Page 132 - Mechanics of Microelectromechanical Systems

2. Microcantilevers, microhinges, microbridges 119
A check was performed by considering that the cross-section is constant, and
the compliances of Eq. (2.183) reduced to the simpler form:

By substituting Eqs. (2.184) into Eq. (2.183), the stiffness becomes:

which is indeed the stiffness of a constant cross-section fixed-fixed beam of
length l.

Example 2.17
Compare the bending stiffness of a right elliptic microbridge, as the one
sketched in Fig. 2.25 (b), to the bending stiffness of a constant rectangular
cross-section microbridge. The two microstructures have the same length,
thickness, minimum width and material properties.

Solution:
The right elliptic microbridge is formed of two identical right elliptically-
filleted microhinges (as the one sketched in Fig. 2.14). As a consequence, by
using the compliances of Eqs. (2.81), (2.82) and (2.83), the stiffness of Eq.
(2.183) can be found for the right elliptic microbridge.

Figure 2.38 Bending stiffness comparison between right elliptic microbridge and constant
rectangular cross-sectionmicrobridge