161 A dramatic drop of output power and resonant frequency, however, was measured when
the sample was excited to a greater acceleration level of 0.75 g as shown in Figure 7-8. This is because fracture starts to develop on the anchor of the cantilever, which connects
the free-standing structure to the base, and further increments of acceleration level with the same proof mass may break the free-standing structure completely. The maximum
stress that the structure can withstand before failure can be calculated by substituting equations 3-4, 3-18, 7-5 and 7-10 into,
7-11
From the experiment with sample BA1, the maximum stress allowed was calculated as 115 MPa and 65 MPa on the surface of the electrode and PZT layers respectively.
7.5 Evaluation of Electrical Output
The electrical output from both the series and parallel polarised samples was obtained by connecting the electrode terminals in a configuration that resembles series, parallel
and a combination between these two connections. For example, a connection between electrode number 1 and 2 is denoted as 1;2. A connection to make electrode number 2
and 4 as a terminal shorting 2 and 4 and electrode number 1 and 3 shorting 1 and 3 as another terminal, is denoted
as 2+4; 1+3. The ‘;’ denotes a separation between two terminals.
The PZT network configuration of a multimorph structure can be analysed as a conventional electrical circuit consisting of capacitors, resistors and voltage sources.
The resultant capacitance of the configuration was obtained by direct measurement with a Wayne Kerr LCR meter, by connecting a combination of electrode terminals of the
multimorph structure. The measurements of the capacitance are summarised in Table 7-2.
The resultant resistance of the PZT layer network corresponds to the optimum resistive load at the maximum output power of the PZT layer when the structure is excited to its
mm b
mm eff
I l
d z
y M
2
162 resonant frequency. The resultant voltage is simply the sum of the voltages produced by
the network of individual PZT sections.
Table 7-2: Measurement of capacitance of all the possible configurations of terminal connection for series and parallel polarised samples.
Connection configuration
Capacitance nF BA2
Series Polarised BA3
Parallel Polarised 1;2
21.3 21.3
1;2 Short 3+4 21.3
21.3 1;3
10.3 10.1
1;3 Short 2+4 14.1
13.8 1;4
7.0 19.8
1;4 Short 2+3 10.6
31.0 2;3
20.0 6.9
2;3 Short 1+4 30.1
10.7 2;4
10.3 10.2
2;4 Short 1+3 14.1
13.9 3;4
21.3 21.1
3;4 Short 1+2 21.3
21.1 1+2; 3+4
61.5 63.7
1+3; 2+4 20
19.8 1+4; 2+3
42.8 42.0
7.5.1 Series polarised multimorph
A series polarised Figure 7-6 a sample, BA2, with dimensions as shown in Table 7-1 was excited to its resonant frequency at 403 Hz with a constant acceleration level of 0.5
g. The output power from each of the PZT sections was obtained by measuring the voltages across the electrode terminals sandwiched between each PZT layer when
driven over a range of resistive loads from 1 kΩ to 150 kΩ.
