Page 260 - Mechanics of Microelectromechanical Systems

4. Microtransduction: actuation and sensing 247
whereas M’ is given by Eq. (4.151). As previously, the subscript M denotes
martensite and the subscript A symbolizes austenite.

Example 4.17
A bimorph cantilever is formed of an SMA layer with thickness and is
deposited on a polysilicon substrate with thickness An external bending
moment M is applied at the free end in the positive manner (the SMA layer is
stretched), followed by a temperature increase that takes the bimorph from an
initial value to a final one, Determine the final configuration
of the SMA-based bimorph.

Solution:
The external moment M which is applied to the SMA bimorph acts as a
constant bias moment, and is plotted in Fig. 4.54 against the curvature of the
bimorph. At the SMA is in martensitic state and the moment-curvature
relationship is of the form:

where the equivalent moment of inertia has been calculated in Chapter 1 by
means of Eq. (1.180) where one has to take instead of The amounts
and are the positions of the symmetry axes of the two layer and the
position of the neutral axis, respectively (they are needed in Eq. (1.180)). The
latter amount, is given in Eq. (1.178).

Figure 4.54 SMA bimorph with bias spring

At the operation point, the bending moment of the martensitic SMA is equal
to the bias moment and therefore the curvature is: