Civil Engineering Reference
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Where
i
e
are material parameters and the matrix relating electric displacement to the
field vector is given by
§
0 0
·
11
¨
¸
0
0
(18.36)
¨
¸
11
¨
¸
0 0
©
¹
33
Equations (18.32) can be combined into one by
ˆ
ˆ
(18.37)
Ȉ Dİ
where
ı
§
T
·
İ
§·
De
§·
ˆ
ˆ
Ȉ
;
D
;
İ
¨
¸
(18.38)
¨¸
¨¸
¨
¸
d
E
e
©¹
©¹
©
¹
z
T
T
r
y
x
TT
Figure 18.11
Calculation of angles
12
The governing differential equation can be written as
Lu
ˆ
0
(18.39)
where
L
is the piezo-electric differential operator
3
and
u
§·
¨
©¹
ˆ
u
(18.40)
M
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