Fukuda, Takehito

Matsusaka, Yasuyuki

Oshima, Nobuo

Osaka City University Repository

1Effects of Waveform and Frequency of Electric Fields on Vibration Responses
of an Electro-Rheological Fluids Based CFRP Cantilevered Beam
NOBUO OSHlMA*, YASUYUKI MATSUSAKA**and TAKEHITO FUKUDA***
(Received September 30, 1996)
Synopsis
Effects of waveform and frequency of electric fields applied to electro-rheological fluids (ERF) are
examined on vibration responses of a CFRP composite cantilevered beam containing ERF. Two types of
sinusoidal and rectangular waveforms are used for the vibration tests. As the experimental results, the
superposed and the beat responses of the composite beam have been observed if applied the electric fields
with frequencies less than the first natural frequency of the composite beam. These peculiar responses are
explained in vibration analysis. For this purpose, a simplified mass-spring-damper system is adopted to
feature the first flexural mode of the composite beam, where the damping factor is changed in time as a
function of electric fields applied to ERF. Numerical analysis is performed to solve the motion ofequation.
KEY WORDS: CFRP laminate, ER fluids actuator, smart composites, waveform and frequency of applied
electric field, beat phenomenon, superposed re~ponse
Electric Field
CFRP laminate
Fig.l. A schematic view of specimen
including an experimental setup.
---' Sinusoidal wave
~--- Rectangular wave
Introduction
Smart fiber composite materials that incorporate embedded or integrated actuators and sensors during their
manufacturing process have recently attracted significant attention for their potential applications in
structural vibration control. To successfully apply this new technology, actuator materials play an important
role.
One candidate for actuator materials is electro-rheological fluids (ERF)l). The apparent viscosity and
rheological properties of ERF can be controlled in a wide range by the applied electric field. In addition,
the response time is very short (several milliseconds) and the change is reversible. Recently, ERF have been
interleaved between aluminumi .Rhosphor bronze plates or CFRP laminates with electrical conductivity tosuppress structural vibration -).
However, few studies have been ~
reported on effects of waveforms Personal computer ~
or frequencies of electric fields ~
applied to ERF on vibration j
responses of the composite beam. High-speed Amplifier
The experimental study was made er(t)
of effects of waveform and
frequency of electric fields
applied to ERF6).
In the present paper, a CFRP
composite cantilevered beam
containing ERF was prepared and
oscillatorily tested by using
sinusoidal and rectangular waves
with various frequencies of
electric fields applied to ERF. An
analytical investigation is also
given by using a simplified
vibration model of the composite
beam having an ERF actuator.
*Sutudent,Doctor Master of Department of Mecchanical Engineerring , Osaka City Univ.
**Sutudent,Doctor Course of Department of Mecchanical Engineerring, Osaka City Univ.
***Professor, Department of Mechanical Engineering, Osaka City Univ.
2Table 1. Material properties.
I CFRP IER fluids I Silicone rubber
Specific gravity 1.4 1.1 1.5
Storage modulus 48GPa 100Pa 1.5 MPa
Loss modulus 1.2 GPa 100Pa 0.15 MPa
Experiments
A specimen is schematically shown in Fig. 1, where the experimental set-up is also briefly illustrated
including a non-contacting laser displacement pick-up, AID and D/A converters, a personal computer.
Electric fields e(t) are produced by a high speed power supply unit. The specimen consists of two CFRP
laminated plates (Toray T300/#2500) and an ERF layer (Nippon Shokubai TX-ER2072). The fiber
orientation of the CFRP laminates is [+45 0 /-45 0 ]5. The specimen is 200mm in length and 20mm in width.
The thickness of CFRP laminate is O.5mm and the thickness of ERF layer is O.2mm. In the specimen,
ERF are filled between two CFRP laminated plates and sealed by a silicone rubber in the same manner as
proposed by Choi et al.2). ERF employed here consist of numerously sulfonated polymer particles (NSP)
in silicone oil with volume fraction of 40% 7). Two CFRP laminated plates are used for electrodes to an
apply electric field to ERF, because CFRP laminates are conductive.
In the experiments, the specimen was supported on the shaker under the clamped-free condition and
ERF were applied by an electric field of sinusoidal or rectangular wave with various frequencies. These
excitation waves were produced by use of a high speed power supply unit controlled by a personal
computer. The deflection responses of the free end of the specimen were observed in steady state by
using a non-contacting laser displacement pick-up. The tests were carried out under resonant conditions.
All tests were performed at the room temperature controlled by an air-conditioner.
Fig.2. Relation among the excitation force,!(t),
. electric field applied to ER fluids, e(t)
Sinusoidal
e(t) =J2. ere sin(OJI+ lJI) ,
1/1: initial phase
Deflection
y(t)
(n=0,1,2,· .)
(2n+ 1)1r
O~t~ OJ
e
(2n+l' < <2mf
(J) _t - OJ
e e
,for
,for
Composite beam
((t)
Rectangular
Excitation Force
Experimental Results
Waveform Effects of Electric Fields
First, the first flexural mode frequency of the
cantilevered specimen was examined by a
vibration test. It was 12.3Hz, while its predicted
value obtained by using Rayleigh's method was
12.0Hz5). The material properties used in
calculation are listed in Table 1. Secondly, in
order to investigate the effects of waveform of
electric fields applied to ERF, the deflection
responses in resonant state were observed with
changing the frequencies, Ie of electric fields
applied to ERF. The resonant conditions were
produced by tuning the frequency of the excitation
force, 1; to the first natural frequency of the
composIte beam, f. Fig. 2 illustrates the relation
among the excitation force, !(t), the electric field,
e(t) applied to ERF and the deflection of the free
end of the composite beam, y(t). An example of
comparison between steady-state responses
subjected to rectangular and sinusoidal waveforms
is given in Fig.3, where the response under in
electric field is also illustrated. As shown in this
example, it was found that the rectangular wave is
more effective for control of ER effects than the
sinusoidal wave when the amplitude and the
frequency of both waves are the same. The
3amplitude means the effective value. The reason is because the damping effect of the electric field
waveform depends on its area in a cycle, as will be explained by Eq. (2) in Section of Analysis and
Discussion and therefore the former is more effective than the latter.
Frequency Effects of Electric Fields
The deflection responses of the free end of the specimen were observed by changing the frequency of
electric fields applied to ERF under the same resonant condition. The frequency range of electric fields was
from 0.5Hz to 100Hz. If the frequency of electric fields was below the first natural frequency of the
composite beam, the superposed responses of the deflection y(t) with the first natural frequency and the
frequency of electric fields applied to ERF were appeared. Examples of these responses were shown in
Fig.4 (a) for 0.5Hz and Fig.4 (b) for 1.OHz of the sinusoidal wave applied to ERF, respectively. Such a
tendency was more significant for the sinusoidal waveform than the rectangular one. The beat phenomena
in response of the composite beam have been observed when the frequencies of electric fields close to the
1st natural frequency of the composite beam were utilized to ERF. An example of such a beat phenomenon
for the rectangular waveform is shown in Fig.5. If the frequency of electric fields was over the first natural
Sinusoidal wave Responses
e .. ....---r----r----,---------,
~
Time l,s
in no electric field
Time l,s
Rectangular wave
, . .
fA': :, . .::::::::T:::~::::r:::::::T::::::::
· , ,
: : :
· , ,................... __ .
I • ,
I • •
· , ,
· ,: : :
•
•
Time l,s
Responses
e ..
~ '-----------j------------(--------j-----------
§ , -~-~- i ~ - ~ --
~ -, ----------T----------:----------r---------
o ·4
Time l,s Time l,s
Fig.3. An example of comparison between steady-state responses.
subjected to rectangular and sinusoidal waves.
2.01.51.0
Time t,s
0.5
-2.0 "'--A.__--........--....-...-----...----&.........&....-.............-........a.......&--I......a.....-............--I
0.0
e 1.0
E"
~
~ 0.0
~(1)
~ -1.0
o
2.01.51.0
Time t,s
0.5
2.0
E 1.0
E"
~
~ 0.0c
0
.....
Co)
(1)
t=
-1.0(1)
0
-2.0
0.0
(a) For 0.5 Hz. (b) For 1.0 Hz.
Fig. 4. Superposed deflection responses with the first natural frequency
and the frequency of sinusoidal waveform electric fields applied to ERF .
4frequency, there appeared no beat phenomena. However, it is shown that less vibration suppression takes
place as the frequencies of an electric field increase as shown in Figs.6. In Fig.6 (a), a symbol.. • means
the range of amplitude variations of the deflection responses which appeared in the case of electric field of
the sinusoidal waveform with lower frequencies than the 1st natural frequency of the composite beam.
. . .
........ ··~····················r···················T·········· .
1.0
E 0.5E.-
~
~ 0.0s::
0
...
(,)
Q)
C
-0.5Q)
0
-1.0
2.0 2.5 3.0 3.5 4.0
Time t,s
Fig.5. Beat phenomenon of the composite beam due to
a rectangular wave with frequency close to the first natural frequency.
10010
..........................J. 1 ~ ()
··························;--·························1· -
:::::::::::::::::::::::::1:::::::::::::::::::::::::1:::::::::::::::::::::::::
! 10
o 6 0 <P
2.5
E 2.0
~
~ 1.5
~
s::
1.00
...(,)
Q)
l;:
0.5Q)
0
0.0
0.1
(~
laO10
o~----......................-----.......................--..-..---.......................
0.1
2.5 ..--_.,.....,................,..,...... ......--,.........,.,...--~_.....~~
:
~ ~ i
E
E.,
Frequency.f;,Hz
(a) In case of sinusoidal wave.
Frequency.£,Hz
(b) In case of rectangular wave.
Fig.6. Effect of frequency of electric fields applied
to ERF on vibration suppression.
Analysis and Discussion
Recently, M.Yalcintas et al. have given a series of reports on analytical studies of ER material based
adaptive model 8,9). In their papers, they use a basic model for multi-layered damped composite beam,
where structural adaptability is incorporated by assuming that the complex shear modulus of the ER material
is a function of electric field. However, a simplified mass-spring-damper system is here available only to
feature the first flexural mode of the cantilevered composite beam which is used in our vibration tests. That
is, the lumped mass system of the composite beam can be decomposed to the concentrated mass system of
one degree-of-freedom in which the damping factor is changed in time as a function of the waveform of
electric fields.
Then, the equation of motion of the composite beam is given by
(1)
. 3
where m=12.2xlO- kg and wn =77.3 rad/s.
The darnping factor ~(t) includes the damping ratio of the composite beam ~ and the ER effect e(t) as
follows:
(2)
5First, referring to the waveform of Fig.2 used in the experiments, let an electric field e(t) for the sinusoidal
waveform be represented by Eq.(3). This function is adopted taking acount of a little bit time lag between
the ER effect and the input of electric field. That is, a first-order lag element between them is assumed with
time constant of 8ms which was given by the other measurement method. Thus, damping factor' (t) due
to sinusoidal waveform with a frequency of 1Hz is illustrated in Fig.7(a). Numerically solving Eq.(l) by
using the Runge-Kutta method, we have an example of a superposed response of the composite beam with
e(t)=
(3)
0.4
~~ 0.3
....
0
~(,,)
~ 0.2
bJ)
c
·a§ 0.1
Q
2.5 3.0 3.5 4.0
Time (sec)
(a) Damping factor ~ (t) due to
a sinusoidal waveform
E 1.0
e
""-"
.§ 0.0
~(,,)
~
~Q -1.0
-2.0 ......... .......--.....a.-..........--'-.........-..... -..........
2.0 2.5 3.0 3.5 4.0
Time (sec)
(b) Steady-state response of the composite beam.
Fig7. An analytical example of steady-state response of the composite beam
in case of a sinusoidal waveform (superposed), forJ;=fn and~=1 Hz.
4.03.53.02.5
--- ----~--'T--L,- ...
-1.0 ~-----..-...._..........--.~---'---..I----.... ......
2.0
E 0.5
e
""-"
§ 0.0
..=
(,,)
~
tt=Q -0.5
2.102.082.062.042.02
0.00 ......... --..a-..... ~ ..................._ .......--a-_-..........
2.00
~ 0.30
~
....
o
~ 0.20
~
bJ)
c
.~ 0.10
~
Q
Time (sec)
(a)Damping factor ~ (t) due to
a rectangular waveform
Time (sec)
(b) Steady-state response of the composite beam.
FigS. An anal}1ical example of steady-state response of the composite beam
in case ofa sinusoidal waveform (beat pnenomenon), forJf=fn and~=12.3 Hz.
6,for
,for
(2n+l)nO~t< ro
e
t= (2n +1)1r
me
(4)
(
4.03.52.5
E 0.5 A·· r .q ..i q .. j··q··A··l·' .. ··rrn-
5 II
c
.2 0.0 .. ... . .. .. ... .. ... ... .. .
~
to)
Q)
~ -0.5 p.l ..tv .. J.U.J ..U.u "1" Lv..1..i
-1.0 -.....-----..........----...................~~ --L- ---..I
2.0 3.0
Time (sec)
(b) Steady-state response of the composite beam
r ( r
...............................................................................-
................................................................................-
. . .
~···················t·····················:··········· : -
....................... ·····················1·····················("·········· -
Time (sec)
(a) Damping factor t (t) due to
a rectangular waveform
Fig.9 An analytical example of steady-state response of the composite beam
in case ofa rectangular waveform forJ;=J" andJ;=l Hz.
... ··v· .. . .. . .. . .. . . .
'.0 r--r-......---r--T--,--~-.,......,..--,.....,........---r--T'---po-~~~
!
E 0.5 ~.... . 1... . .
5
.§ 0.0
.....
t)
Q)
t=o -0.5
-'.0 .............................. --...........~........... ~--Io-. ..................................,
2.0 2.5 3.0 3.5 4.0
Time (sec)
(b) Steady-state response of the composite beam
I • • •
.................................•...................................•...............
, . . .
· . . .
· .,
· . . .
· . . .
• • I •
::::·:::::·:::;:··:::::::::::::r::::·:::::·:::;:··:::::::::::::r::::::::::··
:::::···::::::1:::::::::::::::::1:::::::·:·::::::1::::::::::::::::I::::::: :.::::
Time (sec)
(a) Damping factor t (t) due to
a rectangular waveform
Fig. lOAn analytical example of steady-state response of the composite beam
in case of a rectangular waveform (beat phenomenon), forJ;=f" and.l:=12.3 Hz.
frequencies of 1Hz and 12.3Hz as illustrated in Fig.7(b). This case is corresponding to experimental result
shown in Fig.4. For the case of 12.3Hz shown in Fig.8(a), the beat phenomenon of the response can be
simulated similarly by waveform function of Eq.(3). Next, by using an electric field e(t) for the rectangular
waveform represented by Eq.(4) in the same manner, analytical results are given in Figs.9 and 10. In cases
of rectangular waveform, no superposed phenomenon appeares for a frequency of 1Hz, but for the case of
12.3Hz, the beat phenomenon can be seen as shown in Fig. 10(b). This is corresponding to experimental
results shown in Fig.5.
Conclusion
A CFRP composite beam with an ERF actuator was tested subjected to electric fields of two types of
waveforms with various frequencies. Analytical examinations were made by using a simplified vibration
model having the time-dependent damping factor. These results are summarized as follows;
7(1) The rectangular waveform is more effective for control ofER effects than the sinusoidal wave.
(2) The superposed deflection responses with the first natural frequency and the frequency of electric
fields applied to ERF appear for the frequency of electric fields below the first natural frequency of the
composite beam. Such a tendency is more significant for the sinusoidal waveform than the rectangular
one.
(3) The beat phenomena in response of the composite beam have been observed subjected to the electric
fields with frequency close to the natural frequency of the composite beam.
Acnowledgement
The authors would like to thank Toray Co. Ltd. for providing CFRP laminated plates and Nippon
Shokubai Co. for ERF.
References
1. M.V. Gandhi and B.S.Thompson, Smart Materials and Structures, London, Chapman & Hall 80 (1992)
2. Y. Choi, A.F. Sprecher and H. Conrad, J. Intelligent Mater., Syst. and Struct.,l, 91 (1990)
3. Y. Chen, F-G. Yuan and H. Conrad, Proc. 2nd ICIM, 328 (1994)
4. S. Morishita, T. Komatuzaki and M. Sasaki, Proc. 5th Int. Conf. Adaptive Struct., 219 (1994)
5. T. Fukuda and N. Oshima, Proc. the 10th Inter'l Conf. on Compo Mater.,V/299 (1995)
6. T. Fukuda and N. Oshima, Proc. the 3rd Inter 'I Con! on Intelligent Mater., 331(1996)
7. Y. Asako, S. Ono, R. Aizawa and T. Kawakami, Polymer Preprints, 35(2), 352 August (1994)
8. M. Yalcintas and J.P. Coulter, J. Intelligent Mater., Syst. and Struct., 6, 488 (1995)
9. M. Yalcintas and J.P. Coulter, J. Intelligent Mater., Syst. and Struct., 6 ,498 (1995)


Effects of Waveform and Frequency of Electric Fields on Vibration Responses of an Electro-Rheological Fluids Based CFRP Cantilevered Beam

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Effects of Waveform and Frequency of Electric Fields on Vibration Responses of an Electro-Rheological Fluids Based CFRP Cantilevered Beam

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