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Multimode shunt damping of piezoelectric smart panel
for noise reduction
Jaehwan Kim
a)
and Joon-Hyoung Kim
Department of Mechanical Engineering, Inha University, 253 Younghyun-Dong, Nam-Ku,
Incheon 402-751, Korea
共Received 14 March 2003; revised 31 March 2004; accepted 17 May 2004兲
Multimode shunt damping of piezoelectric smart panel is studied for noise reduction. Piezoelectric
smart panel is a plate structure on which a piezoelectric patch is attached with an electrical shunt
circuit. When an incidence sound is impinged on the panel structure, the structure vibrates and the
attached piezoelectric patch produces an electrical energy, which can be effectively dissipated as
heat via the electrical shunt circuit. Since the energy dissipation strongly depends on the vibration
mode of the panel structure, many patches are required for multiple vibration modes. Instead of
using multiple piezoelectric patches, a single piezoelectric patch is used in conjunction with a
blocked shunt circuit for multimode shunt damping. Modeling, shunt parameter tuning, and
implementation of the blocked shunt circuit along with an acoustic test of the panel are explained.
A remarkable reduction of the transmitted noise was achieved for multiple modes of the panel. Since
this technology has many merits in terms of compactness, low cost, robustness, and ease of
installation, practical applications in many noise problems can be anticipated. © 2004 Acoustical
Society of America. 关DOI: 10.1121/1.1768947兴
PACS numbers: 43.50.Ki, 43.55.Rg 关KAC兴 Pages: 942–948
I. INTRODUCTION
Noise reduction of panels is increasingly required in air-
crafts, vehicles, ships, buildings, etc., to provide a comfort-
able living environment. There are two categories in reduc-
ing the noise of panels: active and passive methods. Active
control uses sensors and actuators along with a proper con-
trol so as to minimize the noise at a certain frequency band.
Successful noise reductions have been obtained by using pi-
ezoelectric sensors and actuators along with a controller.
1
However, this method becomes infeasible at high frequencies
due to the increased complexity of the controller to take into
account many radiating modes of the structure. In contrast,
passive control does not bring any complexity and instability
of the system brought out from active control.
2
Also, it is
easy to set up with low cost. The most popular approach in
passive control is the use of sound absorbing materials.
However, since an increasing amount of material is required
for the effective noise reduction at low frequencies, the pas-
sive approach is impractical for low frequency applications.
In order to get over such a limit, a new passive method
has been proposed, which is based on piezoelectric shunt
damping. Piezoelectric shunt damping has been discussed by
Forward and experimentally demonstrated in an optical
system.
3
This system is composed of piezoelectric elements
and a simple electrical circuit. Briefly, the concept of piezo-
electric shunt damping is energy conversion and energy dis-
sipation, similar to a dynamic absorber of mechanical sys-
tems. Hagood and von Flotow have investigated the
possibility of dissipating mechanical energy with passive
electrical circuits.
4
They optimally tuned an electrical reso-
nance of shunt circuit to structural resonance in a manner
analogous to the mechanical vibration absorber for a selected
model. Recently, an electrical impedance model of piezo-
electric structures determined by the measured impedance
data was proposed, and the optimal parameter tuning of the
shunt circuit was performed based on the maximum energy
dissipation near the target frequency.
5
A remarkable suppres-
sion of the transmitted noise was achieved for broadband
frequencies by utilizing a hybrid concept that combines the
use of sound absorbing materials for the midfrequency range
and piezoelectric shunt damping for the low frequency
range.
6
However, several piezoelectric patches were used to
take into account the multiple vibration modes of the panel.
Hollcamp has expanded the theory of piezoelectric shunting
for single mode so that a single piezoelectric element can be
used to suppress two modes by optimally designing the shunt
parameters.
7
Wu has accomplished a multimode shunt damp-
ing with blocking circuit.
8
The blocking circuit consists of
one parallel capacitor and inductor antiresonance circuit.
This antiresonance circuit is designed to produce infinite
electrical impedance at the natural frequencies of all other
resonant shunt circuits.
In this paper, multimode shunt damping of the piezo-
electric smart panel is studied for the noise reduction of the
panel. On a single piezoelectric patch, a blocked shunt circuit
is connected to implement the multimode shunt damping
共Fig. 1兲. The tuning process for shunt parameters is based on
the electrical impedance model and the maximum energy
dissipation method. Implementation of the shunt circuit, the
tuning process of the circuit, as well as the acoustic test of
the panel for noise reduction are addressed.
II. PIEZOELECTRIC SHUNT DAMPING
The concept of piezoelectric shunt damping is the en-
ergy conversion by piezoelectric effect. Piezoelectric materi-
a兲
Electronic mail: jaehwan@inha.ac.kr
942 J. Acoust. Soc. Am. 116 (2), August 2004 0001-4966/2004/116(2)/942/7/$20.00 © 2004 Acoustical Society of America
als convert mechanical energy into electrical energy and vice
versa. The converted energy can be dissipated as heat
through a load resistor of the shunt circuit. Eventually, me-
chanical vibration level is reduced due to the energy dissipa-
tion. Usually, resonant shunt damping is used to effectively
dissipate out the energy at the resonance. However to maxi-
mize the energy dissipation at the resonance frequency of the
system, the choice of the optimal inductance and resistance
of the shunt circuit is very important. An optimal tuning
method for shunt parameters has been developed based on an
electrical impedance model.
5
An electrical impedance model
of piezoelectric structures has been derived to take into ac-
count the coupled structure in conjunction with the shunt
circuit. The new shunt parameter tuning method based on the
electrical impedance model and the maximum dissipation en-
ergy criterion has been applied. This method can be ex-
panded to the problem of multimode shunt damping because
the same tuning process can be applied for multimode in the
presence of blocking circuit. Details of the modeling and
tuning process for single-mode shunt damping are summa-
rized, and they are subsequently expanded to the multimode
shunt damping.
A. Modeling
Piezoelectric materials can be approximately represented
as an equivalent electric circuit at a resonance frequency. Van
Dyke’s model is well known for the equivalent resonance
model of piezoelectric materials. Figure 2 shows Van Dyke’s
equivalent model. Here, C
0
describes an inherent dielectric
capacity of piezoelectric material, while L
1
, R
1
, and C
1
imply mass, damping, and compliance of the material, re-
spectively. The model has five variables including the dielec-
tric loss, R
0
. However, since the dielectric loss is small, it is
neglected in the model.
By invoking Van Dyke’s model, the piezoelectric smart
structure on which the piezoelectric patch is bonded along
with a shunt circuit can be modeled as shown in Fig. 3. This
is an equivalent circuit model for the piezoelectric smart
panel. The impedance at each branch of the equivalent circuit
is described as
Z
1
共
s
兲
⫽ m
1
s⫹
k
1
s
⫹ c
1
⫽ j
L
1
⫹
1
j
C
1
⫹ R
1
,
Z
2
共
s
兲
⫽
k
2
s
⫽
1
j
C
2
,
Z
3
共
s
兲
⫽ Ls⫹ R⫽ j
L⫹ R, 共1兲
where Z
1
is the impedance of the first system, Z
2
and Z
3
express impedances of the secondary system. The total im-
pedance of the equivalent circuit can be written as
Z⫽ Z
1
⫹
Z
2
Z
3
Z
2
⫹ Z
3
. 共2兲
Also, the transfer function can be defined as the ratio of
the velocity output to the applied force of the mechanical
system. In other words, the transfer function, T
r
, can be
expressed in terms of electrical admittance of piezoelectric
structure including shunt circuit,
T
r
⫽
冏
v
F
冏
⫽
冏
i
V
冏
⫽
1
兩
Z
兩
⫽
兩
Y
兩
, 共3兲
where
v
is the velocity, F the force, i the current, V the
voltage, and Y the admittance. To use the electrical imped-
ance model, coefficients of Van Dyke’s model should be de-
termined. To determine the parameters, the electrical imped-
ance at the piezoelectric patch bonded on the structure is
measured by using the impedance analyzer 共HP4192A兲, and
FIG. 1. Schematic diagram of piezoelectric smart panels.
FIG. 2. Van Dyke’s circuit model of piezoelectric materials.
FIG. 3. Equivalent electrical circuit of piezoelectric structure.
943J. Acoust. Soc. Am., Vol. 116, No. 2, August 2004 J. Kim and J.-H. Kim: Smart panel for noise reduction
the equivalent parameters are extracted from the impedance
data by PRAP 共Piezoelectric Resonance Analysis Program兲.
9
B. Parameter tuning
It is essential to maximize the performance of piezoelec-
tric shunt damping by adjusting parameters of the shunt cir-
cuit. The shunt circuit is composed of an inductor and a
resistor for single-mode shunt damping. Therefore, values of
each parameter should be optimized to achieve effective
noise reduction, which is called the optimal parameter tun-
ing. Instead of tuning the transfer function geometrically as
used in the conventional tuning method for dynamic
absorber,
4
a new parameter tuning method based on the
maximum dissipated power at the shunt circuit is adopted.
5
From the equivalent impedance model shown in Fig. 2, the
induced electrical power of the system associated with exter-
nal excitation is
P
IN
⫽
1
2
兩
V• i
*
兩
⫽
1
2
兩
共
Z• i
兲
• i
*
兩
⫽
1
2
兩
Z
兩
•
兩
i
兩
2
, 共4兲
where i
*
is the complex conjugate of the current i. This
power can be referred to as input power for the shunt circuit.
In Fig. 3, the current through the load resistor is
i
3
⫽
Z
2
Z
2
⫹ Z
3
i, 共5兲
where i is the input current generated by the excitation. The
dissipated power at the shunt circuit can be described in
terms of impedance and the current of the equivalent circuit,
P
D
⫽
1
2
兩
V
R
• i
3
*
兩
⫽
1
2
兩
共
Re
共
Z
3
兲
• i
3
兲
• i
3
*
兩
⫽
1
2
Re
共
Z
3
兲
•
冏
冉
Z
2
Z
2
⫹ Z
3
冊
冏
2
•
兩
i
兩
2
. 共6兲
Also, the ratio of the dissipated power to the input power is
J⫽
P
D
P
IN
⫽
Re
共
Z
3
兲
•
冏
冉
Z
2
Z
2
⫹ Z
3
冊
冏
2
兩
Z
兩
. 共7兲
This ratio is given at a specific frequency near the resonance
frequency. In the tuning process, however, this should be
maximized by optimally changing the shunt circuit param-
eters. Thus, the objective function in the optimization is
taken as the averaged J at a certain frequency band near the
targeted resonance frequency. The optimal design variables,
L
*
, R
*
, are found by maximizing the objective function:
关
L
*
,R
*
兴
⫽ Max
L
R
冋
1
n
兺
k⫽1
n
兩
J
k
兩
册
, 共8兲
where n is the number of single frequency points in the fre-
quency band. Optimization is performed with optimization
toolbox in
MATLAB®.
III. MULTIMODE SHUNT DAMPING
In general, piezoelectric shunt damping includes a single
piezoelectric patch and a shunt circuit for one target fre-
quency. In order to deal with several strong-radiation modes
of the panel, several piezoelectric patches should be attached
on the structure as many as the number of modes. However,
increasing the number of piezoelectric patches increases the
weight of the system. Thus, the multimode shunt damping
with single piezoelectric patch is very useful for lightweight
structures. When multimode shunt circuit is connected to a
piezoelectric element, the circuit can resonate at multiple fre-
quencies. In this study, a blocking circuit is adopted to con-
struct a multimode shunt circuit.
8
Figure 4 represents the
concept of the multimode shunt circuit for two resonance
modes. R
1
*
and L
1
*
are shunt circuit parameters for the first
mode. A blocking circuit is connected to the second shunt
circuit such that the blocking circuit blocks the current flow
passing through the branch at the first mode. In other words,
at the first mode the current i
1
flows through the first shunt
circuit only since the blocking circuit protects the current at
the first mode, and at the second mode the current i
2
flows
through the second shunt circuit. Of course some current
flows through the first shunt circuit at the second mode also.
The tuning process for multimode shunt circuit has three
steps. At first, optimal shunt parameters are found for a reso-
nance mode by using the new tuning method based on the
maximum dissipated power. Second, a blocking circuit is
designed, which will block the current flow at the resonance
mode. Third, other shunt circuit parameters are determined
for an additional mode in the presence of the first shunt cir-
cuit and the blocking circuit.
As shown in Fig. 4, two resonance modes are investi-
gated in this study. Before determining parameters for mul-
timode shunt circuit, shunt parameters for a single mode are
employed from the previous tuning process. Next the block-
ing circuit is designed for the first mode by satisfying the
resonance equation,
1
2
⫽
1
L
1
block
C
1
block
. 共9兲
While tuned parameters for the first mode and the block-
ing circuit are kept in the tuning process, optimal parameters
for the next resonance mode are found according to the
maximum dissipated power. According to Ref. 8, the reac-
tance of the entire circuit can be calculated and the modified
inductance, L
˜
2
*
, can be given as
L
˜
2
*
⫽
L
1
*
L
2
*
⫹ L
2
*
L
1
block
⫺ L
1
*
L
1
block
⫺
2
2
L
1
*
L
2
*
L
1
block
C
1
block
共
L
1
*
⫺ L
2
*
兲
共
1⫺
2
2
L
1
block
C
1
block
兲
.
共10兲
FIG. 4. Schematic of shunt circuit for multimode.
944 J. Acoust. Soc. Am., Vol. 116, No. 2, August 2004 J. Kim and J.-H. Kim: Smart panel for noise reduction
Also, the modified resistance, R
˜
2
*
, can be written in the same
manner as
R
˜
2
*
⫽
R
1
*
R
2
*
R
1
*
⫺ R
2
*
. 共11兲
When the excitation frequency is near the first resonance
frequency, the current only flows into the first branch such
that two parameters, L
1
*
and R
1
*
, only work due to the op-
eration of the blocking circuit. On the other hand, near the
next resonance frequency, whole parameters of the circuit are
related with the shunt damping at the frequency since the
blocking circuit passes the current flow at this frequency.
When multimode shunt circuit is used, however, as the
number of target modes 共n兲 increases, the complexity of the
circuit increases. This is due to the fact that (n⫺ 1) blocking
circuits are needed at each branch. Also the expression for
optimal inductance and resistance becomes complicated.
Fortunately, a single piezoelectric patch does not exhibit
many modes of the host structure in dominant noise fre-
quency band. Thus, two or three modes on a single piezo-
electric patch are practical. In real applications, a couple of
piezoelectric patches should be optimally located to take into
account several modes that will radiate noise dominantly.
IV. EXPERIMENTS
A. Piezoelectric smart panel and shunt circuit
Piezoelectric smart panel is designed to reduce the trans-
mitted noise at the low frequency range. A 300⫻300⫻1.5
mm aluminum plate is used as host structure for the panel.
To implement the shunt damping, a piezoceramic patch
共PZT-5H, 100⫻50⫻0.5 mm兲 is bonded on the plate with
epoxy adhesives. Figure 1 is a schematic diagram of the
piezoelectric smart panel. The location of piezoceramic patch
is important for multimode shunt damping. Generally, strong
radiation modes of rectangular plate are odd modes such as
共1,1兲 and 共1,3兲, which are the first and second symmetric
modes. By locating the piezoceramic patch at the center of
the panel, the first and second symmetric modes can be taken
into account.
In order to build the shunt circuit, an inductor that has
large inductance is necessary. So far, a synthetic inductor has
been used to accomplish such a large inductance. However,
the use of a synthetic inductor requires an external power to
drive OP amps of the circuit, which is an obstacle for prac-
tical application. Furthermore, synthetic inductor circuits can
interfere with each other. Thus, a coil inductor is used instead
of the synthetic inductor. The use of coil inductor has many
advantages—cheap, less interference with other components,
no external power requirement, and easy to install. Also to
implement an independent system of piezoelectric smart
panel, the coil inductor can be integrated into the panel with-
out any external power. However, when high inductance
value is needed to suppress low modes of realistic large
structure, the use of a synthetic inductor or the use of capaci-
tance in conjunction with the piezoelectric patch can be re-
quired.
B. Acoustic test setup for piezoelectric smart panel
To test the noise reduction performance of piezoelectric
smart panel, the transmission measurement from low to high
frequencies should be available. For most panel materials the
transmission loss has been measured under strict control.
10
Since this test facility is too expensive, a simple acoustic
tunnel has been innovated 共Fig. 5兲.
6
Figure 5 shows the dia-
gram of the experimental apparatus for the acoustic panel
test. The tunnel is a square tube of 300 mm ⫻ 300 mm and
4 m long. It is divided into two sections—upper and lower
sections in equal length. A loudspeaker is set up at the end of
the upper section and an anechoic terminator made with
wedge is installed at the other end of the lower section. A
specially designed flange is provided where two sections
meet such that smart panels can be mounted in both. Four
edges of the smart panel are clamped using bolts and two
sections are tightly connected so as to secure pressure leak.
The function generator 共Wavetek178兲 generates a sine sweep
signal and the signal is fed to the loudspeaker through the
power amplifier. The loudspeaker produces an incident sound
and when it excites the panel, the transmitted and reflected
sounds occur. Sound pressure levels of the transmitted signal
through the panel are measured using microphones and they
are analyzed and displayed at the dynamic signal analyzer
共HP35665A兲. Through the measurement of sound pressure
level, plane wave is guaranteed below 800 Hz.
6
Before conducting smart panel tests, modal analysis of
the panel structure was performed numerically by using a
finite element program,
NASTRAN. Figure 6 shows the mode
shapes of the panel structure. With these results, target
modes are determined to be the first mode 共133 Hz兲 and the
fifth mode 共513 Hz兲, and the location of piezoceramic patch
is chosen at the center of panel. After bonding the piezocer-
amic patch at the center of the panel, the admittance at the
patch was measured to tune the shunt circuit.
FIG. 5. A schematic diagram of experimental apparatus.
945J. Acoust. Soc. Am., Vol. 116, No. 2, August 2004 J. Kim and J.-H. Kim: Smart panel for noise reduction
V. RESULTS AND DISCUSSION
Two experiments were accomplished for the transmitted
noise reduction: first and fifth modes were tuned separately,
and two modes were tuned simultaneously. Figure 7 shows
the measured admittance of piezoelectric smart panel in
terms of conductance 共real part兲 and susceptance 共imaginary
part兲. From the measured admittance, the first and fifth reso-
nance frequencies are found to be 127 and 518 Hz, respec-
tively, which are somewhat different from the modal analysis
results. This is due to the effect of bonded piezoelectric
patch. From the measured admittance curves, the parameters
for the equivalent impedance model 共Van Dyke兲 were ex-
tracted using the piezoelectric resonance analysis program
共PRAP兲, for the first and fifth modes, respectively. The sec-
ond column in Table I shows these values.
At first, the piezoelectric shunt damping was tested for
the first and fifth modes individually. The third column in
Table I exhibits the shunt circuit parameters found by the
optimization for each mode. The optimally searched values
共Simul兲 are found according to Eq. 共8兲. However, due to the
presence of uncertainties in the system, the optimally found
FIG. 6. Modal analysis for piezoelectric panel.
FIG. 7. Measured admittance of piezoelectric panel.
TABLE I. Van Dyke’s coefficients (C
0
,C
1
,L
1
,R
1
) are founded by analyzing the measured admittance, and the
optimal parameters (L
1
*
,R
1
*
,L
1
block
,C
1
block
) for multimode shunt damping are determined in order to dissipate
the maximum power through the load resistor.
Freq.
Parameters Single Mode Multimode
Coeff Values Simul Expt. Simul Expt.
First mode
共127.3 Hz兲
C
0
(F)
3.3161E⫺ 7
L
1
*
⫽ 4.42 L
1
*
⫽ 3.98 L
1
*
⫽ 4.42 L
1
*
⫽ 3.98
C
1
(F)
9.413E⫺ 9
L
1
(H) 162.9
R
1
*
⫽ 511.02 R
1
*
⫽ 600 R
1
*
⫽ 511.02 R
1
*
⫽ 150
R
1
(⍀) 9097
Fifth mode
共518.1 Hz兲
C
0
3.160E⫺ 7
L
2
*
⫽ 0.30 L
2
*
⫽ 0.30
L
˜
2
*
⫽ 0.458 L
˜
2
*
⫽ 0.446
C
1
1.161E⫺ 8
L
1
8.421
R
2
*
⫽ 125.25 R
2
*
⫽ 100
R
˜
2
*
⫽ 165.9 R
˜
2
*
⫽ 120
R
1
644
Blocking freq Parameters
First mode 共127 Hz兲
L
1
block
⫽ 1.07
C
1
block
⫽ 1.647E⫺ 6
946 J. Acoust. Soc. Am., Vol. 116, No. 2, August 2004 J. Kim and J.-H. Kim: Smart panel for noise reduction
parameters are necessarily adjusted in the experiment. Thus,
the inductance (L
1
) and resistance (R
1
) are adjusted from
the optimal simulation results. The experimental values are
also shown in Table I. The simulation and experimental val-
ues show a closer comparison. Figure 8 shows the sound
pressure levels near the first resonance. R⫽ 600 ⍀ is the op-
timal resistance experimentally found for the resonant shunt.
When R⫽ 0 ⍀ was plotted for a comparison, 7 dB reduction
of the transmitted sound pressure level was obtained near the
first resonance frequency. Figure 9 shows the sound pressure
levels near the fifth resonance frequency. At the fifth mode,
much more reduction is obtained by 20 dB down since there
is much strain at the center of panel, which results in larger
electrical energy generation from the piezoelectric patch.
Second, the experiment for multimode shunt damping
was performed. By keeping the shunt circuit parameters for
the first mode L
1
*
, R
1
*
, those for the fifth mode were tuned.
During the tuning process, the impedance analyzer was em-
ployed to measure the inductance and resistance of the cir-
cuit directly. The last two columns in Table I show the simu-
lation and experimental values. All values of the experiment
parameters are almost identical with the simulation param-
eters, except R
1
*
. This is due to the presence of internal
resistance of coil inductors in the shunt circuits as well as the
blocking circuit. Figure 10 shows the transmitted sound pres-
sure levels when two modes were reduced simultaneously.
The sound pressure levels in two resonance modes were re-
duced by 6 and 20 dB, respectively. The reduction level at
the first mode is 1 dB less than the individual tuning result.
This is due to a slight leakage of the current flowing into the
blocking branch.
When this multimode shunt technology is combined
with the use of several piezoelectric patches, the application
for large-scale structures will be possible for broadband
noise reduction. Also, the use of coil inductor for the circuit
may be attractive for real application since coil inductor is
compact and does not require any external power.
VI. CONCLUSIONS
Multimode shunt damping of piezoelectric smart panel
was studied for the noise reduction of the panel. Single pi-
ezoceramic patch was bonded on a host panel and shunt cir-
cuit was connected to the patch to accomplish multimode
shunt damping. As tuning method, the maximum dissipated
energy method in conjunction with the electrical impedance
model was adopted. In implementing the shunt circuit, a coil
inductor was used instead of a synthetic inductor, which does
not require external power to drive the circuit. The optimal
values of shunt parameters were verified by measuring these
values of the shunt circuit.
Before testing the multimode shunt damping of the
panel, single mode tests were individually performed, and 7
and 20 dB noise reduction obtained at the first and fifth reso-
nance modes of the panel, respectively. By implementing the
multimode shunt damping, 6 and 20 dB noise reductions
were obtained simultaneously for each mode, which are al-
most same as the single-mode test results.
When this multimode shunt technology is combined
with the use of several piezoelectric patches, the application
for large-scale structures will be possible for broadband
noise reduction.
FIG. 8. Shunt damping for first mode.
FIG. 9. Shunt damping for fifth mode.
FIG. 10. Experimental result for multimodes shunt damping.
947J. Acoust. Soc. Am., Vol. 116, No. 2, August 2004 J. Kim and J.-H. Kim: Smart panel for noise reduction
ACKNOWLEDGMENTS
This work was supported by Korea Research Foundation
Grant 共No. KRF-2002-041-D00031兲 and the Creative Re-
search Initiatives.
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