Page 267 - Mechanics of Microelectromechanical Systems
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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
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