smart technologies for safety engineering

308 Smart Technologies for Safety Engineering
Table 8.3 Material properties of (transversally isotropic) PZT4 ceramic (mass
density ρpz = 7500 kg/m 3 , ɛ0 = 8.854 × 10 −12 F/M)
Elastic constants GPa
Ĉ pz pz
11 = Ĉ22 Ĉ pz
12
Ĉ pz
13
Ĉ pz
33
Ĉ pz
44
Ĉ pz
66
= Ĉ pz
23
= Ĉ pz
= 1
2
55
Ĉ pz
11
pz
− Ĉ12 107.60
63.12
63.85
100.40
19.62
22.24
Piezoelectric C/m 2
ê pz
15 = êpz 24
ê pz
31
ê pz
33
= êpz
32
12.0
−9.6
15.1
Dielectric ɛ0
ɛ pz
11 = ɛpz 22
ɛ pz
33
1936
2109
Several configurations of piezoelectric transducers were checked, for example:
one square patch 30 mm × 30 mm in the center of the upper side of the plate;
four square patches of 10 mm × 10 mm fixed symmetrically around the center of the plate
(as shown in Figure 8.8).
In the latter configuration it is assumed that the transducers are to be excited simultaneously
by the same voltage, so they act in the same way on the plate and form one multipatch piezoactuator.
This approach gave a better performance (a bigger deflection of the center of the plate
and a better deformation shape) using less piezoelectric material so it was used in the later
analysis. Another effective configuration can be triangularly shaped piezoelectric actuators for
vibroacoustic control systems, proposed in Reference [40].
8.10 Modeling and Analysis of an Active Single-Plate Panel
8.10.1 Kinds and Purposes of Numerical Tests
Several numerical tests concerning the modeling and design of particular components or the
whole assembly of a panel cell were carried out. In some of them the panel or (only) the elastic
plate is coupled to the acoustic medium (i.e. the air waveguide). Some of the finite element
tests were matched with the corresponding analytical solutions. Three kinds of tests can be
distinguished:
Plate tests (eigenvalue and frequency-response analyses) are used to identify elastic plate
resonances and to discover a specific resonance of the coupled system of the elastic plate
and acoustic medium waveguide.
Multilayer tests (analytical one-dimensional frequency-response analyses of multilayered
media) are used to confirm the coupled resonance and to select the thickness and material of
the poroelastic layer.
Panel tests (frequency-response and single-frequency FE analyses) are used to test active
and passive behavior (performance) of the panel.