Page 334 - Mechanical design of microresonators _ modeling and applications

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Microcantilever and Microbridge Systems for Mass Detection

Microcantilever and Microbridge Systems for Mass Detection 333

4
0.8
r m
2.
2.5
5
c w
c l
0.4
4 4
Figure 6.35 Full versus simplified model of paddle microbridge: comparison of the
deposited mass quantities through bending.

symmetry axis

∆m
w 1 b w 2

w 2 / 2

l 1 l 2 l 1
Figure 6.36 Paddle microbridge with eccentrically localized mass.

The mass prediction by the simplified model is given in Eq. (6.81)
whereas the mass equation corresponding to the fully compliant, full-
inertia, half-length paddle microbridge is
/
2
1 (1– f ) –1
Ȧ
ǻm = m f (6.86)
f
4
2/
2/
(l + l 2– 2a) (l + l 2+4a) 2 (l + l 2) 6
2/
1 1 / 1
where m is the mass given in Eq. (4.126). The mass ratio of Eq. (6.83) is
f
plotted in Fig. 6.35 for the particular value a = 0 (which means that the
deposited mass is localized at the midpoint of the paddle microbridge)
3
as well as for l = 200 “m, t = 1 “m, E = 160 GPa, ȡ = 2200 kg/m , and
1
ǻȦ = 0.0001.
Torsion. The attached particle can be localized as shown in Fig. 6.36,
and in this case the torsional resonance of the paddle microbridge can
be utilized to analyze the mass addition phenomenon.

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