Developments in Ceramic Materials Research

Progress in Porous Piezoceramics 223
The acoustic impedance ( Z aco ) data estimated using Eq.2 and obtained from the values
of fr and fa [35] are shown in Figure 6c. The deviations in the experimental values of k t and
Z aco from the analytical results may be due to the broadening of resonance for lower ceramic
volume ratios and difficulties involved in precisely determining the resonance and anti
resonance frequencies. The electrical impedance spectra of the composite discs are estimated
using Eq.11 and a representative plot for the case of 82 % ceramic volume fraction is shown
in Figure 6d. The resonance peak corresponds to the thickness-mode vibrations. It can be seen
from the figures that the experimental results are in good agreement with the analytical
results. This indicates that this analytical model gives rise to reasonably acceptable results.
Electrical impedance spectra of a 3-3 piezocomposite are plotted for different volume
fractions and are shown in Figure 7. The thickness-mode resonance behaviour does not vary
linearly with piezoceramic content. The resonance and antiresonance frequencies show a
minimum for a ceramic volume fraction of about 45%. Lower value of electrical impedance
at resonance is desirable for ultrasonic transmitting application, because this leads to
enhanced transmitting response. For such an application, a 3-3 piezocomposite transducer
with about 45% piezoceramic volume fraction is preferable.
Figure 7. Variations in (a) electrical impedance spectrum and (b) resonance and anti-resonance
frequencies, with ceramic volume fraction.
4. FINITE ELEMENT MODELLING OF POROUS PIEZOCERAMICS
Several analytical models have been proposed to study the characteristics of ideal 3-3
piezocomposites [36, 37, 20]. All these models deal only with materials aspects of the
composites. However, the transducer characteristics of these materials have not been studied
extensively, for which Finite Element Modelling (FEM) would be a simple and effective tool.
FEM studies on 1-3 piezocomposite transducers have been reported by several authors, for
example [Ref. [38]. In these studies, only one unit cell of the composite block has been
modelled, assuming that it represents the entire piezocomposite structure. Although these
models can give material parameters like piezoelectric coefficients, to considerable accuracy,
they are inadequate to predict the lateral-mode resonance of a transducer of finite dimensions.
Hence, real-size 3-dimensional FEM studies are necessary to evaluate the device