120
6 Nonlinear Analysis of Piezoceramic Laminated Structures
Fig. 6.23 Dynamic response
of the fully clamped plate
under a step pressure of
2 × 10 4 Pa: a mid-point
displacement, b sensor
output voltage, reprinted
from Ref. [6], copyright
2014, with permission from
ELSEVIER
(a)
0
1
2
3
4
5
x 10
−3
0
0.5
1
1.5
2
2.5
3
3.5
x 10
−4
Time (s)
Displacement (m)
LRT56 (SH851URI)
RVK5 (SH851URI)
Nonlinear (Lentzen, 2005)
Linear (SH851URI)
Linear (Lentzen, 2005)
(b)
0
1
2
3
4
5
x 10
−3
−50
0
50
100
150
200
250
300
350
400
Time (s)
Voltage (V)
LRT56 (SH851URI)
RVK5 (SH851URI)
Nonlinear (Lentzen, 2005)
Linear (SH851URI)
Linear (Lentzen, 2005)
from nonlinear strain-displacement terms. From the sensor output voltage results,
given in Fig. 6.26b, it shows identical load-voltage curves of all nonlinear models
are achieved.
6.3.3.2 Dynamic Analysis
In the dynamic analysis, the Newmark method is employed for solving linear and
nonlinear dynamic equations. For the linear case, the time step is chosen 1 × 10
−5 s,
while for the nonlinear case, the time step is 1 × 10
−7 s. A uniformly step surface
force is applied on the shell structure. The transient response of the mid-point dis-