122
6 Nonlinear Analysis of Piezoceramic Laminated Structures
Table 6.4 Material properties of the fully clamped smart cylindrical shell
Host shell
PZT
E 1 = 124 GPa
E = 67 GPa
E 2 = 96.53 GPa
ν = 0.33
ν 12 = ν 23 = 0.34
ρ = 7800 kg/m 3
G 12 = G 13 = G 23 = 6.205 GPa
d 31 = d 32 = −1.7119 × 10 −10 C/N
ρ = 1520 kg/m 3
33 = 2.03 × 10 −8 F/m
ear models are in good agreement. This implies that the cylindrical shell undergoes
deformations only in the range of moderate rotations. The results agree excellently
with those obtained by Ref. [18], who applied MRT5 theory in the computation.
To investigate the smart shell occurring strong geometrically nonlinear phenomenon, the step surface load increases to 6 × 10
5 Pa, with the results shown
in Fig. 6.29a, b. The dynamics response of LRT56 and RVK5 models is still identical. This again implies that the clamped boundary conditions mostly permit the
structures undergoing only moderate rotations.
6.3.4 PZT Laminated Semicircular Cylindrical Shell
In this analysis, a PZT laminated semicircular cylindrical shell is considered for the
geometrically nonlinear simulation, which was first proposed and calculated by Tzou
and Ye [20], as shown in Fig. 6.30. The cylindrical shell consists of one metallic layer
in the middle as the host structure and two PZT layers bonded on the both inner and
outer surfaces. The material properties are shown in Table 6.5. A clamped boundary
condition is imposed on one straight edge of the cylindrical shell. The semicircular
cylindrical shell is meshed by 1 × 10 SH851URI elements along the Θ
1 - and Θ
2 -
direction, respectively.
6.3.4.1 Linear Analysis
For linear analysis, the first five eigen-frequencies are analyzed and compared with
those presented in the reference, as shown in Table 6.6. From the table, the results
show that the present five eigen-frequencies in a good agreement with the results
of Sze and Yao [21], who used the commercial software ABAQUS and self coded
program. It can be seen that a large discrepancy between the present results and those
of Ref. [20]. The reason might be that a different Young’s modulus of the metal are
employed in the reference.
6 Nonlinear Analysis of Piezoceramic Laminated Structures
Table 6.4 Material properties of the fully clamped smart cylindrical shell
Host shell
PZT
E 1 = 124 GPa
E = 67 GPa
E 2 = 96.53 GPa
ν = 0.33
ν 12 = ν 23 = 0.34
ρ = 7800 kg/m 3
G 12 = G 13 = G 23 = 6.205 GPa
d 31 = d 32 = −1.7119 × 10 −10 C/N
ρ = 1520 kg/m 3
33 = 2.03 × 10 −8 F/m
ear models are in good agreement. This implies that the cylindrical shell undergoes
deformations only in the range of moderate rotations. The results agree excellently
with those obtained by Ref. [18], who applied MRT5 theory in the computation.
To investigate the smart shell occurring strong geometrically nonlinear phenomenon, the step surface load increases to 6 × 10
5 Pa, with the results shown
in Fig. 6.29a, b. The dynamics response of LRT56 and RVK5 models is still identical. This again implies that the clamped boundary conditions mostly permit the
structures undergoing only moderate rotations.
6.3.4 PZT Laminated Semicircular Cylindrical Shell
In this analysis, a PZT laminated semicircular cylindrical shell is considered for the
geometrically nonlinear simulation, which was first proposed and calculated by Tzou
and Ye [20], as shown in Fig. 6.30. The cylindrical shell consists of one metallic layer
in the middle as the host structure and two PZT layers bonded on the both inner and
outer surfaces. The material properties are shown in Table 6.5. A clamped boundary
condition is imposed on one straight edge of the cylindrical shell. The semicircular
cylindrical shell is meshed by 1 × 10 SH851URI elements along the Θ
1 - and Θ
2 -
direction, respectively.
6.3.4.1 Linear Analysis
For linear analysis, the first five eigen-frequencies are analyzed and compared with
those presented in the reference, as shown in Table 6.6. From the table, the results
show that the present five eigen-frequencies in a good agreement with the results
of Sze and Yao [21], who used the commercial software ABAQUS and self coded
program. It can be seen that a large discrepancy between the present results and those
of Ref. [20]. The reason might be that a different Young’s modulus of the metal are
employed in the reference.