6th National Congress on Theoretical and Applied Mechanics, Ghent, May 26-27, 2003.
NCTAM-2003-124
1
A novel electrode design for piezoelectric film sensors:
experimental validation
A. François, P. De Man and A. Preumont
Active Structures Laboratory - Université Libre de Bruxelles
CP.165-42, Av. F.D. Roosevelt 50, B-1050 Brussels, Belgium
email: arfranco@ulb.ac.be, pdeman@ulb.ac.be, andre.preumont@ulb.ac.be
Abstract— This paper describes and demonstrates a technology for making distributed piezoelectric sensors with spatial filtering properties. The concept is based on a porous
electrode with variable porosity, which allows to tailor the
effective piezoelectric coefficients in two dimensions. The
technology is illustrated with an application to a volume displacement sensor for a simply supported plate and a transparent implementation on a glass plate is presented.
Keywords— piezoelectric film,
tributed sensor, modal filter
porous electrode,
dis-
I. Introduction
T
HERE are two broad ways to achieve spatial filtering:
(i) arrays of discrete sensors [1] and (ii) continuous
distributed sensors. When wired with independent conditioning electronics and connected to a linear combiner,
discrete array sensors are very flexible, because they are
reconfigurable, and the weighing coefficients can easily be
changed, sometimes in real time, to achieve the desired output, for example a modal filter. Unfortunately, discrete array sensors are prone to spatial aliasing which brings strong
limitations when they are used in structural control applications [2]. Distributed sensors are free of spatial aliasing,
but they lack the flexibility of their discrete counterparts.
The modal filtering of one-dimensional structures with continuous PVDF film has been known for some time [3], [4],
[5]; it is achieved by tailoring the width of the electrode
(and possibly reversing the polarity). Although the spatial
filtering of plates and shells with two-dimensional PVDF
films has been suggested [5], it has never been implemented
in practice, for lack of capability of continuously shaping
the piezoelectric properties of the sensor material. A way
to turn around this difficulty by a proper electrode design
was proposed by the present authors [6], [7], [8]. It was applied to a cantilever beam covered with a PVDF film [2] and
compared to the classical modal filter of the beam theory.
More recently [9], the sensor concept was extended to twodimensional structures: an electrode profile was designed in
order to achieve a volume velocity (or displacement) sensor
[10], [11] of a simply supported rectangular plate; the close
agreement of the output with measurements from a laser
scanner vibrometer confirms the soundness of the proposed
concept. The present paper summarizes the main features
of the technology of porous electrode and presents a transparent implementation on a glass plate. Section 2 recalls
the background of distributed sensors, section 3 shows experimental results of a volume displacement sensor for a
simply supported plate and section 4 unveils the possibility of integrating the volume displacement sensor into a
transparent layer on a glass plate.
II. Distributed sensor
The need for distributed sensors arises from the necessity to reduce the spatial aliasing of discrete array filters,
which occurs for all vibration modes with wavenumbers beyond the size of the sensor array. Although the theory of
modal distributed piezoelectric sensors has been known for
some time [4], [5], they have never been implemented in
practice to two-dimensional structures, because the theory
is based on tailoring the piezoelectric coefficients, which
cannot be done in practice. A practical way of designing
distributed modal filters is discussed in this paper. The
theory of modal filtering with distributed sensors can be
addressed in two different ways: (i) based on the orthogonality relationships for distributed structures or (ii) as a
limit case of a discrete array filter when the number of elements in the array increases to infinity. The first approach
was addressed by Lee and Moon [4], [5], while the second
one was used by the present authors [2]; it has the advantage of being more intuitive, especially when one analyses
the impact on spatial aliasing.
The distributed sensor can be viewed as the limit discrete array sensor where the number of sensing elements
increases and the electrode density is such that the local
production of electric charges matches the desired local effective weighing coefficient. A practical way to achieve this
is to use a ”porous” electrode as shown in Fig.1; the max(a)
(b)
(c)
S1
S1
1 mm
(d)
Fig. 1. (a) Porous electrode, (b) detail of the motif with
variable porosity, (c) double sided motif (fraction of
electrode area = 50 %), (d) single sided motif (the
other electrode is continuous).
6th National Congress on Theoretical and Applied Mechanics, Ghent, May 26-27, 2003.
NCTAM-2003-124
2
Local weighing
coefficient a(x,y)
(a) Bi-oriented PVDF
(c)
d31 = 2.5 pC/N
d32 = 2.5 pC/N
(a)
x
(b)
0
y
Local weighing
coefficient a(x,y)
(b) Mono-oriented PVDF
d31 = 22.5 pC/N
d32 = 2.5 pC/N
Fig. 3. (a) Top view of the PVDF film mounted on the
plate, (b) PCB plate without PVDF film, showing the
honeycomb electrode, (c) detail of the honeycomb.
x
0
piezoelectric properties of the PVDF film. This profile depends also on the physical properties and boundary conditions of the structure on which the sensor is bonded.
y
Fig. 2. Weighing coefficient profile α(x, y) of the piezoelectric properties to achieve a volume displacement sensor
with a (a) bi-oriented PVDF film (d32 = d31 ) and (b)
mono-oriented PVDF film (d32 = 0.1 d31 ) for a simply
supported plate.
imum sensitivity is obtained where the electrode is continuous (in the center in Fig 1.a) and the local sensitivity
is decreased continuously by introducing some porosity in
the continuous electrode, by means of a honeycomb design
(Fig.1.b). The local electrode density is selected in such a
way that the local production of electric charges matches
the desired local weighing coefficient α(x, y) (Fig. 2). The
exact relationship between the porosity and the equivalent
piezoelectric coefficients can be explored with a tridimensional finite element analysis [7], [12].
III. Volume displacement sensor of a simply
supported plate
The distribution of the effective piezoelectric properties
to achieve a volume displacement (or velocity) sensor has
been described in [2], [6], [7]. Figure 2 shows this distribution, computed for two different PVDF films; Fig.
2.(a) corresponds to a bi-oriented PVDF with isotropic
piezoelectric properties, and Fig. 2.(b) to a mono-oriented
PVDF with anisotropic piezoelectric properties [13]. It
clearly appears that the weighing profile depends on the
The first test article is shown in Fig.3; it is a 180 mm x
260 mm x 1.6 mm (glass epoxy) PCB board with a 37 µm
thick copper electrode. The electrode is full in the center of
the plate and a honeycomb structure with variable width
appears when one moves towards the edges. The honeycomb pattern is etched with standard PCB technology in
the copper electrode, and a 40 micron thick bi-oriented
PVDF film with a one-sided continuous electrode is glued
on top of it to form the distributed sensor with variable effective piezoelectric properties. The electrode density has
been taken proportional to the effective piezoelectric properties, without correction to account for tridimensional effects in the electric field distribution within the thickness of
the piezo film. The test plate is mounted in an aluminium
frame and the simply supported boundary conditions are
materialized by a dual elastomer joint (on both sides) with
a circular cross section.
The experimental set-up is illustrated Fig. 4. Four voice
coil actuators are located symmetrically near the corner of
the plate and are working in parallel, driven by the same
current. The volume displacement is measured with a scanner laser vibrometer (the mesh used for the laser measurement is also shown in Fig. 4). Figure 5 compares the transfer functions between the current applied to the actuators
and the volume displacement sensed with (i) the PVDF
sensor and (ii) the laser scanner vibrometer. The curves
are very close to each other in amplitude. Nevertheless,
an unexpected non minimum phase zero [14] is observed in
the PVDF sensor signal. Similarly good results have been
obtained with a loudspeaker excitation [9].
6th National Congress on Theoretical and Applied Mechanics, Ghent, May 26-27, 2003.
NCTAM-2003-124
Laser vibrometer
measurement mesh
3
Voice coil actuators
Fig. 6. Transparent volume displacement sensor on a glass
plate.
Electrode layer on PET film
25 µm glue layer
40 µm PVDF film
Fig. 4. Experimental set-up.
25 µm glue layer
(1,1)
(1,3)
Etched
electrode
Glass
(1,5)
(3,1) (3,3)
Fig. 7. Detail of the transparent electrode.
spectively with the transparent sensor and the laser scanner
vibrometer. The agreement between the transfer functions
is good, but a phase shift is observed in the PVDF sensor
response.
V. Conclusions
Fig. 5. PCB board. Transfer functions between the current
applied to the voice coil actuators and the volume displacement. Comparison between the honeycomb piezoelectric sensor and the laser measurement.
A concept of honeycomb electrode design has been proposed to tailor the effective piezoelectric properties of
PVDF films in two dimensions [2, 6-8]; this offers new
prospects for developing distributed sensors with spatial filtering properties. This technique has been validated with
various experiments, in particular a volume displacement
sensor for a simply supported rectangular plate. The technology for making transparent electrodes has also been presented.
Acknowledgments
IV. Transparent implementation
Figure 6 shows a transparent implementation of the volume displacement sensor. It consists of a 40 µm monooriented PVDF film glued on a glass plate with 25 µm
connecting layers (Fig. 7). The transparent electrodes are
made of ITO (Indium Tin Oxide). A laser lithography
process is used to shape the electrode. Figure 8 shows a
comparison of the transfer functions between the current
applied to the actuators and the sensor output obtained re-
This work was supported by the Ministry of Région
Wallonne (DGTRE) under grant n◦ 014427 (SAAB) and
the Inter University Attraction Pole IUAP 5 on Advanced
Mechatronic Systems.
References
[1]
[2]
L. Meirovitch and H. Baruh, “The implementation of modal
filters for control of structures,” AIAA Journal of Guidance,
vol. 8, no. 6, pp. 707–716, 1985.
A. Preumont, A. François, P. De Man, and V. Piefort, “Spatial
6th National Congress on Theoretical and Applied Mechanics, Ghent, May 26-27, 2003.
NCTAM-2003-124
(1,1)
[4]
(1,3)
(3,1) (3,3) & (1,5)
[5]
[6]
[7]
[8]
[9]
[10]
Fig. 8. Transparent sensor on a glass plate. Transfer
functions between the current applied to the voice coil
actuators and the volume displacement. Comparison
between the honeycomb piezoelectric sensor and the
laser measurement.
[11]
[12]
[13]
[3]
filters in structural control,” Journal of Sound and Vibration,
2003, To appear.
S. E. Burke and J. E. Hubbard, “Active vibration control of a
simply supported beam using a spatially distributed actuator,”
[14]
4
IEEE Control Systems Magazine, pp. 25–30, August 1987.
C. K. Lee, “Theory of laminated piezoelectric plates for the
disign of distributed sensors/actuators. part i : Governing equations and reciprocal relationships,” J. Acoust. Soc. Am., vol. 87,
no. 3, pp. 1144–1158, 1990.
C.K. Lee and F.C. Moon, “Modal sensors/actuators,” ASME
Journal of Applied Mechanics, vol. 57, pp. 434–441, 1990.
A. Preumont, P. De Man, and A. François, “Some issues related
to the feedback control of a baffled plate,” Journal of Structural
Control, vol. 9, pp. 153–167, 2002.
A. Preumont, Vibration Control of Active Structures, An Introduction, Kluwer Academic Publishers, Dordrecht, second edition, February 2002.
A. Preumont, Method for Shaping Laminar Piezoelectric Actuators and Sensors and Related Devices, March 2002, International patent application PCT/BE02/00026.
A. Preumont, A. François, and P. De Man, “A novel electrode
design for spatial filtering with piezoelectric films: Experimental
validation,” in Photonics Fabrication Europe SPIE Conference,
Brugge, Belgium, October 2002.
M.E. Johnson and S.J. Elliott, “Active control of sound radiation
using volume velocity cancellation,” J. Acoust. Soc. Am., vol.
98, no. 4, pp. 2174–2186, 1995.
J. Rex and S.J. Elliott, “The QWSIS - a new sensor for structural
radiation control,” in MOVIC, Yokohama, September 1992, pp.
339–343.
V. Piefort, Finite Element Modeling of Piezoelectric Active
Structures, Ph.D. thesis, Université Libre de Bruxelles, 2001,
(The software is currently part of SAMCEFTM of SAMTECH
S.A. Liège - Belgium).
Piezotech S.A., “Films piezo- et pyro-electriques,” Documentation technique DT-96/a, St-Louis, France, 1997.
N. Loix, J. Kozanek, and E. Foltete, “On the complex zeros of
non-colocated systems,” Journal of Structural Control, vol. 3,
no. 1-2, pp. 79–87, June 1996.