Page 192 - Mechanical design of microresonators _ modeling and applications

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Microbridges: Lumped-Parameter Modeling and Design

Microbridges: Lumped-Parameter Modeling and Design 191
y

first segment

anchor symmetry line

3 2 1
x anchor

first mirrored segment l/2

l

Figure 4.15 Top view of microbridge formed of identical and mirrored compliant
segments.

4.4.3 Serially compounded microbridges
Microbridges of more complex geometric configurations can be formed
by serially combining basic shapes, similar to the procedure that de-
tailed in Chap. 3 where several compound microcantilever and micro-
hinge designs have been studied. Two generic cases of serially
compound microbridges with associated applications that are imple-
mented in MEMS design are studied in this section, namely, two-
segment and three-segment configurations.

Two-segment microbridges. One class of serially compounded micro-
bridges is formed of configurations containing two identical basic units
that are placed in mirror with respect to the midpoint of the resulting
microbridge, as shown in Fig. 4.15. This category resembles the single-
profile microbridge class which has just been studied. While the single-
profile microbridges are defined by one curve only over the whole
length, the two-segment designs, although preserving the transverse
symmetry property, can be defined by several curves over one half. As
a consequence, the two-segment fixed-fixed flexible component has
transverse symmetry, and the structurally identical case of a generic
fixed-free member was analyzed in Chap. 3 based on the sketch of
Fig. 3.7, which is reproduced here in Fig. 4.15 to highlight the changes
in boundary conditions.
As shown in the following, the bending and torsional resonant
frequencies of the entire structure can be expressed in terms of
compliances and inertia-related properties that define only one-half the

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