Smart adaptive structures and structronic systems have been increasingly investigated and developed in the last two decades. Although smart structures made of piezoelectrics, shape-memory materials, electrostrictive materials, and electro-/magnetorheological fluids have been evaluated extensively, studies of magnetostrictive continua, especially generic mathematical model(s), are still relatively scarce. This study is to develop a generic mathematical model for adaptive and controllable magnetostrictive thin shells. Starting with fundamental constitutive magnetostrictive relations, both elastic and magnetostrictive stresses, forces, and moments of a generic double-curvature magnetostrictive shell continuum subject to small and moderate magnetic fields are defined. Dynamic magnetomechanical system equations and permissible boundary conditions are defined using Hamilton's principle, elasticity theory, Kirchhoff-Love thin shell theory and the Gibb's free energy function. Magnetomechanical behavior and dynamic characteristics of magnetostrictive shells are evaluated. Simplifications of magnetostrictive shell theory to other common geometries are demonstrated and magnetostrictive/dynamic coupling and actuation characteristics are discussed.

1.
Wan
,
Y. P.
,
Fang
,
D.
, and
Hwang
,
K. C.
, 2003, “
Non-linear Constitutive Relations for Magnetostrictive Materials
,”
Int. J. Non-Linear Mech.
0020-7462,
38
, pp.
1053
l065
.
2.
Shkel
,
Y. M.
, and
Klingenberg
,
D. J.
, 2001, “
Magnetorheology and Magnetostriction of Isolated Chains of Nonlinear Magnetizable Sphere
,”
J. Rheol.
0148-6055,
45
, pp.
351
368
.
3.
Carman
,
G. P.
, and
Mitrovic
,
M.
, 1995, “
Nonlinear Constitutive Relations for Magnetostrictive Materials With Applications to 1-D Problems
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
6
, pp.
673
683
.
4.
Ambartsumian
,
S. A.
, 1982, “
Magneto-Elasticity of Thin Plates and Shells
,”
Appl. Mech. Rev.
0003-6900,
35
, pp.
1
5
.
5.
Smith
,
R. C.
, 1998, “
A Nonlinear Optimal Control Method for Magnetostrictive Actuators
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
9
, pp.
468
486
.
6.
Pradhan
,
S. C.
,
Ng
,
T. Y.
, and
Reddy
,
J. N.
, 2001, “
Control of Laminated Composite Plates Using Magnetostrictive Layers
,”
Smart Mater. Struct.
0964-1726,
10
, pp.
657
667
.
7.
Kumar
,
J. S.
,
Ganesan
,
N.
,
Swarnamani
,
S.
, and
Padmanabhan
,
C.
, 2003, “
Active Control of Beam With Magnetostrictive Layer
,”
Comput. Struct.
0045-7949,
81
, pp.
1375
1382
.
8.
Reddy
,
J. N.
, and
Barbosa
,
J. I.
, 2000, “
On Vibration Suppression of Magnetostrictive Beams
,”
Smart Mater. Struct.
0964-1726,
9
, pp.
49
58
.
9.
Chang
,
C. T.
, 1991,
Theory and Design of a Magnetostrictive Actuator
, Master thesis, Clemson University.
10.
Anjanappa
,
M.
, and
Bi
,
J.
, 1994, “
Magnetostrictive Mini Actuators for Smart Structure Applications
,”
Smart Mater. Struct.
0964-1726,
3
, pp.
383
390
.
11.
Tzou
,
H. S.
, and
Zhong
,
J. P.
, 1993, “
Electromechanics and Vibrations of Piezoelectric Shell Distributed Systems: Theory and Applications
,”
J. Dyn. Syst., Meas., Control
0022-0434,
115
, pp.
506
517
.
12.
Tzou
,
H. S.
, 1993,
Piezoelectric Shells-Distributed Sensing and Control of Continua
,
Kluwer Academic
, Boston.
13.
Tzou
,
H. S.
, and
Bao
,
Y.
, 1995, “
A Theory on Anisotropic Piezothermoelastic Shell Laminates With Sensor/Actuator Applications
,”
J. Sound Vib.
0022-460X,
184
, pp.
453
473
.
14.
Tzou
,
H. S.
,
Bao
,
Y.
, and
Zhou
,
Y.
, 1997, “
Nonlinear Piezothermoelasticity and Multi-Field Actuations, Part-1: Nonlinear Anisotropic Piezothermoelastic Shell Laminates; Part-2: Control of Nonlinear Buckling and Dynamics
,”
ASME J. Vibr. Acoust.
0739-3717,
119
, pp.
374
389
.
15.
Tzou
,
H. S.
, and
Yang
,
R. J.
, 2000, “
Nonlinear Piezothermoelastic Shell Theory Applied to Control of Variable-Geometry Shells
,”
Theor Appl. Mech.
0285-6042,
38
, pp.
623
644
.
16.
Mason
,
W. P.
, 1958,
Physical Acoustics and the Properties of Solids
,
Van Nostrand
, New York.
17.
Bozorth
,
R. M.
, 1951,
Ferromagnetism
,
Van Nostrand
, New York.
18.
Tzou
,
H. S.
, and
Ye
,
R.
, 1996, “
Analysis of Piezoelectric Structures With Laminated Piezoelectric Triangle Shell Elements
,”
AIAA J.
0001-1452,
34
, pp.
110
115
.
19.
Tzou
,
H. S.
, and
Wang
,
D. W.
, 2002, “
Distributed Dynamics Signal Analysis of Piezoelectric Laminated Linear and Nonlinear Toroidal Shells
,”
J. Sound Vib.
0022-460X,
254
, pp.
203
218
.
This content is only available via PDF.
You do not currently have access to this content.