The piezoelectric layer is unelectroded on its lateral surfaces. The electric field in the
surrounding free space is neglected as usual as an approximation.
To develop a one-dimensional model for bending in the x 1 -x 3 plane with shear
deformation, we make the following approximations of the relevant mechanical
displacements and electric potential:
Fig. 6.11 Δp(L ) Â 2cbdz
versus h/c for different
material combinations when
p 0 ¼ n 0 ¼ 10
23 /m
3
, F ¼ 20
pN, dz ¼ 10 nm, and z ¼ x 3
(1) PZT
(2) Si
x1
L
P
F
(2) Si
x3
x2
x3
b
2c
h
h
Fig. 6.12 Side view and
cross section of a composite
beam of piezoelectric
dielectrics and
nonpiezoelectric
semiconductors
162
6 Composite Structures
surrounding free space is neglected as usual as an approximation.
To develop a one-dimensional model for bending in the x 1 -x 3 plane with shear
deformation, we make the following approximations of the relevant mechanical
displacements and electric potential:
Fig. 6.11 Δp(L ) Â 2cbdz
versus h/c for different
material combinations when
p 0 ¼ n 0 ¼ 10
23 /m
3
, F ¼ 20
pN, dz ¼ 10 nm, and z ¼ x 3
(1) PZT
(2) Si
x1
L
P
F
(2) Si
x3
x2
x3
b
2c
h
h
Fig. 6.12 Side view and
cross section of a composite
beam of piezoelectric
dielectrics and
nonpiezoelectric
semiconductors
162
6 Composite Structures