Piezoelectric materials create electrical charge when mechanically stressed. Among the natural materials with this property are quartz, human skin, and human bone, though the latter two have very low coupling efficiencies. Table 3 shows properties of common industrial piezoelectric materials: polyvinylidene fluoride (PVDF) and lead zirconate titanate (PZT). For convenience, references for data sheets and several advanced treatments of piezoelectricity are included at the end of this paper [AMP, 1995,Cady, 1964,Fraden, 1993,Holland, 1969,Rogacheva, 1994].
Table: Piezoelectric characteristics of PVDF and PZT (adapted from
[AMP, 1995,Fraden, 1993,PSI data sheet]).
Figure:
Definition of axes for piezoelectric materials. Note that the
electrodes are mounted on the 3 axis [PSI data sheet].
The coupling constant shown in Table 3 is the efficiency with which a material converts mechanical energy to electrical. The subscripts on some of the constants indicate the direction or mode of the mechanical and electrical interactions (see Figure 2). "31 mode" indictates that strain is caused to axis 1 by electrical charge applied to axis 3. Conversely, strain on axis 1 will produce an electrical charge along axis 3. Bending elements, made by an expanding upper layer and a contracting bottom layer, are made to exploit this mode in industry. In practice, such bending elements have an effective coupling constant of 75 storage of mechanical energy in the mount and shim center layer.
The most efficient energy conversion, as indicated by the coupling
constants in Table 3, comes from compressing PZT (
).
Even so, the amount of effective power that could be
transferred this way is minimal since compression follows the formula
where F is force, H is the unloaded height, A is the area over
which the force is applied, and Y is the elastic modulus. The
elastic modulus for PZT is 
N/m
. Thus, it would take an
incredible force to compress the material a small amount. Since energy
is defined as force through distance, the effective energy generated
through human-powered compression of PZT would be vanishingly small,
even with perfect conversion.
On the other hand, bending a piece of piezoelectric material
to take advantage of its 31 mode is much easier. Because it is
brittle, PZT does not have much range of motion in this direction.
Maximum surface strain for this material is 
.
Surface strain can be defined as
where x is the deflection, t is the thickness of the beam, and 
is the cantilever length. Thus, the maximum deflection or bending for
a beam (20 cm) of a piezoceramic thin sheet (0.002 cm) before failure
is
Thus, PZT is unsuitable for jacket design or applications where flexibility is necessary.
PVDF, on the other hand, is very flexible. In addition, it is easy to
handle and shape, exhibits good stability over time, and does not
depolarize when subjected to very high alternating fields. The cost,
however, is that PVDF's coupling constant is significantly lower than
PZT's. Also, shaping PVDF can reduce the effective coupling of
mechanical and electrical energies due to edge effects. Furthermore,
the material's efficiency degrades depending on the operating climate
and the number of plies used. Fortunately, from an industry
representative [Halvorsen, 1995], we know a 116 cm
40 ply
triangular plate with a center metal shim deflected 5 cm by 68 kg 3 times every 5 seconds results in the generation of 1.5 W of
power. This result is a perfect starting point for the calculations
in the next section.