In this article, a dynamical model of the vibrations and acoustic radiation of a circular clamped plate excited by a voice coil and two annular piezoelectric patches is derived. This model is used to perform an optimization of the geometries with the objective to minimize the vibration of the plate along its second and third modes, so that the plate's radiation is equilibrated between its first and fourth eigenfrequencies. Experiments are then performed and show a good agreement with the model. Radiation of the designed system presents improvements when compared to a system when only a voice coil is used.

References

References
1.
Thiele
,
N.
,
1971
, “
Loudspeakers in Vented Boxes: Part 1
,”
J. Audio Eng. Soc.
,
19
, pp.
181
191
.
2.
Thiele
,
N.
,
1971
, “
Loudspeakers in Vented Boxes: Part 2
,”
J. Audio Eng. Soc.
,
19
(
6
), pp.
471
483
.
3.
Small
,
R. H.
,
1972
, “
Closed-Box Loudspeaker Systems—Part 1: Analysis
,”
J. Audio Eng. Soc.
,
20
(
10
), pp.
798
808
.
4.
Small
,
R. H.
,
1973
, “
Closed-Box Loudspeaker Systems—Part 2: Synthesis
,”
J. Audio Eng. Soc.
,
21
(
1
), pp.
11
18
.
5.
Kuo
,
D.
,
Shiah
,
Y. C.
, and
Huang
,
J. H.
,
2011
, “
Modal Analysis of a Loudspeaker and Its Associated Acoustic Pressure Field
,”
ASME J. Vib. Acoust.
,
133
(
3
), p.
031015
.10.1115/1.4003268
6.
Bédard
,
M.
, and
Berry
,
A.
,
2008
, “
Development of a Directivity-Controlled Piezoelectric Transducer for Sound Reproduction
,”
J. Sound Vib.
,
311
(
3-5
), pp.
1271
1285
.10.1016/j.jsv.2007.10.016
7.
Prokofieva
,
E.
,
Horoshenkov
,
K. V.
, and
Harris
,
N.
,
2002
, “
Intensity Measurements of the Acoustic Emission From a DML Panel
,” 112th Audio Engineering Society Convention, München, Germany, May 10–13.
8.
Zhang
,
S.
,
Shen
,
Y.
,
Shen
,
X.
, and
Zhou
,
J.
,
2006
, “
Model Optimization of Distributed-Mode Loudspeaker Using Attached Masses
,”
J. Audio Eng. Soc.
,
54
(
4
), pp.
295
305
.
9.
Berkhout
,
A. J.
,
1993
, “
Acoustic Control by Wave Field Synthesis
,”
J. Acoust. Soc. Am.
,
93
(
5
), pp.
2764
2778
.10.1121/1.405852
10.
Pueo
,
B.
,
López
,
J. J.
,
Escolano
,
J.
, and
Hörchens
,
L.
,
2010
, “
Multiactuator Panels for Wave Field Synthesis: Evolution and Present Developments
,”
J. Audio Eng. Soc.
,
58
(
12
), pp.
1045
1063
.
11.
Alper
,
S.
, and
Magrab
,
E. B.
,
1970
, “
Radiation From Forced Harmonic Vibrations of a Clamped Circular Plate in an Acoustic Fluid
,”
J. Acoust. Soc. Am.
,
48
, pp.
681
691
.10.1121/1.1912190
12.
Preumont
,
A.
,
2002
,
Vibration Control of Active Structures: An Introduction
,
2nd ed.
,
Kluwer Academic
, Dordrecht, The Netherlands.
13.
Lin
,
Y. H.
, and
Chu
,
C. L.
,
1996
, “
Active Flutter Control of a Cantilever Tube Conveying Fluid Using Piezoelectric Actuators
,”
J. Sound Vib.
,
196
(
1
), pp.
97
105
.10.1006/jsvi.1996.0470
14.
Block
,
J. J.
, and
Strganac
,
W.
,
1998
, “
Applied Active Control for a Nonlinear Aeroelastic Structure
,”
J. Guid. Control
,
21
(
6
), pp.
838
845
.10.2514/2.4346
15.
Hagood
,
N.
, and
von Flotow
,
A.
,
1991
, “
Damping of Structural Vibrations With Piezoelectric Materials and Passive Electrical Networks
,”
J. Sound Vib.
,
146
(
2
), pp.
243
268
.10.1016/0022-460X(91)90762-9
16.
Tylikowski
,
A.
,
2001
, “
Control of Circular Plate Vibrations Via Piezoelectric Actuators Shunted With a Capacitive Circuit
,”
Thin-Walled Struct.
,
39
, pp.
83
94
.10.1016/S0263-8231(00)00055-0
17.
Bisegna
,
P.
,
Caruso
,
G.
, and
Maceri
,
F.
,
2006
, “
Optimized Electric Networks for Vibration Damping of Piezoactuated Beams
,”
J. Sound Vib.
,
289
(
4-5
), pp.
908
937
.10.1016/j.jsv.2005.02.045
18.
Anton
,
S. R.
, and
Sodano
,
H. A.
,
2007
, “
A Review of Power Harvesting Using Piezoelectric Materials (2003-2006)
,”
Smart Mater. Struct.
,
16
, pp.
1
21
.10.1088/0964-1726/16/3/R01
19.
De Marqui, C., Jr.
,
Erturk
,
A.
, and
Inman
,
D. J.
,
2009
, “
An Electromechanical Finite Element Model for Piezoelectric Energy Harvester Plates
,”
J. Sound Vib.
,
327
(
1-2
), pp.
9
25
.10.1016/j.jsv.2009.05.015
20.
Masana
,
R.
, and
Daqaq
,
M. F.
,
2011
, “
Electromechanical Modeling and Nonlinear Analysis of Axially Loaded Energy Harvesters
,”
ASME J. Vib. Acoust.
,
133
(
1
), p.
011007
.10.1115/1.4002786
21.
Doaré
,
O.
, and
Michelin
,
S.
,
2011
, “
Piezoelectric Coupling in Energy-Harvesting Fluttering Flexible Plates: Linear Stability Analysis and Conversion Efficiency
,”
J. Fluids Struct.
,
27
(
8
), pp.
1357
1375
.10.1016/j.jfluidstructs.2011.04.008
22.
Fuller
,
C. R.
,
Hansen
,
C. H.
, and
Snyder
,
S. D.
,
1991
, “
Experiments on Active Control of Sound Radiation From a Panel Using a Piezoceramic Actuator
,”
J. Sound Vib.
,
150
(
2
), pp.
179
190
.10.1016/0022-460X(91)90614-P
23.
Tzou
,
H.
, and
Zhou
,
Y.
,
1995
, “
Dynamics and Control of Non-Linear Circular Plates With Piezoelectric Actuators
,”
J. Sound Vib.
,
188
(
2
), pp.
189
207
.10.1006/jsvi.1995.0586
24.
Lee
,
J. C.
, and
Chen
,
J. C.
,
1999
, “
Active Control of Sound Radiation From Rectangular Plates Using Multiple Piezoelectric Actuators
,”
Appl. Acoust.
,
57
(
4
), pp.
327
343
.10.1016/S0003-682X(98)00057-7
25.
Chen
,
K.
,
Chen
,
G.
,
Pan
,
H.
, and
Li
,
S.
,
2008
, “
Secondary Actuation and Error Sensing for Active Acoustic Structure
,”
J. Sound Vib.
,
309
(
1–2
), pp.
40
51
.10.1016/j.jsv.2006.12.027
26.
Larbi
,
W.
,
Deü
,
J. F.
,
Ciminello
,
M.
, and
Ohayon
,
R.
,
2010
, “
Structural-Acoustic Vibration Reduction Using Switched Shunt Piezoelectric Patches: A Finite Element Analysis
,”
ASME J. Vib. Acoust.
,
132
(
5
), p.
051006
.10.1115/1.4001508
27.
Gardonio
,
P.
,
Bianchi
,
E.
, and
Elliott
,
S. J.
,
2004
, “
Smart Panel With Multiple Decentralized Units for the Control of Sound Transmission. Part I: Theoretical Predictions
,”
J. Sound Vib.
,
274
(
1–2
), pp.
163
192
.10.1016/j.jsv.2003.05.004
28.
Gardonio
,
P.
,
Bianchi
,
E.
, and
Elliott
,
S. J.
,
2004
, “
Smart Panel With Multiple Decentralized Units for the Control of Sound Transmission. Part II: Design of the Decentralized Control Units
,”
J. Sound Vib.
,
274
(
1–2
), pp.
193
213
.10.1016/j.jsv.2003.05.007
29.
Bianchi
,
E.
,
Gardonio
,
P.
, and
Elliott
,
S. J.
,
2004
, “
Smart Panel With Multiple Decentralized Units for the Control of Sound Transmission. Part III: Control System Implementation
,”
J. Sound Vib.
,
274
(
1–2
), pp.
215
232
.10.1016/j.jsv.2003.05.006
30.
Lee
,
C. K.
, and
Moon
,
F. C.
,
1989
, “
Laminated Piezopolymer Plates for Torsion and Bending Sensors and Actuators
,”
J. Acoust. Soc. Am.
,
85
, pp.
2432
2439
.10.1121/1.397792
31.
Lee
,
C. K.
,
1990
, “
Theory of Laminated Piezoelectric Plates for the Design of Distributed Sensors Actuators. 1. Governing Equations and Reciprocal Relationships
,”
J. Acoust. Soc. Am.
,
87
, pp.
1144
1158
.10.1121/1.398788
32.
Lee
,
C. K.
, and
Moon
,
F. C.
,
1990
, “
Modal Sensors/Actuators
,”
ASME J. Appl. Mech.
,
57
(
2
), pp.
434
441
.10.1115/1.2892008
33.
Pierce
,
A. D.
,
1989
,
Acoustics: An Introduction to Its Physical Principles and Applications
,
Acoustical Society of America
, Melville, NY.
34.
Donoso
,
A.
, and
Bellido
,
J. C.
,
2009
, “
Distributed Piezoelectric Modal Sensors for Circular Plates
,”
J. Sound Vib.
,
319
(
1–2
), pp.
50
57
.10.1016/j.jsv.2008.05.033
35.
Ducarne
,
J.
,
Thomas
,
O.
, and
Deü
,
J. F.
,
2012
, “
Placement and Dimension Optimization of Shunted Piezoelectric Patches for Vibration Reduction
,”
J. Sound Vib.
,
331
(
14
), pp.
3286
3303
.10.1016/j.jsv.2012.03.002
36.
Quaegebeur
,
N.
, and
Chaigne
,
A.
,
2008
, “
Nonlinear Vibrations of Loudspeaker-like Structures
,”
J. Sound Vib.
,
309
(
1–2
), pp.
178
196
.10.1016/j.jsv.2007.06.040
37.
Mansfield
,
E. H.
,
1989
,
The Bending and Stretching of Plates
,
2nd ed.
,
Cambridge University
,
Cambridge, UK
.
You do not currently have access to this content.