Page 107 - The Mechatronics Handbook

0066_Frame_C07 Page 17 Wednesday, January 9, 2002 3:39 PM

FIGURE 7.15 Example of electric force on the elements of a comb-drive actuator.

FIGURE 7.16 Decrease in natural frequency of a MEMS device with applied voltage as an example of negative
electric stiffness [From Adams (1996)].

Using the force expressions derived from Lagrange’s equations (7.44), the electric charge force on the
plate is given by

2
∂
∗
F e = ------W e V, x( ) = e 0 V A x (7.48)
------------------------------------------
∂x d 0 ( 1 x /d– 2 2 2
)
This expression shows that the electric stiffness is negative for small x, which means that the voltage will
decrease the natural frequency of the plate. This idea has been applied to a MEMS comb-drive actuator
by Adams (1996) in which the voltage could be used to tune the natural frequency of a MEMS acceler-
ometer, as shown in Fig. 7.16.

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