Page 266 - Mechanics of Microelectromechanical Systems

4. Microtransduction: actuation and sensing 253
and the common width of the layers is Use the analytic model
developed herein, as well as an independent finite element simulation.

Solution:
The Ansys software has been used to run the finite element analysis, with
two-dimensional elements having the material properties of Table 1. The tip
slope was 0.02° which translated into a curvature radius of approximately R =
0.11 m. The analytic model proposed here resulted in a curvature radius of R
= 0.1 m, and therefore there is agreement between the two methods, and this
particular example constitutes another check of the accuracy of the proposed
model.

Example 4.20
An anti-parallel trimorph is formed of two identical active layers that are
laminated on a middle structural layer. When the two external layers are
actuated such that one compresses and the other one stretches, desirably by
the same amount of strain, an anti-parallel configuration is achieved with
enhanced actuation/sensing capabilities. Assuming the two active layers are
made of PZT material and that the middle layer is a polysilicon substrate,
determine the bending moment that can be achieved by this structure when
applying a +120/ -120 V variation on the two PZT layers.

Solution:
Assuming the top PZT layer shrinks under the negative voltage variation,
and the other PZT layer stretches when subject to the positive voltage
variation, the strains induced in the two layers are:

By utilizing the conditions of Eq. (4.168) into the generic multimorph model,
one obtains the following particular equation for the curvature radius R:

The tip bending moment is: