Dynamic Singular Moments in a Perfectly Conducting Mindlin Plate With a Through Crack Under a Magnetic Field

1998 ◽  
Vol 67 (3) ◽  
pp. 503-510 ◽  
Author(s):  
Y. Shindo ◽  
I. Ohnishi ◽  
S. Toyama
Keyword(s):  
Magnetic Field ◽  
Integral Equations ◽  
Fourier Transforms ◽  
Mindlin Plate ◽  
Crack Plane ◽  
Flexural Waves ◽  
Dual Integral Equations ◽  
Conducting Plate ◽  
Time Harmonic ◽  
The Magnetic Field

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]

Flexural Wave Scattering at a Through Crack in a Conducting Plate Under a Uniform Magnetic Field

1997 ◽  
Vol 64 (4) ◽  
pp. 828-834 ◽  
Author(s):  
Y. Shindo ◽  
I. Ohnishi ◽  
S. Tohyama
Keyword(s):  
Magnetic Field ◽  
Integral Equations ◽  
Uniform Magnetic Field ◽  
Fourier Transforms ◽  
Flexural Wave ◽  
Crack Plane ◽  
Dual Integral Equations ◽  
Conducting Plate ◽  
Time Harmonic ◽  
The Magnetic Field

Following a classical plate bending theory of magneto-elasticity, we consider the scattering of time-harmonic flexural waves by a through crack in a 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 higher singular moments near the crack tip.

Dynamic Singular Stresses for a Griffith Crack in a Soft Ferromagnetic Elastic Solid Subjected to a Uniform Magnetic Field

1983 ◽  
Vol 50 (1) ◽  
pp. 50-56 ◽  
Author(s):  
Y. Shindo
Keyword(s):  
Magnetic Field ◽  
Integral Equations ◽  
Fourier Transforms ◽  
Dynamic Stress Intensity Factor ◽  
Elastic Solid ◽  
Griffith Crack ◽  
Dual Integral Equations ◽  
Singular Stress ◽  
Magnetostatic Field ◽  
Soft Ferromagnetic

The problem of the diffraction of normally incident longitudinal waves on a Griffith crack located in an infinite soft ferromagnetic elastic solid is considered. It is assumed that the solid is a homogeneous and isotropic one and is permeated by a uniform magnetostatic field normal to the crack surfaces. Fourier transforms are used to reduce the problem to two simultaneous dual integral equations. The solution to the integral equations is expressed in terms of a Fredholm integral equation of the second kind having the kernel that is a finite integral. The dynamic singular stress field near the crack tip is obtained and the influence of the magnetic field on the dynamic stress intensity factor is shown graphically in detail. Approximate analytical expressions valid at low frequencies are also obtained and the range of validity of these expressions is examined.

scholarly journals Integral Equations for Problems on Wave Propagation in Near-Earth Plasma

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1395
Author(s):  
Danila Kostarev ◽  
Dmitri Klimushkin ◽  
Pavel Mager
Keyword(s):  
Magnetic Field ◽  
Integral Equations ◽  
Field Potential ◽  
Low Frequency ◽  
Fredholm Equation ◽  
Compression Waves ◽  
Parallel Component ◽  
Electric Field Potential ◽  
The Magnetic Field ◽  
Low Frequency Waves

We consider the solutions of two integrodifferential equations in this work. These equations describe the ultra-low frequency waves in the dipol-like model of the magnetosphere in the gyrokinetic framework. The first one is reduced to the homogeneous, second kind Fredholm equation. This equation describes the structure of the parallel component of the magnetic field of drift-compression waves along the Earth’s magnetic field. The second equation is reduced to the inhomogeneous, second kind Fredholm equation. This equation describes the field-aligned structure of the parallel electric field potential of Alfvén waves. Both integral equations are solved numerically.

scholarly journals Warped Accretion Discs

2003 ◽  
Vol 208 ◽  
pp. 385-386
Author(s):  
D. Chakrabarty ◽  
J. Murray ◽  
G.A. Wynn ◽  
A.R. King
Keyword(s):  
Magnetic Field ◽  
Modal Analysis ◽  
Numerical Investigation ◽  
Fourier Transforms ◽  
Small Difference ◽  
Accretion Discs ◽  
Stellar Systems ◽  
Hydrodynamic Simulations ◽  
Companion Star ◽  
The Magnetic Field

In this article we report the results of our numerical investigation of warped accretion discs in binary stellar systems. We perform complete 3-D hydrodynamic simulations of binary discs. The disc is rendered unstable to the warp mode under the action of the magnetic field of the companion star in the binary. The disc thus warped is noted to undergo retrograde precession with a precession period just slightly less than the binary period. This small difference in periods can explain the phenomenon of negative superhumps observed in a number of binaries. Besides the modal analysis based on Fourier transforms, warps were also studied by a simple and robust technique that we developed; this is based on an analysis of the azimuthal distributions of particles that lie above and below the mid-plane of the disc.

Dual integral equations associated with Fourier transforms

1986 ◽  
Vol 38 (2) ◽  
pp. 165-171
Author(s):  
Nguyen Van Ngok ◽  
G. Ya. Popov
Keyword(s):  
Integral Equations ◽  
Fourier Transforms ◽  
Dual Integral Equations

On the boundary operator in electromagnetic scattering

1986 ◽  
Vol 103 (1-2) ◽  
pp. 91-98 ◽  
Author(s):  
Rainer Kress
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Electromagnetic Scattering ◽  
Maxwell Equations ◽  
Boundary Operator ◽  
Hölder Continuous ◽  
Operator Mapping ◽  
Time Harmonic ◽  
Continuous Surface ◽  
The Magnetic Field

SynopsisFor radiating solutions to the time-harmonic Maxwell equations, it is shown that the boundary operator mapping the tangential components of the electric field into the tangential components of the magnetic field is a bounded bijective operator from the space of Holder continuous tangential fields with Hölder continuous surface divergence onto itself.

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