An analytical solution is presented for the static deformation and steady-state vibration of simply supported hybrid cylindrical shells consisting of fiber-reinforced layers with embedded piezoelectric shear sensors and actuators. The piezoelectric shear actuator, which is poled in the circumferential direction, will induce transverse shear deformation of the hybrid shell when it is subjected to an electric field in the radial direction. Suitable displacement and electric potential functions that identically satisfy the boundary conditions at the simply supported edges are used to reduce the governing equations of static deformation and steady-state vibrations of the hybrid laminate to a set of coupled ordinary differential equations in the radial coordinate, which are solved by employing the Frobenius method. Natural frequencies, mode shapes, displacements, electric potential, and stresses are presented for four-layer hybrid laminates consisting of a piezoelectric shear sensor and actuator sandwiched between fiber-reinforced composite layers. Active vibration damping is implemented using a positive position feedback controller. Frequency response curves for different controller frequencies, controller damping ratio, and feedback gain demonstrate that the embedded shear actuator can be used for active damping of the fundamental flexural mode. In addition, it is demonstrated that vibration suppression of thickness modes is also feasible using the piezoelectric shear actuator.

1.
Fuller
,
C. R.
,
Elliott
,
S. J.
, and
Nelson
,
P. A.
, 1997,
Active Control of Vibration
,
Academic
, New York.
2.
Bailey
,
T.
, and
Hubbard
Jr,
J. E.
, 1985, “
Distributed Piezoelectric Polymer Active Vibration Control of a Cantilever Beam
,”
AIAA J.
0001-1452,
8
, pp.
605
611
.
3.
Garcia
,
E.
,
Dosch
,
J.
, and
Inman
,
D. J.
, 1992, “
The Application of Smart Structures to the Vibration Suppression Problem
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
3
, pp.
659
667
.
4.
Clark
,
R. L.
, and
Fuller
,
C. R.
, 1992, “
Experiments on Active Control of Structurally Radiated Sound Using Multiple Piezoelectric Actuators
,”
J. Acoust. Soc. Am.
0001-4966,
91
, pp.
3313
3320
.
5.
Crawley
,
E. F.
, and
Anderson
,
E. H.
, 1990, “
Detailed Models of Piezoceramic Actuation of Beams
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
1
, pp.
4
25
.
6.
Lee
,
C. K.
, 1990, “
Theory of Laminated Piezoelectric Plates for the Design of Distributed Sensors/Actuators 1. Governing Equations and Reciprocal Relationships
,”
J. Acoust. Soc. Am.
0001-4966,
87
, pp.
1144
1158
.
7.
Batra
,
R. C.
,
Liang
,
X. Q.
, and
Yang
,
J. S.
, 1996, “
The Vibration of a Simply Supported Rectangular Elastic Plate due to Piezoelectric Actuators
,”
Int. J. Solids Struct.
0020-7683,
33
, pp.
1597
1618
.
8.
Heyliger
,
P.
, and
Brooks
,
S.
, 1995, “
Free-vibration of Piezoelectric Laminates in Cylindrical Bending
,”
Int. J. Solids Struct.
0020-7683,
32
, pp.
2945
2960
.
9.
Heyliger
,
P.
, and
Saravanos
,
D. A.
, 1995, “
Exact Free-vibration Analysis of Laminated Plates with Embedded Piezoelectric Layers
,”
J. Acoust. Soc. Am.
0001-4966,
98
, pp.
1547
1557
.
10.
Chen
,
C.-Q.
,
Shen
,
Y.-P.
, and
Wang
,
X.-M.
, 1996, “
Exact Solution of Orthotropic Cylindrical Shell with Piezoelectric Layers under Cylindrical Bending
,”
Int. J. Solids Struct.
0020-7683,
33
,
4481
4494
.
11.
Dumir
,
P. C.
,
Dube
,
G. P.
, and
Kapuria
,
S.
, 1997, “
Exact Piezoelastic Solution of Simply-supported Orthotropic Circular Cylindrical Panel in Cylindrical Bending
,”
Int. J. Solids Struct.
0020-7683,
34
, pp.
685
702
.
12.
Chen
,
C.-Q.
, and
Shen
,
Y.-P.
, 1998, “
Three-dimensional Analysis for the Free Vibration of Finite-length Orthotropic Piezoelectric Circular Cylindrical Shells
,”
J. Vibr. Acoust.
0739-3717,
120
, pp.
194
198
.
13.
Sun
,
C. T.
, and
Zhang
,
X. D.
, 1995, “
Use of Thickness-shear Mode in Adaptive Sandwich Structures
,”
Smart Mater. Struct.
0964-1726,
4
, pp.
202
206
.
14.
Electro Ceramic Division, Data for Designers, Morgan Matroc, Bedford, OH.
15.
Zhang
,
X. D.
, and
Sun
,
C. T.
, 1996, “
Formulation of an Adaptive Sandwich Beam
,”
Smart Mater. Struct.
0964-1726,
5
, pp.
814
823
.
16.
Zhang
,
X. D.
, and
Sun
,
C. T.
, 1999, “
Analysis of a Sandwich Plate Containing a Piezoelectric Core
,”
Smart Mater. Struct.
0964-1726,
8
, pp.
31
40
.
17.
Benjeddou
,
A.
,
Trindade
,
M. A.
, and
Ohayon
,
R.
, 1997, “
A Unified Beam Finite Element Model for Extension and Shear Piezoelectric Actuation Mechanisms
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
8
, pp.
1012
1025
.
18.
Trindade
,
M. A.
,
Benjeddou
,
A.
, and
Ohayon
,
R.
, 1999, “
Parametric Analysis of the Vibration Control of Sandwich Beams through Shear-based Piezoelectric Actuation
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
10
, pp.
377
385
.
19.
Benjeddou
,
A.
, and
Deü
,
J.-F.
, 2002, “
A Two-dimensional Closed-form Solution for the Free-vibrations Analysis of Piezoelectric Sandwich Plates
,”
Int. J. Solids Struct.
0020-7683,
39
, pp.
1463
1486
.
20.
Vel
,
S. S.
, and
Batra
,
R. C.
, 2001, “
Exact Solution for Cylindrical Bending of Laminated Plates with Embedded Shear Actuators
,”
Smart Mater. Struct.
0964-1726,
10
, pp.
240
251
.
21.
Vel
,
S. S.
, and
Batra
,
R. C.
, 2001, “
Exact Solution for Rectangular Sandwich Plates with Embedded Piezoelectric Shear Actuators
,”
AIAA J.
0001-1452,
39
, pp.
1363
1373
.
22.
Benjeddou
,
A.
,
Gorge
,
V.
, and
Ohayon
,
R.
, 2001, “
Use of Piezoelectric Shear Response in Adaptive Sandwich Shells of Revolution 1. Theoretical Formulation
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
12
, pp.
235
245
.
23.
Benjeddou
,
A.
,
Gorge
,
V.
, and
Ohayon
,
R.
, 2001, “
Use of Piezoelectric Shear Response in Adaptive Sandwich Shells of Revolution 2. Finite Element Implementation
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
12
, pp.
247
257
.
24.
Baillargeon
,
B.
, and
Vel
,
S.
, 2005, “
Exact Solution for the Vibration and Active Damping of Composite Plates with Piezoelectric Shear Actuators
,”
J. Sound Vib.
0022-460X,
282
, pp.
781
804
.
25.
Goh
,
C. J.
, and
Caughey
,
T. K.
, 1985, “
On the Stability Problem Caused by Finite Actuator Dynamics Collected Control of Large Space Structures
,”
Int. J. Control
0020-7179,
41
, pp.
787
802
.
26.
Fanson
,
J. L.
, and
Caughey
,
T. K.
, 1990, “
Positive Position Feedback for Large Space Structure
,”
AIAA J.
0001-1452,
28
, pp.
717
724
.
27.
Friswell
,
M.
, and
Inman
,
D. J.
, 1999, “
The Relationship Between Positive Position Feedback and Output Feedback Controllers
,”
Smart Mater. Struct.
0964-1726,
8
, pp.
285
291
.
28.
Tiersten
,
H. F.
, 1969,
Linear Piezoelectric Plate Vibrations
,
Plenum
, New York.
29.
Kreyszig
,
E.
, 1999,
Advanced Engineering Mathematics
,
Wiley
, New York,
8 Ed.
30.
von Wagner
,
U.
, 2003, “
Non-linear Longitudinal Vibrations of Piezoceramics Excited by Weak Electric Fields
,”
Int. J. Non-Linear Mech.
0020-7462,
38
, pp.
565
574
.
31.
von Wagner
,
U.
, 2004, “
Non-linear Longitudinal Vibrations of Non-slender Piezoceramic Rods
,”
Int. J. Non-Linear Mech.
0020-7462,
39
, pp.
673
688
.
32.
Tang
,
Y. Y.
,
Noor
,
A. K.
, and
Xu
,
K.
, 1996, “
Assessment of Computational Models for Thermoelectroelastic Multilayered Plates
,”
Comput. Struct.
0045-7949,
61
, pp.
915
933
.
33.
ABAQUS Users Manual, Version 6.3, Hibbit, Karlsson & Sorensen, Inc., 2002.
34.
von Wagner
,
U.
, and
Hagedorn
,
P.
, 2003, “
Non-linear Effects of Piezoceramics Excited by Weak Electric Fields
,”
Nonlinear Dyn.
0924-090X,
31
, pp.
133
149
.
You do not currently have access to this content.