6.4 Electroelastic Nonlinear Analysis of Smart Structures
127
W
=
5 0 . 8 m
m
1
4
5
6
3
2
Θ
3
Θ
1
10
Metal
h metal =5.842 mm
h=6.35 mm
7
R =
3 1 8 . 3 1
m
m
Θ
2
PZT
h PZT =254 μm
F 1
F 2
Fig. 6.30 PZT laminated semicircular cylindrical shell
Table 6.5 Material properties of the PZT laminated semicircular cylindrical shell
Host shell
PZT
E = 68.95 GPa
E = 63 GPa
ν = 0.3
ν = 0.3
ρ = 7750 kg/m 3
ρ = 7600 kg/m 3
d 31 = d 32 = −1.79 × 10 −10 C/N
33 = 1.65 × 10 −8 F/m
Table 6.6 First five eigen-frequencies of the PZT laminated semicircular cylindrical shell (Hz)
Mesh
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Present
1 × 10
SH851URI
3.7199
5.8530
11.7782
33.4356
40.3605
Sze and
Yao [21]
1 × 10
S9R5
3.7475
5.8971
11.856
33.634
40.626
Sze and
Yao [21]
2 × 20
4-node
3.6810
5.8041
11.691
33.231
40.450
Tzou and
Ye [20]
2 × 10
Triangular
8.17
25.66
86.93
194.14
346.08
6.4 Electroelastic Nonlinear Analysis of Smart Structures
6.4.1 Validation Test
In most of cases, the piezoelectric smart structures are under strong electric field
in order to achieve large actuation forces. In such a case, electroelastic materially
nonlinear effect should be considered during the analysis of piezoelectric integrated
smart structures. To verify the current nonlinear finite element model under strong
driving electric field, a cantilevered bimorph beam is analyzed, which was first studied
by Wang et al. [22]. The bimorph beam consists of two soft PZT (3203HD) layers,
with the dimensions of 35 × 7 × 0.5 mm
3 for each layer, as shown in Fig. 6.33.
127
W
=
5 0 . 8 m
m
1
4
5
6
3
2
Θ
3
Θ
1
10
Metal
h metal =5.842 mm
h=6.35 mm
7
R =
3 1 8 . 3 1
m
m
Θ
2
PZT
h PZT =254 μm
F 1
F 2
Fig. 6.30 PZT laminated semicircular cylindrical shell
Table 6.5 Material properties of the PZT laminated semicircular cylindrical shell
Host shell
PZT
E = 68.95 GPa
E = 63 GPa
ν = 0.3
ν = 0.3
ρ = 7750 kg/m 3
ρ = 7600 kg/m 3
d 31 = d 32 = −1.79 × 10 −10 C/N
33 = 1.65 × 10 −8 F/m
Table 6.6 First five eigen-frequencies of the PZT laminated semicircular cylindrical shell (Hz)
Mesh
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Present
1 × 10
SH851URI
3.7199
5.8530
11.7782
33.4356
40.3605
Sze and
Yao [21]
1 × 10
S9R5
3.7475
5.8971
11.856
33.634
40.626
Sze and
Yao [21]
2 × 20
4-node
3.6810
5.8041
11.691
33.231
40.450
Tzou and
Ye [20]
2 × 10
Triangular
8.17
25.66
86.93
194.14
346.08
6.4 Electroelastic Nonlinear Analysis of Smart Structures
6.4.1 Validation Test
In most of cases, the piezoelectric smart structures are under strong electric field
in order to achieve large actuation forces. In such a case, electroelastic materially
nonlinear effect should be considered during the analysis of piezoelectric integrated
smart structures. To verify the current nonlinear finite element model under strong
driving electric field, a cantilevered bimorph beam is analyzed, which was first studied
by Wang et al. [22]. The bimorph beam consists of two soft PZT (3203HD) layers,
with the dimensions of 35 × 7 × 0.5 mm
3 for each layer, as shown in Fig. 6.33.