Page 89 - Mechanics of Microelectromechanical Systems

76 Chapter 2
changes can be monitored quasi-statically or dynamically. The amount of
mass, as well as its position on the microcantilever’s plane, can be
determined by combining experimental data with modeling as shown in the
following examples.

Example 2.3
Calculate the amount of deposited mass, as well as its position on a
constant rectangular cross-section microcantilever, as the one sketched in Fig.
2.6 when the following amounts are known: E = 180 GPa,

Figure 2.6 Mass added to a microcantilever as a gravitational force
Solution:
Assume that a certain amount of mass attaches locally on the
microcantilever such that it can be treated as a point load. If a sensitive layer
is set over the length measured from the free end, the attached mass
(positioned at length which is measured as shown in Fig. 2.6) will deflect
the microcantilever a tip slope that can be determined experimentally for
instance. The tip rotation is related to the force owing to the deposited mass
as:

The gravitational force is equal to mass times the gravity constant, and
therefore Eq. (2.35) changes to:

As Eq. (2.36) indicates it, a given tip rotation can be produced by different
mass quantities because they can attach at different locations over the
sensitive length Figure 2.7 shows the plot of mass in terms of the
deposition location, and it can be seen that all the points located on the curve
satisfy the condition of Eq. (2.36).