Page 236 - Mechanics of Microelectromechanical Systems

4. Microtransduction: actuation and sensing 223

The tip angle produced through torsion about the longitudinal x-axis is:

Equation (4.95) has taken into account that for a thin cantilever, the torsional
rigidity is 4 times higher than the bending one – see Chapter 2. By taking the
ratio of the two tip angles results in:

As a consequence, for is solution to Eq. (4.96)) and:

When which gives:

5 PIEZOELECTRIC (PZT) TRANSDUCTION

The piezoelectric materials have the property of becoming electrically
polarized in the presence of an externally applied load/deformation. The
degree of polarization is proportional to the level of mechanical deformation,
as well as is dependent on the direction of the applied strain. This
mechanical-to-electrical energy conversion is known as direct piezoelectric
effect, and crystals such as the quartz naturally exhibit this property.
Piezoelectric materials are also capable to responding in a linear manner to
the reverse excitation, in the sense that external application of a field will
generate mechanical deformation through the reverse piezoelectric effect
(also called electrostriction). Examples of piezoelectric materials largely
utilized in industrial/research applications are polycrystalline ceramic
materials such as the PZT (lead zirconate titanate) or semi-crystalline
polymers such as the PVDF (polyvinylidene fluoride). For such materials,
the component dipoles (molecules that are partly charged positively and
partly charged negatively) are randomly arranged in a lattice, but application
of an external electric field to such an unpoled structure will pole it, namely
arrange and direct the dipoles about a direction parallel to that of the external
field, as sketched in Fig. 4.40.