The study of the magnetoelastic vibrations of a flat plate immersed in a uniform applied external magnetic field is presented. Kirchhoff’s plate theory and the model of a perfect conductive medium are used. The conditions for the existence of localized bending vibrations in the vicinity of the free edge of the plate are established. It is shown that the localized vibrations can be detected and eventually can be eliminated by means of an applied magnetic field.

Issue Section:
Technical Papers
Keywords:
magnetoelastic effects, bending, vibrations, plates (structures), condition monitoring
Topics:
Magnetic fields, Vibration, Waves, Elastic plates
1.
Doebling
,
S. W.
,
Farrar
,
C. R.
,
Prime
,
M. B.
, and
Shevitz
,
D. W.
, 1996, “
Damage Identification and Health Monitoring of Structural and Mechanical Systems From Changes in Their Vibration Characteristics: A Literature Review
,”
Los Alamos National Laboratory
, Los Alamos, NM, Technical Rep. No. LA-13070-MS.
2.
Konenkov
,
Y. K.
, 1960, “
On Rayleigh Type Bending Waves
,”
Akust. Zh.
0320-7919,
6
(
1
), pp.
124
–
126
(in Russian).
3.
Belubekyan
,
M. V.
, and
Engibaryan
,
J. A.
, 1996, “
Waves Localized Along the Free Edge of the Plate With Cubic Symmetry
,”
Proceedings of RAS, MTT
,
Springer
,
New York
, Vol.
16
, pp.
139
–
143
(in Russian).
4.
Ambartsumian
,
S. A.
, and
Belubekyan
,
M. V.
, 1994, “
On Bending Waves Localized Along the Edge of a Plate
,”
Int. Appl. Mech.
1063-7095,
30
(
2
), pp.
135
–
140
.
Crossref
Search ADS
 
5.
Mkrtchyan
,
H. P.
, 2003, “
Localized Bending Waves in an Elastic Orthotropic Plate
,”
Proceedings of NAS Armenia
, Mechanics, Vol.
56
, No.
4
, pp.
66
–
68
.
6.
McKenna
,
J.
,
Boyd
,
G. D.
, and
Thurston
,
R. N.
, 1974, “
Plate Theory Solution for Guided Flexural Acoustic Waves Along the Tip of a Wedge
,”
IEEE Trans. Sonics Ultrason.
0018-9537,
21
, pp.
178
–
186
.
Crossref
Search ADS
 
7.
Norris
,
A. N.
,
Krylov
,
V. V.
, and
Abrahams
,
I. D.
, 1998, “
Flexural Edge Waves and Comments on a New Bending Wave Solution for the Classical Plate Equation
,”
J. Acoust. Soc. Am.
0001-4966,
104
, pp.
2220
–
2222
.
8.
Norris
,
A. N.
, 1994, “
Flexural Edge Waves
,”
J. Sound Vib.
0022-460X,
171
, pp.
571
–
573
.
Crossref
Search ADS
 
9.
Belubekyan
,
M. V.
, 2003, “
Magnetoelastic Vibrations Localized in the Vicinity of the Free Edge of a Thin Plate
,”
Proceedings of Armenian National Academy of Sciences
, Mechanics,
Yerevan, Armenia
, Vol.
56
, No.
2
.
10.
Kaliski
,
S.
, 1962, “
Magnetoelastic Vibration of a Perfectly Conducting Plates and Bars Assuming the Principle of Plane Sections
,”
Proc. Vib. Probl.
0032-9576,
3
(
14
), pp.
225
–
234
.
11.
Ambartsumian
,
S. A.
,
Bagdasaryan
,
G. E.
, and
Belubekian
,
M. V.
, 1971, “
On the Three-Dimensional Problem of the Plate Magnetoelastic Vibration
,”
Prikladnaia Matematica i Mekhanika
,
35
(
12
), pp.
216
–
228
.
12.
Ambartsumian
,
S. A.
,
Bagdasaryan
,
G. E.
, and
Belubekian
,
M. V.
, 1977,
The Magnetoelasticity of Thin Shells and Plates
,
Nauka
,
Moscow
, pp.
272
(in Russian).
13.
Ambartsumian
,
S. A.
, 2002, “
Nontraditional Theories of Shells and Plates
,”
Appl. Mech. Rev.
0003-6900,
5
, pp.
R35
–
R44
.
14.
Rudnicki
,
M.
, 2002, “
Eigenvalue Solutions for Motion of Electroconductive Plate in Magnetic Field
,”
Int. J. Eng. Sci.
0020-7225,
40
, pp.
93
–
107
.
Crossref
Search ADS
 
15.
Ambartsumian
,
S. A.
,
Belubekyan
,
M. V.
, and
Minassyan
,
M. M.
, 1983, “
On the Problem of Non-Linear Elastic Electroconductive Plates in Transverse and Longitudinal Magnetic Fields
,”
Int. J. Non-Linear Mech.
0020-7462,
19
(
2
), pp.
141
–
149
.
Crossref
Search ADS
 
16.
Ambartsumian
,
S. A.
, and
Belubekian
,
M. V.
, 1979, “
On the Approximate Methods in the Problems of the Plate Magnetoelastic Vibration
.”
Thermal Stresses in the Elements of Constructions
,
Institute of Mechanics, Academy of Sciences
,
Ukrainian SSR, Kiev
, Vol.
19
, pp.
3
–
6
(in Russian).
17.
Ambartsumian
,
S. A.
, and
Bagdasaryan
,
G. E.
, 1996, “
Conductive Plates and Shells in Magnetic Fields
.” M.: Phys-Math. Lit., pp.
288
(in Russian).
18.
Librescu
,
L.
,
Hasanyan
,
D.
, and
Ambur
,
D. R.
, 2004, “
Electromagnetically Conducting Elastic Plates in a Magnetic Field: Modeling and Dynamic Implications
,”
Int. J. Non-Linear Mech.
0020-7462,
39
, pp.
723
–
739
.
Crossref
Search ADS
 
19.
Librescu
,
L.
,
Hasanyan
,
D.
,
Qin
,
Z.
, and
Ambur
,
D. R.
, 2003, “
Nonlinear Magnetothermoelasticity of Anisotropic Plates Immersed in a Magnetic Field
,”
J. Therm. Stresses
0149-5739,
26
, pp.
1277
–
1304
.
Crossref
Search ADS
 
20.
Soedel
,
W.
, 1993,
Vibrations of Plates and Shells
,
Marcel Dekker
,
New York
.
21.
Moon
,
F. C.
, 1984,
Magneto-Solid Mechanics
,
Wiley
,
New York
.
Copyright © 2007
 by American Society of Mechanical Engineers
You do not currently have access to this content.