Page 95 - Mechanics of Microelectromechanical Systems

82 Chapter 2
In order to render this problem determinate, another set of experimental
measurements, for instance the deflection at a point placed at a distance
from the free end, is needed. In this case, the deflection at the experimental
point of detection is:

Equations (2.47) and (2.53), together with Eqs. (2.38), enable solving for
and from experimental measurements.
All these calculations are valid for and have been applied thus far to a
constant cross-section microcantilever. The following example will solve this
problem for the cases where the cross-section of the microcantilever is
variable.

Example 2.6
Determine the force components and that are applied at a
microcantilever’s tip when contacting a three-dimensional surface. The tip
slopes and tip deflection are experimentally available. Assume
that the microcantilever’s cross-section is variable and neglect the axial
deformation.

Solution:
The Castigliano’s displacement theorem is utilized again to express the
tip displacements. The torsion, for instance, is produced by the force
which is offset by the quantity h and the corresponding tip slope is given by
the equation:

where the torsional compliance has been defined in Eq. (2.12). The tip slope
in bending is produced by the combined action of the forces and and
is:

whereas the tip deflection is:

Equations (2.54), (2.55) and (2.56) enable finding the tip force components
when and are available experimentally.