Page 267 - Mechanics of Microelectromechanical Systems
P. 267
254 Chapter 4
The PZT-generated strain, as defined in Eq. (4.141), has been used in Eq.
(4.170). It should be mentioned here that the neutral axis coincides with the
longitudinal symmetry axis of the middle layer, namely:
and that the axial force on the middle layer is zero, whereas the forces on the
two external layers are equal and opposite:
Example 4.21
A multimorph can combine three of the active effects analyzed so far,
namely the thermal, piezoelectric and shape memory effects in order to
produce actuation, sensing or both. Figure 4.59 shows the longitudinal
disposition, from top to bottom, of a piezoelectric (PZT) layer, an electric
insulator layer (such as silicon nitride and whose thickness is negligible
compared to the other layers’ thicknesses), a shape memory alloy (SMA)
layer and a structural layer (made up of polysilicon). Analyze the behavior of
this multimorph transducer.
Figure 4.59 Side view of a PZT-SMA-based multimorph
Solution:
One can assume that initially the PZT layer can function as the actuator
agent, when subject to a voltage variation which will shrink its original length
and this will bend the multimorph, as shown in Fig. 4.58 (b) for a generic