Page 245 - Mechanical design of microresonators _ modeling and applications

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Resonant Micromechanical Systems

244 Chapter Five

2.5 10
ω I , be / ω III , be
1.5

1
c w

c l
5
5
Figure 5.18 Bending resonant frequency ratio: model I predictions against model III
predictions (paddle microbridge).

0.85
ω I / ω III 10
, te , te 0.8

1
c w

c l 5
5
Figure 5.19 Torsion resonant frequency ratio: model I predictions against model III
predictions (paddle microbridge).

Compared to the paddle microbridge where the subscript 1 indicated
the wider segment, the subscript 1, as also indicated in Fig. 5.18, de-
notes the narrower, root segment, and therefore the values of parame-
ters c and c have been chosen accordingly. As Fig. 5.18 shows, the
w
l
bending resonant frequency prediction by model I (the simplest model)
is larger than the prediction yielded by model III (the fully compliant,
full-inertia model). Figure 5.19 has been drawn for the following par-
ticular parameter values: l 1 = 100 ȝm, w 1 = 20 ȝm, and t 1 = 0.5 ȝm. For

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