This paper presents a theoretical and experimental study of the frequency response function of a matched volume velocity sensor and uniform force actuator for active structural acoustic control. The paper first reviews the design of a volume velocity sensor and uniform force actuator on a panel, using piezoelectric film with quadratic shaping of the electrodes. The frequency response function of a matched volume velocity sensor and uniform force actuator bonded on either sides of a panel is then studied in detail. This analysis shows that below 100 Hz the sensor–actuator response is controlled by the bending vibration of the panel and a good estimate of the volumetric component of the transverse vibration of the panel is achieved. At higher frequencies, however, the sensor–actuator response is controlled by the in-plane longitudinal and shear vibration of the panel, which causes the real part of the frequency response function to be not strictly positive and to be characterized by large amplitudes at higher frequencies. These two phenomena are important since they limit the possibility of implementing a stable direct velocity feedback control system using these transducers.

1.
C. R.
Fuller
and
R. J.
Silcox
, “
Active structural acoustic control
,”
J. Acoust. Soc. Am.
91
,
519
(
1992
).
2.
C. R. Fuller, S. J. Elliott, and P. A. Nelson, Active Control of Vibration (Academic, London, 1996), Chaps. VIII and IX.
3.
M. E. Johnson, “Active Control of Sound Transmission,” Ph.D. thesis, University of Southampton (1996).
4.
S. J.
Elliott
and
M. E.
Johnson
, “
Radiation modes and the active control of sound power
,”
J. Acoust. Soc. Am.
94
,
2194
2204
(
1993
).
5.
M. E.
Johnson
and
S. J.
Elliott
Active control of sound and vibration using volume velocity cancellation
,”
J. Acoust. Soc. Am.
98
,
2174
2186
(
1995
).
6.
S. J.
Elliott
and
T. J.
Sutton
, “
Performance of feed-forward and feedback methods for active control
,”
IEEE Trans. Speech Audio Process.
4
,
214
223
(
1996
).
7.
M. E. Johnson, T. Sors, S. J. Elliott and B. Rafaely, “Feedback control of broadband sound radiation using a volume velocity sensor,” Proceedings of Active 97, Budapest, HU, 21–23 August (1997), pp. 1007–1020.
8.
M. J.
Balas
, “
Direct velocity feedback of large space structures
,”
J. Guid. Control
2
,
252
253
(
1979
).
9.
P.
Curie
and
J.
Curie
,
Comptes Rendus
91
,
294
(
1880
).
10.
A. van der Ziel, Solid state physical electronics (1968).
11.
C. K.
Lee
, “
Theory of laminated piezoelectric plates for the design of distributed sensor/actuators. Part I: governing equations and reciprocal relationships
,”
J. Acoust. Soc. Am.
87
,
1144
1158
(
1990
).
12.
J. Rex and S. J. Elliott, “A new sensor for structural radiation control,” Proceedings of the 1st International Conference on Motion and Vibration Control, 1992, pp. 339–343.
13.
P.
Gardonio
,
Y.-S.
Lee
,
S. J.
Elliott
, and
S.
Debost
, “
A panel with matched PVDF volume velocity sensor and uniform force actuator pair for the active control of sound transmission
,”
Proc. Inst. Mech. Eng.
215
(Part G),
187
206
(
2001
).
14.
H.
Kawai
, “
The piezoelectricity of polyvinylidene floride
,”
Jpn. J. Appl. Phys.
8
,
975
976
(
1969
).
15.
D. M.
Carey
and
F. B.
Stulen
, “
Experiments with a two-dimensional multi-modal sensor
,”
Recent Advances in Active Control of Sound and Vibration, supplement
,
41
52
(
1993
).
16.
F. Charette, C. Guigou and A. Berry, “Development of volume velocity sensors for plates using PVDF film,” Proceedings of ACTIVE 95 (1995), pp. 241–252.
17.
R. L. Clark, W. R. Saunders, and G. P. Gibbs, Adaptive Structures (Wiley, New York, 1998).
18.
A. Preumont, Vibration Control of Active Structures (Kluwer Academic, City, 1997).
19.
T.
Bailey
and
J. E.
Hubbard
, “
Distributed piezoelectric-polymer active vibration control of a cantilever beam
,”
J. Guid. Control
8
,
605
611
(
1985
).
20.
C. K.
Lee
and
F. C.
Moon
, “
Modal sensors/actuators
,”
ASME Trans. J. Appl. Mech.
57
,
434
441
(
1990
).
21.
P. Gardonio and S. J. Elliott, 1998 ISVR University of Southampton, Technical Report No. 277, “Driving point and transfer mobility matrices for thin plates excited in flexure.”
22.
W. Soedel, Vibrations of Shells and Plates (Marcel Dekker, New York, 1993).
23.
J. N. Reddy, Mechanics of Laminated Composite Plates (CRC Press, New York, 1993).
24.
M.
Tohyama
and
R. H.
Lyon
, “
Zeros of a transfer function in a multi-degree-of-freedom vibrating system
,”
J. Acoust. Soc. Am.
86
,
1854
1863
(
1997
).
25.
Y.-S. Lee, “Active Control of Smart Structures using Distributed Piezoelectric Transducers,” Ph.D. thesis, University of Southampton (2000).
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