Page 65 - Mechanics of Microelectromechanical Systems

52 Chapter 1
6.2.2 Axial Loading and Torsion

The equivalence operation in the case where axial forces or torsion
moments act on the serially-connected member of Fig. 1.27 is quite
straightforward because in either of the situations the two components do
behave as springs that are connected in series, and therefore the equivalent
stiffness will be given by:

Specifically, in the case of axial loading, Eq. (1.205) gives:

whereas for torsion, the equivalent stiffness is:

Example 1.14
A microcantilever is formed of a structural layer of thickness on top of
which another layer of thickness is deposited, as shown in Fig. 1.29 (a).
Determine the deflection that is produced by a given tip force
when:

Solution:
The two components overlap over the length and therefore the rigidity
of that portion can be determined by means of the substitutions used in
Example 1.12, namely:

Now, the three portions shown in Fig. 1.29 (b) are serially connected, and
therefore the direct stiffness about the z-direction can be calculated by means
of Castigliano’s displacement theorem, such that the required deflection is:

and the numerical value is