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.

Magnetoelastic Buckling of Thin Magnetically Soft Plates in Cylindrical Mode

1974 ◽  
Vol 41 (1) ◽  
pp. 145-150 ◽  
Author(s):  
J. M. Dalrymple ◽  
M. O. Peach ◽  
G. L. Viegelahn
Keyword(s):  
Magnetic Field ◽  
Experimental Data ◽  
Rectangular Plate ◽  
Empirical Formula ◽  
Uniform Magnetic Field ◽  
Critical Value ◽  
Elliptical Plate ◽  
Wide Face ◽  
Magnetically Soft Material ◽  
Plate Width

When a plate of magnetically soft material is supported with its wide face normal to a uniform magnetic field, it will buckle when the field reaches a critical value. It is shown theoretically that the critical buckling field for a “half-restrained” rectangular plate should be 0.833 of that for a half-restrained elliptical plate of identical dimensions and material. Limited experimental data support this conclusion. The effect of plate width upon critical buckling field is investigated experimentally and an empirical formula is presented which fits the data reasonably well.

scholarly journals INFLUENCE OF A UNIFORM MAGNETIC FIELD ON DYNAMICAL CHIRAL SYMMETRY BREAKING IN QED3

2012 ◽  
Vol 27 (09) ◽  
pp. 1250026 ◽  
Author(s):  
JIAN-FENG LI ◽  
HONG-TAO FENG ◽  
YU JIANG ◽  
WEI-MIN SUN ◽  
HONG-SHI ZONG
Keyword(s):  
Magnetic Field ◽  
High Temperature ◽  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Uniform Magnetic Field ◽  
Cuprate Superconductors ◽  
Chiral Symmetry Breaking ◽  
Critical Value ◽  
Dynamical Chiral Symmetry Breaking ◽  
The Magnetic Field

We study dynamical chiral symmetry breaking (DCSB) in an effective QED3 theory of d-wave high temperature cuprate superconductors under a uniform magnetic field. At zero temperature, the external magnetic field induces a mixed state by generating vortices in the condensate of charged holons. The growing magnetic field suppresses the superfluid density and thus reduces the gauge field mass which is opened via the Anderson–Higgs mechanism. By numerically solving the Dyson–Schwinger gap equation, we show that the massless fermions acquires a dynamical gap through DCSB mechanism when the magnetic field strength H is above a critical value H c and the fermion flavors N is below a critical value N c . Further, it is found that both N c and the dynamical fermion gap increase as the magnetic field H grows. It is expected that our result can be tested in phenomena in high temperature cuprate superconductors.

THE EFFECT OF A VARYING MAGNETIC FIELD ON THE DIRAC FERMION SPECTRUM OF GRAPHENE

2011 ◽  
Vol 25 (03) ◽  
pp. 365-370 ◽  
Author(s):  
M. R. SETARE ◽  
D. JAHANI
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Ground State ◽  
Uniform Magnetic Field ◽  
Energy Levels ◽  
Single Layer ◽  
The Other ◽  
Dirac Fermion ◽  
Zero Energy ◽  
Special Case

We examine the effect of a magnetic field that varies inversely as the square of distance on the Dirac fermion spectrum of graphene, a single layer of graphite. We find that unlike the case of the uniform magnetic field for which zero-energy modes exhibit half the degeneracy of the other levels in the energy spectrum, the ground state in this case, as well as the other energy levels, is doubly degenerate. We also get zero-energy solutions for the special case of ky = 0.

Experimental and Theoretical Study on Magnetoelastic Buckling of a Ferromagnetic Cantilevered Beam-Plate

1978 ◽  
Vol 45 (2) ◽  
pp. 355-360 ◽  
Author(s):  
K. Miya ◽  
K. Hara ◽  
K. Someya
Keyword(s):  
Magnetic Field ◽  
Theoretical Study ◽  
Critical Value ◽  
The Finite Element Method ◽  
Wide Face ◽  
Field Distortion ◽  
Cantilevered Beam ◽  
Magnetically Soft Material ◽  
Experimental Values ◽  
The Magnetic Field

When a cantilever of magnetically soft material is inserted with its wide face normal to a uniform magnetic field and the magnetic field is increased to a critical value the cantilever will buckle. The experimental magnetoelastic buckling fields and the theoretical ones differ by a factor of two. A magnetic field distortion near an edge of the specimen is here evaluated based on the finite-element method and the results are applied to the experimental results so as to explain the discrepancy between the experiment and the theory. The corrected experimental values are within 15 percent of the theoretical values. The effect of demagnetization on the buckling field is here demonstrated as well as the effect of specimen dimensions.

Effect of finite ion Larmor radius on the Kelvin–Helmholtz instability

1978 ◽  
Vol 20 (2) ◽  
pp. 149-160 ◽  
Author(s):  
Hirosh Nagano
Keyword(s):  
Magnetic Field ◽  
Flow Velocity ◽  
Wave Vector ◽  
Uniform Magnetic Field ◽  
Critical Value ◽  
Larmor Radius ◽  
Helmholtz Instability ◽  
Finite Larmor Radius ◽  
Compressible Plasma ◽  
The Difference

The effect of finite ion Larmor radius on the Kelvin–Helmholtz instability is investigated in the cases of an incompressible and a compressible plasma. When a wave vector is perpendicular to a uniform magnetic field, the effect of finite Larmor radius (FLR) stabilizes perturbations with a wavenumber exceeding a critical value, while there exists another case that the FLR effect destabilizes still more than the usual MHD approximation. The difference between these cases is decided from the configuration of flow velocity and magnetic field. When a wave vector is parallel to a magnetic field, the FLR effect tends to stabilize perturbations with a larger wavenumber.

Magnetoelastic Buckling of a Thin Plate

1968 ◽  
Vol 35 (1) ◽  
pp. 53-58 ◽  
Author(s):  
F. C. Moon ◽  
Yih-Hsing Pao
Keyword(s):  
Magnetic Field ◽  
Axial Load ◽  
Uniform Magnetic Field ◽  
Field Experiments ◽  
Equilibrium Configuration ◽  
Critical Value ◽  
Transverse Magnetic ◽  
Field Equations ◽  
Magnetostatic Field ◽  
Characteristic Values

The instability of a column under axial load is well known. A similar phenomenon is discussed in this paper for a beam-plate in a transverse magnetic field. Experiments show that the beam may buckle (in the sense of an Euler column) when the uniform magnetic field strength reaches a critical value. A mathematical model is proposed with distributed magnetic torques along the plate. A nontrivial adjacent equilibrium configuration satisfying the magnetostatic field equations is shown to exist for characteristic values of the external magnetic field. Results as predicted from this model compare favorably with experiments.

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.

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