Eddy Current Flow Near Cracks in Thin Plates

1985 ◽  
Vol 52 (4) ◽  
pp. 841-846 ◽  
Author(s):  
C. Y. Hui ◽  
A. Ruina
Keyword(s):  
Magnetic Field ◽  
Eddy Current ◽  
Uniform Magnetic Field ◽  
Current Flow ◽  
Small Crack ◽  
Thin Plates ◽  
Mathematical Methods ◽  
Round Plate ◽  
Special Cases ◽  
Eddy Current Problem

The problem of magnetically induced eddy current flow in a thin cracked plate is posed and solved for a few special cases. The current density is singular at the tip of a nonconducting crack. The strength of this singularity, denoted M, is found by reducing the eddy current problem to a conduction problem and then using the mathematical methods of fracture mechanics. M is found for a small crack in a current field, a small crack in a round plate with spatially uniform magnetic field, and a half-cracked round plate with spacially uniform magnetic field.

A sufficient condition for instability of BGK type waves in both unmagnetized and magnetized plasmas

1977 ◽  
Vol 17 (1) ◽  
pp. 57-68 ◽  
Author(s):  
E. Infeld ◽  
G. Rowlands
Keyword(s):  
Magnetic Field ◽  
Linear Theory ◽  
General Problem ◽  
Uniform Magnetic Field ◽  
Magnetized Plasmas ◽  
Sufficient Condition ◽  
General Sufficient Condition ◽  
Special Cases

This paper investigates the general problem of stability of Bernstein—Greene— Kruskal type waves. By investigating perturbations perpendicular to the wave, we obtain a general sufficient condition for instability. This is then extended to the case of magnetized plasmas with a uniform magnetic field in the direction of the BGK wave. New perturbed modes, having no counterpart in linear theory, are also found. Various special cases are considered and previous, more particular results confirmed.

scholarly journals Electromagnetic induction noise in a towed electromagnetic streamer

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. E187-E199 ◽  
Author(s):  
Axel Tcheheumeni Djanni ◽  
Anton Ziolkowski ◽  
David Wright
Keyword(s):  
Magnetic Field ◽  
Noise Level ◽  
Electromagnetic Induction ◽  
Uniform Magnetic Field ◽  
Wave Motion ◽  
Current Flow ◽  
Constant Current ◽  
Simple Analysis ◽  
Faraday’S Law ◽  
Neutrally Buoyant

We have examined the idea that a towed neutrally buoyant electromagnetic (EM) streamer suffers from noise induced according to Faraday’s law of induction. A simple analysis of a horizontal streamer in a constant uniform magnetic field determined that there was no induction noise. We have developed an experiment to measure the induced noise in a prototype EM streamer suspended in the Edinburgh FloWave tank, and we subjected it to water flow along its length and to waves propagating in the same direction, at 45° and 90° to the streamer direction. The noise level was found to increase with increasing flow velocity. The motion of the prototype EM streamer in response to parallel constant current flow and wave motion was found to generate significant noise. The main finding is that wave motion was the major source of noise and was much larger than the noise of a static cable. The noise level can probably be reduced by towing the cable deeper and increasing the cable tension.

Magnetoelastic Buckling of Beams and Thin Plates of Magnetically Soft Material

1972 ◽  
Vol 39 (2) ◽  
pp. 451-455 ◽  
Author(s):  
D. V. Wallerstein ◽  
M. O. Peach
Keyword(s):  
Magnetic Field ◽  
Theoretical Result ◽  
Cantilever Beam ◽  
Uniform Magnetic Field ◽  
Critical Value ◽  
Soft Material ◽  
Thin Plates ◽  
Magnetically Soft Material ◽  
Plate Geometry ◽  
Special Case

When a plate of magnetically soft material is supported with its wide surface normal to a uniform magnetic field, it will buckle when the field reaches a critical value. This paper formulates the problem quite generally for thin plates (including beams) and carries the solution as far as can be done without making specific assumptions as to plate geometry and constraints. The special case of wide cantilever beam, considered earlier by Moon and Pao, is carried through in detail. It is shown that if their theoretical result is modified to take account of the increased field intensity caused by the plate, agreement with experiment is within 20 percent.

Analytical and numerical aspects of the electromagnetic stirring induced by alternating magnetic fields

1981 ◽  
Vol 102 ◽  
pp. 405-430 ◽  
Author(s):  
Y. R. Fautrelle
Keyword(s):  
Magnetic Field ◽  
Circular Cylinder ◽  
Uniform Magnetic Field ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
First Case ◽  
Special Cases ◽  
Alternating Magnetic Fields

The dynamic effects of an alternating magnetic field on containers of conducting fluid are investigated in two special cases: (i) an infinitely long circular cylinder in a uniform magnetic field normal to the generators; (ii) a truncated circular cylinder in a uniform magnetic field parallel to the axis. Neglecting the motion effects in Maxwell's equations, the problem is conveniently decoupled into electromagnetic and dynamic parts. Using either analytical or numerical solutions of the electromagnetic equations, the electromagnetic forces are calculated and introduced in the motion equations. In the first case, asymptotic solutions of the Navier–Stokes equations valid for high frequencies are calculated and compared with numerical solutions obtained for the same geometry. The second case has been studied numerically, and the solutions are presented and interpreted.

Exact nonlinear wave solutions of the incompressible magnetohydrodynamic equations in a non-uniform magnetic field

1989 ◽  
Vol 42 (2) ◽  
pp. 247-256 ◽  
Author(s):  
Hiromitsu Hamabata ◽  
Tomikazu Namikawa
Keyword(s):  
Magnetic Field ◽  
Incompressible Fluid ◽  
Uniform Magnetic Field ◽  
Magnetohydrodynamic Equations ◽  
Wave Solutions ◽  
Laboratory Plasmas ◽  
Special Cases ◽  
Circular Magnetic Field ◽  
Incompressible Magnetohydrodynamic Equations ◽  
Nonlinear Wave Solutions

Exact wave solutions of the nonlinear magnetohydrodynamic equations for a highly conducting incompressible fluid within an axisymmetric container are obtained. It is shown that there are four types of exact wave solutions with large amplitude in a non-uniform magnetic field. These solutions are very useful because they can be expressed in terms of arbitrary scalar functions and they are applicable to astrophysical and laboratory plasmas as well as the earth's core. The solutions also include as special cases the nonlinear Alfvén waves in a uniform magnetic field and in a circular magnetic field found respectively by Walén (1944) and by Namikawa & Hamabata (1987, 1988).

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