Page 202 - Mechanics of Microelectromechanical Systems

4. Microtransduction: actuation and sensing 189
angle increases‚ and is larger for larger lengths – Fig. 4.5‚ as expected.
Increasing the cross-sectional width reduces the free displacement‚ as shown
in Fig. 4.6. The thickness t of the beam cancels out in Eq. (4.8).
The bloc force‚ as previously introduced‚ is the force that has to be
applied at point 1 about the y-direction in order to annihilate the output y-
displacement at the same point produced by application of a temperature
increase – Fig. 4.3 (b). The force is determined by following a procedure
similar to the ones already presented and its equation is:

Example 4.2
Analyze the relationship between the bloc force and the geometric
parameters that define the bent beam actuator of Example 4.1.

Solution:
The same numerical values have been used here as in the case of the
output displacement studied in Example 4.1. Figures 4.7 and 4.8 are two
plots that show the variation of as a function of the defining geometric
parameters‚ namely inclination angle‚ length and cross-sectional dimensions.
The plot of Fig. 4.7 indicates that the bloc force is larger at smaller
lengths where it also reaches a local maximum. For longer elements‚ the bloc
force is almost constant when the inclination angle varies. However‚ the bloc
force is larger for small inclination angles‚ as seen in Fig. 4.7. As expected‚
the bloc force increases quasi-linearly with increasing the cross-sectional
dimensions w and t‚ as shown in Fig. 4.8.

Figure 4.7 Bloc force in a bent beam as a function of beam length and inclination angle