Following Mindlin’s theory of plate bending of magnetoelasticity, we consider the scattering of time-harmonic flexural waves by a through crack in a perfectly conducting plate under a uniform magnetic field normal to the crack surface. An incident wave giving rise to moments symmetric about the crack plane is applied. It is assumed that the plate has the electric and magnetic permeabilities of the free space. By the use of Fourier transforms we reduce the problem to solving a pair of dual integral equations. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. The dynamic moment intensity factor versus frequency is computed and the influence of the magnetic field on the normalized values is displayed graphically. It is found that the existence of the magnetic field produces lower singular moments near the crack tip. [S0021-8936(00)02603-9]

Issue Section:
Technical Papers
Keywords:
crack-edge stress field analysis, bending, magnetic permeability, Fourier transforms, Fredholm integral equations, magnetoelastic effects, elastic waves
Topics:
Fracture (Materials), Magnetic fields, Waves, Stress, Fredholm integral equations, Permeability, Fourier transforms
1.
Dunkin
,
J. W.
, and
Eringen
,
A. C.
,
1963
, “
On the Propagation of Waves in an Electromagnetic Elastic Solid
,”
Int. J. Eng. Sci.
,
1
, pp.
461
–
495
.
2.
Ambartsumian
,
S. A.
,
Bagdasarian
,
G. E.
, and
Belubekian
,
M. V.
,
1971
, “
On the Three-Dimensional Problem of Magnetoelastic Plate Vibrations
,”
J. Appl. Math. Mech.
,
35
, pp.
184
–
195
.
3.
Ambartsumian
,
S. A.
,
Bagdasarian
,
G. E.
, and
Belubekian
,
M. V.
,
1975
, “
On the Equations of Magnetoelastic Thin Plate
,”
J. Appl. Math. Mech.
,
39
, pp.
922
–
926
.
4.
Murakami, Y. ed., 1987, Stress Intensity Factors Handbook, Vols. 1 and 2, Pergamon Press, Oxford, UK.
5.
Murakami, Y. ed., 1993, Stress Intensity Factors Handbook, Vols. 3, Pergamon Press, Oxford, UK.
6.
Shindo, Y., Ohnishi, I., and Suzuki, S., 1993, “Dynamic Singular Moments in a Perfectly Conducting Plate With a Through Crack Under a Magnetic Field,” Mechanics of Electromagnetic Materials and Structures, J. S. Lee, G. A. Maugin, and Y. Shindo, eds., ASME, New York, pp. 87–97.
7.
Shindo
,
Y.
,
Ohnishi
,
I.
, and
Tohyama
,
S.
,
1997
, “
Flexural Wave Scattering at a Through Crack in a Conducting Plate Under a Uniform Magnetic Field
,”
ASME J. Appl. Mech.
,
64
, pp.
828
–
834
.
8.
Moon, F. C., 1984, Magneto-Solid Mechanics, John Wiley and Sons, New York.
9.
Maugin, G. A., 1988, Continuum Mechanics of Electromagnetic Solids, North-Holland, Amsterdam.
10.
Parton, V. Z., and Kudryavtsev, B. A., 1988, Electromagnetoelasticity, Gordon and Beach, New York.
11.
Joseph
,
P. F.
, and
Erdogan
,
F.
,
1989
, “
Surface Crack Problems in Plates
,”
Int. J. Fract.
,
41
, pp.
105
–
131
.
12.
Mindlin
,
R. D.
,
1951
, “
Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic, Elastic Plates
,”
ASME J. Appl. Mech.
,
18
, pp.
31
–
38
.
13.
Kaliski
,
S.
,
1962
, “
Magnetoelastic Vibration of Perfectry Conducting Plates and Bars Assuming the Principle of Plane Sections
,”
Proc. Vib. Probl.
,
3
, pp.
225
–
234
.
14.
Sih, G. C., and Chen, E. P., 1977, “Dynamic Analysis of Cracked Plates in Bending and Extension,” Plates and Shells With Cracks (Mechanics of Fracture 3), G. C. Sih, ed., Noordhoff, Leyden, pp. 231–272.
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