Page 268 - Mechanics of Microelectromechanical Systems
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4. Microtransduction: actuation and sensing                      255
         multimorph. The SMA layer, being at low/martensitic temperature, can easily
         be deformed, as driven by the PZT deformation.
             If a  temperature  increase is  subsequently  applied so that  the  SMA’s
         martensite  phase  transforms  into austenite, the  SMA layer  will  shrink,
         becoming the actuator, and the multimorph will further bend.  If no voltage is
         supplied to the  PZT  during the  SMA  actuation, the PZT can  act as a sensor
         because the change in strain translates in a proportional voltage change. As a
         consequence, the sandwich device can function as both actuator and sensor by
         switching the functions of the PZT layer.
             It  is of  interest  to quantify the  level of  actuation, as well as  the
         relationship defining  the  voltage detection during the  second  phase, when
         SMA  is the actuator and  the  PZT  layer is the sensor. By  using the generic
         multimorph model, it is possible to calculate the curvature radius R, as well as
         the  corresponding  tip moment acting on the bender.  At  the  same  time, the
         voltage generated through SMA-driven deformation into the PZT layer can be
         evaluated by  considering  the  strain on  its  lower  fiber as  being produced
         through bending and axial deformation, namely:






          where the axial force   acting on the PZT layer is:







          and the curvature radius corresponding to  SMA-generated  bending is
          expressed as:




          where:










          and:
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