Abstract
The Euler buckling formula is a simple deduction from the Bernoulli-Euler theory of bending. Perhaps a correct magnetoelastic buckling formula with be obtained as a simple deduction from a correct theory of magnetoelastic bending. The present investigation is a first step toward creating such a theory.
Thin rectangular plates of solft steel were rigidly fixed at one end and caused to bend into a cylindrical shape by applying a uniform magnetic field whose direction made a small angle (five degrees) with the normal to the undeformed plate surface. Strain measurements and field measurements were made along top and bottom surfaces of the plate. A bending-moment diagram was calculated from the strain measurements and a bending-moment diagram was calculated from field measurements, using the integrand of the first Maxwell stress formula to calculate the force distribution acting on the plate. To get agreement between the two diagrams it was necessary to add a concentrated couple and transverse force (not revealed by the field measurements) at the free end of the plate. The postulated couple and force alone accounted for approximately 30 percent of the bending moment values calculated from strains. We conclude that if the external magnetic field at the surface of a magnetic body cann be calculated correctly, the integrand of the Maxwell formula will corretly give the force distribution over the surface, and classical elasticity theory will then given correctly the elalstic deformation.
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References
Carter, G.W., “Distribution of Mechanical Forces in Magnetized Materials,”Proc. IEE,112,1771–1777 (1965).See also in same proceedings:13 (2), (April 1966);113 (4), 719–720 (April 1966); and 113 (7), 1257–1258 (July 1966). See also the monography by R.R. Birss, Electric and Magnetic Forces, American Elserier Publishing Co., Amsterdam (1962).
Maxwell, J.C., A Treatise on Electricity and Magnetism, Oxford Clarendon Press, 3rd Ed., Part III, Art. 425.
Brown, W.F. Jr., Magnetostatic Principles in Ferromagnetism, North-Holland Publishing Co., Amsterdam, Art. 3 of Ch. 5.
Maxwell, J.C., op. cit. A Treatise on Electricity and Magnetism, Oxford Clarendon Press, 3rd Ed., Part III, Art. 425, Art. 395.
Birss, R.R., Electric and Magnetic Forces, American Elsevier Publishing Co., New York, Arts. 2.1., 2.2. of Ch. 2 (1968).
Viegelahn, G.L., “A Study of the Effect of a Transverse Magnetic Field of Plates of High Permeability,” MS Thesis, Michigan Techn. Univ. (1972).
Carter, G.W., The Electromagnetic Field in its Engineering Aspect, American Eleevier Publishing Co., New York, Art. 7.6, 125 (1967).
Darlymple, J.M., Peach, M.O. andViegelahn, G.L., “Edge Effect Influence on Magnetoelastic Buckling of Rectangular Plates,”J. Appl. Mech.,44,Trans. ASME,99,Series E,305–310 (1977).
Dalrymple, J.M., Peach, M.O. and Viegelahn, G.L., “Magnetic Edge Effect in Rectangular Plates of Flow over a Channel Bottom with Vertical Steps,” unpublished paper.
Evan, J.L., “A Study of the Edge Effect of Soft Ferromagnetic Plates as Applied to Magnetoelastic Buckling of Beams,”MS Thesis, Michigan Tech. Univ., Houghton, MI (1975).
Christopherson, N.S., An Experimental Study of the Magnetoelastic Bending of Thin Plates Made of Soft Ferromagnetic Material, PhD Diss., Michigan Techn. Univ., Houghton, MI, University Microfilms International, Ann Arbor, MI (1984).
Christopherson, NS, Peach, M.O. and Dalrymple, J.M., “An Experimental Study of the Magnetoelastic Bendiing of Thin Plates Made of Soft Ferromagnetic Materials,” Proc., 1985 SEM Conf. on Exp. Mech., 222–228 (1985).
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Christopherson, N.S., Peach, M.O. & Dalrymphle, J.M. Magnetostatic deformation experiment: Bending of a thin plate. Experimental Mechanics 29, 432–436 (1989). https://doi.org/10.1007/BF02323863
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DOI: https://doi.org/10.1007/BF02323863