Page 329 - Mechanical design of microresonators _ modeling and applications

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Microcantilever and Microbridge Systems for Mass Detection

328 Chapter Six

3 × 10 -14
0.005
∆m [kg]
0
34
0.
0.34
f ω
c l 0.0001
0.65
0.65
Figure 6.29 Deposited mass in terms of position and frequency shift ratio.
segments which are clearly compliant. Another simplifying assumption
that is often made with such microdevices is that mass/inertia comes
from only the more massive components (the ones that are also
considered rigid) while the inertia fractions of the compliant members
are neglected. While this approach, which is based on the two above-
mentioned simplifying assumptions, substantially reduces the calcula-
tion volume and effort and is in the majority of situations of sufficient
accuracy, there might be designs, especially of nanoresonators that
are built as thin films where the dissociation rigid-compliant and
with-without inertia is more nuanced. In such cases, by not considering
the compliance and inertia properties of all components, errors might
be generated that could play an important role in the accuracy of
predictions.
Two examples are analyzed in this subsection, namely, a paddle
microcantilever and a paddle microbridge, by comparing their mass
detection performance in the resonant regime when a segment is
considered rigid (partially compliant model) and only inertia pertains
to it, as compared to the situation where all segments are considered
compliant (fully compliant model) and inertia contributions for all
segments are accounted for (full-inertia model).

6.5.1 Paddle microcantilevers
The paddle microcantilever of Fig. 6.30 is used to compare the mass
detection by means of two models. One is the fully compliant (where the
stiffnesses of both segments are taken into account), full-inertia (inertia
contributions from both segments are lumped at the free end) model,
and the other one is a simplified model which considers only the stiff-
ness of the root segment (the thinner one) and the mass of the wider
one as being applied at the end of the root segment.
Obviously, the simplified model is not capable of capturing the
location of the deposited mass ǻm on the paddle, and it is interesting

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