Page 305 - Mechanical design of microresonators _ modeling and applications

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Microcantilever and Microbridge Systems for Mass Detection

304 Chapter Six
deposited particle y
z
F z
3
1 l y
x 2 l x x
l
microcantilever
(a) (b)
Figure 6.11 Point-mass detection by constant-cross-section microcantilever: (a) side view;
(b) top view.

either case to evaluate the deposited mass, as two approaches can be
pursued, namely, the static (quasi-static) procedure and the modal
(resonant) one.

6.3.1 Constant-cross-section
microcantilevers
Constant (usually rectangular) cross-section microcantilevers are con-
structively simple devices that enable mass deposition detection. This
section details the mass detection process by considering first that the
deposition occurs in a pointlike manner and then in a layer. For each
situation, a static approach is presented as well as a resonance-based
procedure.

Point-mass detection. Mass can deposit (attach) locally on a very small
area of the microcantilever, which may well be considered a point. When
the microcantilever is monitored quasi-statically, the deposited mass
might bend the member, and this deflection change can be determined
experimentally. In case the experiment is conducted modally, the bend-
ing resonant response is altered by mass deposition, and the resulting
resonant frequency shift enables quantification of the deposited mass.
Both approaches are studied in the following subsections.
Static approach. The problem of static detection of mass presence is
briefly discussed next. A more detailed presentation of this subject is
21
given by Lobontiu and Garcia. A pointlike mass is first assumed that
attaches to a microcantilever, as shown in Fig. 6.11. In essence, the
mass quantity ǻm, as well as its position on the microcantilever (quan-
tified by l x and l y ), can be determined by considering the deformations
produced under the action of the deposited mass gravitational effects
through bending and torsion at the free end, which are u 1z , ș 1y , and
ș 1x , and which can be measured experimentally.

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