Environmental Engineering Reference
In-Depth Information
1 mm
FIGURE 2.35
Piezoelectric wind energy harvester under a wind speed of V a =3m/sand V b =1m/s.
results. Hence, for further expansion in the research work, these derived equa-
tions can be used as the baseline to predict and estimate the performance of
the piezoelectric wind energy harvester for the required specification and
operating condition. Furthermore, with good understanding on the working
concept and technical derivation of the piezoelectric wind energy harvester,
the present design of the harvester can be easily altered and optimized for
different operating conditions. Take, for instance, by altering the geometric
moment of inertia I discussed in Equation 2.16 , which describes the effect
of the rectangular shape of the beam cross section, the tip deflection of the
harvester is expected to change. The remaining step is to find the relation-
ship between the deflection of the cantilever wind energy harvester and the
electric power generation from the piezoelectric material.
2.2.1.3 Piezoelectric Theory
For a piezoelectric generator mounted in cantilever form, the transverse mode
(mode 31) of operation is considered. The mechanical force F applied on the
piezoelectric generator is perpendicular to its output electrodes; hence, the
surface where the charge is collected and the surface where the force is applied
are independent. According to Smits, Dalke, and Cooney [78] and Wang et
al. [80], for a series-connected bimorph bender subjected to the excitations
of an electric voltage V across its thickness, a uniformly distributed external
body load p ,anexternal tip force F perpendicular to the beam, and an external
moment M at the free end, the generated electrical charge can be expressed
as
33 Lw 1
4
3 d 31 L 2
2 t 2
d 31 wL 3
2 t 2
+
X
k 31 /
3 d 31 L
t 2
Q
=
M
+
F
+
p
V
(2.25)
t
 
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