Page 126 - Mechanics of Microelectromechanical Systems

2. Microcantilevers, microhinges, microbridges 113
rigid thus far), in addition to the bending of the relatively-long beams. By
applying a force perpendicularly to the plane of the microhinge, as well as
a moment as sketched in Fig. 2.33, the out-of-the-plane bending (which
is the operational deformation of the system) can be studied.

Figure 2.33 Folded microcantilever with torsional hinges included in the model

The system is three times indeterminate because three equations of static
equilibrium can only solve for three unknown reactions out of the six
unknowns introduced by the two fixed supports 1 and 6. By applying again
Castigliano’s displacement theorem, the three reactions at point 1,
and can be determined by using the following boundary conditions:

Having found these unknown reactions, the free end deflection and slope
can be found and expressed in the known manner:

The equations of the three global compliances entering Eqs. (2.166) are quite
complex and are not given explicitly here. The following example will
however express these compliances for a particular case.

Example 2.16
Calculate the three compliances of Eqs. (2.166) for a two-leg folded
microcantilever defined by: Also
consider that Poisson’s ratio of the material is and that the
microcantilever is very thin.