Page 138 - Mechanics of Microelectromechanical Systems

2. Microcantilevers, microhinges, microbridges 125
previous ones that have already been presented. The unknown reactions have
to be first determined as functions of the distributed load q and the dummy
force followed by calculation of The calculus tool is again
Castigliano’s displacement theorem. The bending moments are next given,
which provides the means of solving the two above-mentioned tasks:

In the end, the deflection at the mid-point 3 is:

5.3.2 Torsion

A similar approach can be applied when a torque is applied to the
compound microcantilever of Fig. 2.39. The reaction moment at the end 1 is
determined to be (by applying the zero rotation angle at that point and
through Castigliano’s displacement theorem):

The torsional stiffness at the midpoint 3 is then calculated as:

For a microbridge formed of three identical segments of identical rectangular
cross-section with Eq. (2.210) simplifies to:

which is the known equation, also given in Eq. (2.189).