Page 232 - Mechanical design of microresonators _ modeling and applications

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Resonant Micromechanical Systems

Resonant Micromechanical Systems 231

1.04 0.1
rω I- II
b
1
1 1
c w

c l 0.01
5 5
Figure 5.3 Bending resonant frequency ratio: model I predictions against model II
predictions (paddle microcantilever of constant thickness).

10
0.1
I- III
rω b

0.
1
0.1
c w
c l 0.01
1 1
Figure 5.4 Bending resonant frequency ratio: model I predictions against model III
predictions (paddle microcantilever of constant thickness).

where the superscripts I, II, and III indicate models I, II, and III, respectively.
The bending resonant frequencies corresponding to models I and II are given
in Eqs. (5.3) and (5.8), whereas the bending resonant frequency according to
model III is formulated in Eq. (3.33). Figures 5.3 and 5.4 are three-dimen-
sional plots of the ratios defined in Eqs. (5.11).
The following nondimensional parameters were used to draw Figs. 5.3 and
5.4:

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