Page 223 - Mechanics of Microelectromechanical Systems
P. 223
210 Chapter 4
but it will be seen a bit later in this chapter that similar cases do exist where
other forms of actuation cannot be separated from the underlying elasticity
properties of structures.
Figure 4.30 Out-of-plane electrostatic transduction by microcantilevers: (a) Boundary
conditions and geometry; (b) Detail with distributed electrostatic loading
A procedure will be detailed next giving the maximum tip deflection (at
point 1 in Fig. 4.30 (b)) under the action of the electrostatic forces, and this
will qualify the actuation side of this microdevice. The variable gap over the
actuation length is:
where is the gap between the undeformed microcantilever and the plate,
and is the deflection at abscissa x. The force acting on an elementary
length dx can be considered constant and equal to:
and therefore the distributed force that acts on the overlapping zone (force
per unit length) can be expressed as:
The tip deflection can be expressed by applying Castigliano’s
displacement theorem which takes into account the strain energy produced
through bending of the entire microcantilever, namely:
