Page 326 - Mechanics of Microelectromechanical Systems

5. Static response of MEMS 313
Equation (5.137) is solved numerically in order to determine the tip
deflections of the microcantilever by means of the large-deformation model,
and Fig. 5.46 (a) plots the values of versus the force F. The non-linear
relationship between load and deformation can be seen again. The tip
deflection is calculated by the small-displacement assumptions by means of
the known relationship:

and Fig. 5.46 (b) shows the linear deflection-force relationship. Again, the
predictions by the small-displacement theory are overestimating the tip
deflection by significant amounts for large values of the force F.

Figure 5.46 Tip deflection according to the: (a) large-displacement theory; (b) small-
displacement theory

The tip position is plotted in Fig. 5.47 against the force F, as calculated by
means of Eq. (5.139) according to the large-displacement theory. Values as
large as are obtained by the large-displacement model predictions.