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 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]

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.

The stability of viscous flow in a curved channel in the presence of a magnetic field

1961 ◽  
Vol 264 (1317) ◽  
pp. 155-164 ◽  
Keyword(s):  
Magnetic Field ◽  
Viscous Flow ◽  
Uniform Magnetic Field ◽  
Axial Direction ◽  
Electrical Conductor ◽  
Curved Channel ◽  
Coaxial Cylinders ◽  
Transverse Pressure ◽  
The Stability ◽  
The Magnetic Field

The stability of viscous flow between two coaxial cylinders maintained by a constant transverse pressure gradient is considered when the fluid is an electrical conductor and a uniform magnetic field is impressed in the axial direction. The problem is solved and the dependence of the critical number for the onset of instability on the strength of the magnetic field and the coefficient of electrical conductivity of the fluid is determined.

scholarly journals Spin-1/2 Particles under the Influence of a Uniform Magnetic Field in the Interior Schwarzschild Solution

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 467
Author(s):  
Fayçal Hammad ◽  
Alexandre Landry ◽  
Parvaneh Sadeghi
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Total Mass ◽  
Uniform Magnetic Field ◽  
Energy Levels ◽  
Relativistic Wave Equation ◽  
Relativistic Wave ◽  
Schwarzschild Solution ◽  
Relativistic Regime ◽  
The Magnetic Field

The relativistic wave equation for spin-1/2 particles in the interior Schwarzschild solution in the presence of a uniform magnetic field is obtained. The fully relativistic regime is considered, and the energy levels occupied by the particles are derived as functions of the magnetic field, the radius of the massive sphere and the total mass of the latter. As no assumption is made on the relative strengths of the particles’ interaction with the gravitational and magnetic fields, the relevance of our results to the physics of the interior of neutron stars, where both the gravitational and the magnetic fields are very intense, is discussed.

scholarly journals Deformation of a magnetic liquid drop in an applied non-stationary uniform magnetic field

2018 ◽  
Vol 185 ◽  
pp. 09006
Author(s):  
Alexander Tyatyushkin
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Steady State ◽  
Uniform Magnetic Field ◽  
Liquid Drop ◽  
Magnetic Liquid ◽  
Stationary Approximation ◽  
The Magnetic Field

Small steady-state deformational oscillations of a drop of magnetic liquid in a nonstationary uniform magnetic field are theoretically investigated. The drop is suspended in another magnetic liquid immiscible with the former. The Reynolds number is so small that the inertia can be neglected. The variation of the magnetic field is so slow that the quasi-stationary approximation for the magnetic field and the quasi-steady approximation for the flow may be used.

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.

Effect of Magnetic Field on the Laminar Heat Transfer Performance of Hybrid Nanofluid in a Lid Driven Cavity Over Solid Block

2020 ◽  
Author(s):  
Rajesh Nimmagadda ◽  
Durga Prakash Matta ◽  
Rony Reuven ◽  
Lazarus Godson Asirvatham ◽  
Somchai Wongwises ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Uniform Magnetic Field ◽  
Conjugate Heat Transfer ◽  
Heat Transfer Performance ◽  
Hybrid Nanofluid ◽  
Transfer Performance ◽  
Driven Cavity ◽  
The Magnetic Field ◽  
Solid Block

Abstract A 2D numerical investigation has been carried out to obtain the heat transfer performance of hybrid (Al2O3 + Ag) nanofluid in a lid driven cavity over solid block under the influence of uniform as well as non-uniform magnetic field. The geometrical domain consists of a cavity containing nanofluid that is driven by means of lid moving in one direction. This circulating nanofluid will extract enormous amount of heat from the solid block underneath the cavity resulting in conjugate heat transfer. A homogenous solver based on the finite volume method with conjugate heat transfer was developed and adopted in the existing study. The heat efficient hybrid nanofluid (HyNF) pair (2.4 vol.% Ag + 0.6 vol.% Al2O3) obtained by Nimmagadda and Venkatasubbaiah [1] is used in the present investigation. Moreover, efficient non-uniform sinusoidal magnetic field identified by Nimmagadda et al. [2] is also implemented and compared with uniform magnetic field. Furthermore, the magnetic field is applied over the geometrical domain along the two axial directions separately and the effective heat transfer performance is obtained. The significant impact of extensive parameters like Reynolds number, nanoparticle type, nanoparticle concentration, magnetic field type, magnetic field location and the strength of the magnetic field on heat transfer performance are systematically analyzed and presented.

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

Construction of a Cost Effective Current Balance for Physics Teaching

2013 ◽  
Vol 770 ◽  
pp. 374-377
Author(s):  
Apichart Sankote ◽  
Kheamrutai Thamaphat ◽  
Supanee Limsuwan
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Magnetic Force ◽  
Magnetic Field Direction ◽  
Horizontal Segment ◽  
Applied Current ◽  
Copper Sheet ◽  
Physics Teaching ◽  
The Magnetic Field ◽  
A Current

In this work, a method to measuring the magnitude of a uniform magnetic field in space using current balance was described. A simple experimental set was designed and constructed using low-cost materials. This constructed current balance consists of copper sheet, weight pan, and acrylic sheet. A copper sheet was cut into a U-shape and attached at the end of acrylic balance arm. A weight pan was hanged in the opposite side of the balance arm with high sensitivity to a small torque. The horizontal segment of the U-shaped copper sheet, which the length l was 3 cm, was located inside the influence of an uniform magnetic field produced by two parallel bar magnets with opposite poles facing each other. The magnetic field direction was perpendicular to the horizontal segment. When a current was supplied to the copper sheet, the magnetic force acting on a horizontal segment of length l carrying a current I in a magnetic field B was given by. In the experiment, the current was varied from 0 1 A. For each value of applied current, the magnetic force on a thin straight sheet of length l was measured by adding masses to the pan until the balance arm moved to the equilibrium between opposing gravitational and magnetic forces. The results showed that the magnetic force increased linearly with increasing applied current. By plotting a linear graph of magnetic force versus applied current, the magnetic field B can be calculated from . The calculated and actual values of B were 100.32 and 100.13 mT, respectively. This constructed current balance is an excellent tool for high school and undergraduate fundamental physics courses. Students will be excited when they see the balance arm rising or going down due to magnitude and direction of current flowing in a conductor wire.

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