14T19:04:44Z 2010 Дослідження передачі енергії хвиль Лемба в електрично зв’язаних пластинах LiNbO₃ / П.В. Бурлій, В.В. Козаченко, О.М. Жабітенко // Український фізичний журнал. — 2010. — Т. 55, № 6. — С. 712-715. — Бібліогр.: 7 назв. — укр. 2071-0194 PACS 43.20.E https://nasplib.isofts.kiev.ua/handle/123456789/56221 534.2:539.2 У роботi дослiджено передачу енергiї мiж хвилями Лемба в п’єзоелектричнiй шаруватiй структурi без акустичного контакту, в якiй зв’язок мiж окремими шарами вiдбувається через електричне поле. Дослiдження виявили ефективну передачу енергiї мiж прямими модами. Крiм того, в дiапазонi частот, де можуть iснувати зворотнi хвилi при передачi енергiї з однiєї пластини в iншу спостерiгалось перетворення прямої моди у зворотню. Energy transfer between Lamb waves in a layered piezoelectric structure without acoustic contact, in which separate layers are coupled by means of an electric field, has been studied. An effective energy transfer between direct modes has been found. In addition, a transformation of the direct mode into the backward one was observed at the energy transfer between the plates in the frequency range allowable for backward waves. В работе исследовалась передача энергии между волнами Лемба в пьезоэлектрической слоистой структуре без акустического контакта, в которой связь между отдельными слоями происходит через электрическое поле. Исследования показали эффективную передачу энергии между прямыми модами. Кроме того, в диапазоне частот, где могут существовать обратные волны, при передаче энергии с одной пластины в другую наблюдалось превращение прямой моды в обратную. uk Відділення фізики і астрономії НАН України Український фізичний журнал Тверде тіло Дослідження передачі енергії хвиль Лемба в електрично зв’язаних пластинах LiNbO₃ Energy Transfer between Lamb Waves in Electrically Coupled LiNbO₃ Plates Исследование передачи энергии волн Лемба в электрически связанных пластинах LiNbO₃ Article published earlier |
| spellingShingle | Дослідження передачі енергії хвиль Лемба в електрично зв’язаних пластинах LiNbO₃ Бурлій, П.В. Козаченко, В.В. Жабітенко, О.М. Тверде тіло |
| title | Дослідження передачі енергії хвиль Лемба в електрично зв’язаних пластинах LiNbO₃ |
| title_alt | Energy Transfer between Lamb Waves in Electrically Coupled LiNbO₃ Plates Исследование передачи энергии волн Лемба в электрически связанных пластинах LiNbO₃ |
| title_full | Дослідження передачі енергії хвиль Лемба в електрично зв’язаних пластинах LiNbO₃ |
| title_fullStr | Дослідження передачі енергії хвиль Лемба в електрично зв’язаних пластинах LiNbO₃ |
| title_full_unstemmed | Дослідження передачі енергії хвиль Лемба в електрично зв’язаних пластинах LiNbO₃ |
| title_short | Дослідження передачі енергії хвиль Лемба в електрично зв’язаних пластинах LiNbO₃ |
| title_sort | дослідження передачі енергії хвиль лемба в електрично зв’язаних пластинах linbo₃ |
| topic | Тверде тіло |
| topic_facet | Тверде тіло |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/56221 |
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