Page 316 - Mechanics of Microelectromechanical Systems

5. Static response of MEMS 303
used for this example. According to Eq. (1.127) of Chapter 1, the rotation
angle at point 2 (which is actually zero) can be written as:

where (there is no vertical reaction at point 1, and therefore
no y-component at point 2) and By solving Eq. (5.105) for
gives:

The displacement about the x (input) direction at point 1 is given by the same
Eq. (1.127) of Chapter 1 as:

By substituting of Eq. (5.106) into Eq. (5.107), produces the following
input stiffness equation:

The compliance equations that define the input stiffness are explicitly given
in Eqs. (1.133), (1.128) and (1.130) in Chapter 1.
The output stiffness is calculated similarly by assuming that a force is
applied vertically upward at node 4, as shown in Fig. 5.39.

Figure 5.39 Quarter-model with load for output stiffness calculation

An equation can be written in order to express the zero rotation at node 4,
and this leads to the unknown moment