Page 263 - Mechanics of Microelectromechanical Systems
P. 263
250 Chapter 4
different layer material properties, results in bending of the multimorph that
can be used for either actuation or sensing purposes. Using three or more
active layers in a compound microcantilever allows for more power to be
produced by the actuator (the stiffness of the resulting structure is larger
because of more beams in parallel) or for combining actuation and sensing
together in the same device. Figure 4.57 shows a three-layer multimorph with
its reference frame.
Figure 4.57 Three-layer multimorph with geometry and reference frame
The model developed next, together with the related solved examples and
more detailed derivation can be found in Garcia and Lobontiu [12]. Figures
4.58 (a) and (b) illustrate the multimorph composition and its deformed shape.
The interface fiber between layers i and i+1 has a unique deformation and
therefore the strains of the two neighboring layers at this interface should be
identical. By applying the principle of linear superposition, the resulting strain
comprises three terms: one is produced by axial deformation of a layer, the
second is produced by bending and the third term considers the strain which
can be induced externally. As a consequence, the strain continuity equation at
the interface between layers i and i+1 is:
Since there is no external load acting axially, the sum of all the forces needs
to be zero:
