Page 88 - Mechanics of Microelectromechanical Systems

2. Microcantilevers, microhinges, microbridges 75

The stiffnesses of Eqs. (2,27) to (2.30) can be written as functions of
and t only, where t enters to its first, second or third power in the respective
stiffnesses. In order to compare the stiffnesses containing t to its first power,
the following ratios are introduced:

According to their definitions given in Eq. (2.31), both and are larger
than 1, and also because the length is at least a few times larger than
the width. It is then clear that In other words, the
smallest is the linear direct-bending stiffness whereas the largest is the
axial stiffness If and range within the intervals with
i= 1, 2 , then can be up to larger than which, for
means 100 times larger. can be up to larger than
which for a value of for instance, signifies 10000 times larger.
The cross-stiffnesses can be related as:

and the interpretation given to the first Eq. (2.32) remains valid. The rotary
stiffnesses can be connected according to:

The second Eq. (2.34) indicates that the ratio of the torsion stiffness to the
direct-bending rotation stiffness is a fixed amount in terms of geometry.
Moreover, the second Eq. (2.34) indicates that for very thin cross-sections,
the torsional stiffness is smaller than the bending-related one.

2.2.2.1 Sensitivity to Position of Applied Load in Mass Deposition
Applications

As previously mentioned, the microcantilevers can be utilized to detect
minute amounts of substances that attach to them, either chemically or
physically (through adsorbtion mainly). The addition of new substances
alters the elastic and inertia properties of the microcantilevers, and these