Page 256 - Mechanics of Microelectromechanical Systems

4. Microtransduction: actuation and sensing 243
where it has to be assumed that the voltage variation is negative, in order
to comply with the assumption of the generic case that the upper layer is
under free compression.

Example 4.15
Calculate the voltage that needs to be applied to a piezoelectric bimorph
in order to achieve the bending capability of a thermal bimorph which has the
same physical configuration. Assume that

Solution:
A piezoelectric bimorph can be compared to a physically-identical
thermal bimorph by means of the free strain, and it can be seen from Eqs.
(4.141) and (4.138) that the ratio of the free strain is:

Equal bending capability of the two bimorphs means equal free strains and
therefore:

Equation (4.143) indicates that for given material and geometric properties of
the two bimorphs, the voltage is proportional to the temperature variation and
the proportionality constant in the parenthesis of Eq. (4.143) is 0.025 V/°C.
Figure 4.52 shows the plot of voltage variation as a function of the
temperature variation in this problem.

Figure 4.52 Voltage variation in terms of temperature variation in a piezoelectric-versus-
thermal bimorph comparison