Doubly curved stiffened shells are essential parts of many large-scale engineering structures, such as aerospace, automotive and marine structures. Optimization of active vibration reduction has not been properly investigated for this important group of structures. This study develops a placement methodology for such structures under motion base and external force excitations to optimize the locations of discrete piezoelectric sensor/actuator pairs and feedback gain using genetic algorithms for active vibration control. In this study, fitness and objective functions are proposed based on the maximization of sensor output voltage to optimize the locations of discrete sensors collected with actuators to attenuate several vibrations modes. The optimal control feedback gain is determined then based on the minimization of the linear quadratic index. A doubly curved composite shell stiffened by beams and bonded with discrete piezoelectric sensor/actuator pairs is modeled in this paper by first-order shear deformation theory using finite element method and Hamilton's principle. The proposed methodology is implemented first to investigate a cantilever composite shell to optimize four sensor/actuator pairs to attenuate the first six modes of vibration. The placement methodology is applied next to study a complex stiffened composite shell to optimize four sensor/actuator pairs to test the methodology effectiveness. The results of optimal sensor/actuator distribution are validated by convergence study in genetic algorithm program, ANSYS package and vibration reduction using optimal linear quadratic control scheme.

References

References
1.
Allik
,
H.
, and
Hughes
,
T. J. R.
,
1970
, “
Finite Element Method for Piezoelectric Vibration
,”
Int. J. Numer. Methods Eng.
,
2
(
2
), pp.
151
157
.
2.
Tzou
,
H. S.
, and
Tseng
,
C. I.
,
1990
, “
Distributed Piezoelectric Sensor/Actuator Design for Dynamic Measurement/Control of Distributed Parameter Systems: A Piezoelectric Finite Element Approach
,”
J. Sound Vib.
,
138
(
1
), pp.
17
34
.
3.
Detwiler
,
D. T.
,
Shen
,
M.-H. H.
, and
Venkayya
,
V. B.
,
1995
, “
Finite Element Analysis of Laminated Composite Structures Containing Distributed Piezoelectric Actuators and Sensors
,”
Finite Elem. Anal. Des.
,
20
(
2
), pp.
87
100
.
4.
Kulkarni
,
S. A.
, and
Bajoria
,
K. M.
,
2003
, “
Finite Element Modeling of Smart Plates/Shells Using Higher Order Shear Deformation Theory
,”
Compos. Struct.
,
62
(
1
), pp.
41
50
.
5.
Reddy
,
J. N.
,
1999
, “
On Laminated Composite Plates With Integrated Sensors and Actuators
,”
Eng. Struct.
,
21
(
7
), pp.
568
593
.
6.
Kumar
,
R.
,
Mishra
,
B. K.
, and
Jain
,
S. C.
,
2008
, “
Static and Dynamic Analysis of Smart Cylindrical Shell
,”
Finite Elem. Anal. Des.
,
45
(
1
), pp.
13
24
.
7.
Balamurugan
,
V.
, and
Narayanan
,
S.
,
2001
, “
Shell Finite Element for Smart Piezoelectric Composite Plate/Shell Structures and Its Application to the Study of Active Vibration Control
,”
Finite Elem. Anal. Des.
,
37
(
9
), pp.
713
718
.
8.
Lim
,
Y.-H.
,
2003
, “
Finite-Element Simulation of Closed Loop Vibration Control of a Smart Plate Under Transient Loading
,”
Smart Mater. Struct.
,
12
(
2
), pp.
272
286
.
9.
Meirovitch
,
L.
,
1990
,
Dynamics and Control of Structures
,
Wiley
,
New York
.
10.
Han
,
J.-H.
, and
Lee
,
I.
,
1999
, “
Optimal Placement of Piezoelectric Sensors and Actuators for Vibration Control of a Composite Plate Using Genetic Algorithms
,”
Smart Mater. Struct.
,
8
(
2
), pp.
257
267
.
11.
Sadri
,
A. M.
,
Wright
,
J. R.
, and
Wynne
,
R. J.
,
1999
, “
Modelling and Optimal Placement of Piezoelectric Actuators in Isotropic Plates Using Genetic Algorithms
,”
Smart Mater. Struct.
,
8
(
4
), pp.
490
498
.
12.
Sadri
,
A. M.
,
Wright
,
J. R.
, and
Wynne
,
R. J.
,
2002
, “
LQG Control Design for Panel Flutter Suppression Using Piezoelectric Actuators
,”
Smart Mater. Struct.
,
11
(
6
), pp.
834
839
.
13.
Peng
,
F.
,
2005
, “
Actuator Placement Optimization and Adaptive Vibration Control of Plate Smart Structures
,”
J. Intell. Mater. Syst. Struct.
,
16
(
3
), pp.
263
271
.
14.
Ramesh Kumar
,
K.
, and
Narayanan
,
S.
,
2007
, “
The Optimal Location of Piezoelectric Actuators and Sensors for Vibration Control of Plates
,”
Smart Mater. Struct.
,
16
(
6
), pp.
2680
2691
.
15.
Daraji
,
A. H.
, and
Hale
,
J. M.
,
2014
, “
Reduction of Structural Weight, Costs and Complexity of a Control System in the Active Vibration Reduction of Flexible Structures
,”
Smart Mater. Struct.
,
23
(
9
), p. 095013.
16.
Roy
,
T.
, and
Chakraborty
,
D.
,
2009
, “
Optimal Vibration Control of Smart Fiber Reinforced Composite Shell Structures Using Improved Genetic Algorithm
,”
J. Sound Vib.
,
319
(
1–2
), pp.
15
40
.
17.
Roy
,
T.
, and
Chakraborty
,
D.
,
2009
, “
Genetic Algorithm Based Optimal Control of Smart Composite Shell Structures Under Mechanical Loading and Thermal Gradient
,”
Smart Mater. Struct.
,
18
(
11
), p.
115006
.
18.
Gawronski
,
W. K.
,
2004
,
Advance Structural Dynamics and Active Control and Structures
,
Springer
,
New York
.
19.
Young
,
A. J.
, and
Hansen
,
C. H.
,
1996
, “
Control of Flexural Vibration in Stiffened Structures Using Multiple Piezoceramic Actuators
,”
Appl. Acoust.
,
49
(
1
), pp.
17
48
.
20.
Mukherjee
,
A.
,
Joshi
,
S. P.
, and
Ganguli
,
A.
,
2002
, “
Active Vibration Control of Piezolaminated Stiffened Plates
,”
Compos. Struct.
,
55
(
4
), pp.
435
443
.
21.
Balamurugan
,
V.
, and
Narayanan
,
S.
,
2010
, “
Finite Element Modeling of Stiffened Piezolaminated Plates and Shells With Piezoelectric Layers for Active Vibration Control
,”
Smart Mater. Struct.
,
19
(
10
), p.
105003
.
22.
Daraji
,
A. H.
, and
Hale
,
J. M.
,
2014
, “
Active Vibration Reduction by Optimally Placed Sensors and Actuators With Application to Stiffened Plates by Beams
,”
Smart Mater. Struct.
,
23
(
11
), p.
115018
.
You do not currently have access to this content.