The purpose of this work is to explore practical limitations associated with the design of distributed modal sensors from induced strain materials for two-dimensional structures and illuminate difficulties associated with positioning sensors on structures in general. Results from this study indicate that a true modal sensor cannot be realized on a two-dimensional structure unless the boundary conditions are all pinned. This result stems from the fact that the sensor aperture must be orthogonal with respect to the structural mode (eigenfunction) and the curvature of the structural mode to render a distributed modal filter. The only class of functions satisfying this condition are sinusoidal functions. In addition, positioning of distributed strain sensing material is shown to be critical to the performance of the sensor over a specified bandwidth, specifically in the vicinity of structural resonances.

1.
Burke, S. E., and Clark, R. L., 1995, “Transducer Tolerance Theory for Structural Control,” Proceedings of the SPIE Smart Structures and Materials Conference, San Diego, CA.
2.
Burke
S. E.
, and
Hubbard
J. E.
,
1990
, “
Spatial Filtering Concepts in Distributed Parameter Control
,”
ASME Journal of Dynamic Systems, Measurement, and Control
, Vol.
112
, pp.
565
573
.
3.
Burke
S. E.
, and
Hubbard
J. E.
,
1991
, “
Distributed Transducer Vibration Control of Thin Plates
,”
Journal of Acoustical Society of America
, Vol.
90
No.
2
, pp.
937
944
.
4.
Clark
R. L.
,
Fuller
C. R.
, and
Wicks
A. L.
,
1991
, “
Characterization of Multiple Piezoelectrics for Structural Excitation
,”
Journal of the Acoustical Society of America
, Vol.
90
, No.
1
, pp.
346
357
.
5.
Clark
R. L.
, and
Fuller
C. R.
,
1992
(a), “
Control of Sound Radiation with Adaptive Structures
,”
Journal of Intelligent Material Systems and Structures
, Vol.
2
, No.
3
, pp.
431
452
.
6.
Clark
R. L.
, and
Fuller
C. R.
,
1992
(b), “
Modal Sensing of Efficient Acoustic Radiators with PVDF Distributed Sensors in Active Structural Acoustic Approaches
,”
Journal of the Acoustical Society of America
, Vol.
91
, No.
6
, pp.
3321
3329
.
7.
Clark
R. L.
,
Burdisso
R. A.
, and
Fuller
C. R.
,
1993
, “
Design Approaches for Shaping Polyvinylidene Fluoride Sensors in Active Structural Acoustic Control
,”
Journal of Intelligent Material Systems and Structures
, Vol.
4
, pp.
354
365
.
8.
Collins, S. A., Miller, D. W., and von Flotow, A. H., 1990, “Sensors for Structural Control Applications Using Piezoelectric Polymer Film,” MIT Report, SERC #12-90.
9.
Graff, K., 1975, Wave Motion in Elastic Solids, Ohio State University Press.
10.
Gu
Yi
,
Clark
R. L.
,
Fuller
C. R.
, and
Zander
A. C.
,
1994
, “
Experiments on Active Control of Plate Vibration Using Piezoelectric Actuators and Polyvinylidene Fluoride Modal Sensors
,”
ASME JOURNAL OF VIBRATION AND ACOUSTICS
, Vol.
116
, pp.
303
308
.
11.
Kynar Piezo Film Technical Manual, 1987, Pennwalt Corporation.
12.
Lee
C. K.
, and
Moon
F. C.
,
1990
, “
Modal Sensors/Actuators
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
57
, pp.
434
441
.
13.
Lee, C. K., Chiang, W. W., and O’Sullivan, T. C, 1991 (a), “Piezoelectric Modal Sensors and Actuators Achieving Critical Damping on a Cantilever Plate,” AIAA Paper, 89-1390, pp. 2018–2026.
14.
Lee
C. K.
,
Chiang
W. W.
, and
O’Sullivan
T. C.
,
1991
(b), “
Piezoelectric Modal Sensor/Actuator Pairs for Critical Active Damping Vibration Control
,”
Journal of the Acoustical Society of America
, Vol.
90
, No.
1
, pp.
374
383
.
15.
Lee
C. K.
, and
O’Sullivan
T. C.
,
1991
, “
Piezoelectric Strain Rate Gages
,”
Journal of Acoustical Society of America
, Vol.
90
, No.
2
, pp.
945
953
.
16.
Love, A., 1944, A Treatise on the Mathematical Theory of Elasticity, Dover, New York, NY.
17.
Miller, S. E., and Hubbard, J. E., 1987, “Observability of a Bernoulli-Euler Beam Using PVF2 as a Distributed Sensor,” Dynamics and Control of Large Structures: Proceedings of the 6th VPl & SU/AIAA Symposium, L. Meirovitch, ed., pp. 375–390.
18.
Miller, D. W., Collins, S. A., and Peltzman, S. P., 1990, “Development of Spatially Convolving Sensors for Structural Control Applications,” AIAA Paper 90-1127-CP, pp. 2283–2297.
19.
Tzou
H. S.
, and
Tseng
C. I.
,
1990
, “
Distributed Piezoelectric Sensor/Actuator Design for Dynamic Measurement/Control of Distributed Parameter Systems: A Piezoelectric Finite Element Approach
,”
Journal of Sound and Vibration
, Vol.
138
, No.
1
, pp.
17
34
.
This content is only available via PDF.
You do not currently have access to this content.