Page 204 - Mechanics of Microelectromechanical Systems

4. Microtransduction: actuation and sensing 191

and is larger than one‚ which indicates that the displacement produced by a
bent beam is always larger than the axial deformation of a fixed-free beam.
Figures 4.9 and 4.10 are the plots of the ratio defined in Eq. (4.11) in terms
of the geometric parameters. The free displacement of the bent beam can be
20 times larger than the one of a straight bar‚ for smaller inclination angles
and larger lengths‚ as shown in Fig. 4.9. For larger cross-sectional widths‚ the
free displacement ratio of Eq. (4.11) decreases almost to unity‚ as illustrated
in Fig. 4.10.

Figure 4.10 Bent beam versus straight bar in terms of displacement output as a function of
leg width

The bloc force ratio of Eq. (4.10) becomes‚ by way of Eqs. (4.9) and
(4.5):

This time‚ as Eq. (4.12) suggests‚ the ratio is less than 1‚ and therefore the
bloc force of the fixed-free bar is always larger than that of the corresponding
bent beam. Figures 4.11 and 4.12 contain two similar plots showing that the
bloc force of the bent beam increases relative to the one of the fixed-free bar
for larger cross-section dimensions (the dimension w‚ specifically)‚ smaller
inclination angles and smaller lengths. Figures 4.12 and Fig. 4.10 are drawn
in terms of the parameter w‚ as t cancelled out in Eqs. (4.12) and (4.11)‚
respectively.