Abstract
As an essential model of magnetoelastic interaction between magnetic field and mechanical deformation, the study on magnetoelastic buckling phenomenon of soft ferromagnetic plates in a magnetic environment has been conducted. One of the key steps for the theoretical prediction of the critical magnetic field is how to formulate magnetic force exerted on the magnetized medium. Till today, the theoretical predictions, from theoretical models in publications, of the magnetoelastic buckling of ferromagnetic cantilevered beam-plate in transverse magnetic field are all higher than their experimental data. Sometimes, the discrepancy between them is as high as 100%. In this paper, the macroscope formulation of the magnetic forces is strictly obtained from the microscope Amperion current model. After that, a new theoretical model is established to describe the magnetoelastic buckling phenomenon of ferromagnetic thin plates with geometrically nonlinear deformation in a nonuniform transverse magnetic field. The numerical method for quantitative analysis is employed by combining the finite elemental method for magnetic fields and the finite difference method for deformation of plates. The numerical results obtained from this new theoretical model show that the theoretical predictions of critical values of the buckling magnetic field for the ferromagnetic cantilevered beam-plate are in excellent agreement with their experimental data. By the way, the region of applicability to the Moon-Pao's model, or the couple model, is checked by quantitative results.
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References
Moon FC. Magneto-Solid Mechanics. New York: Jone Wiley and Sons, 1984
Moon FC, Pao YH. Magnetoelastic buckling of a thin plate.ASME J Appl Mech, 1968, 35(1): 53–58
van de Ven AAF. A variational principle for magneto-elastic buckling.J Eng. Math, 1987, 21: 227–252
van Lieshord PH, van de Ven AAF. A variational approach to the magnetoelastic buckling of an arbitrary number of superconducting beams.J Eng Math, 1991, 25: 353–374
Wolfe P. Bifurcation theory of an elastic conducting wire subject to magnetic forces.J Elasticity, 1990, 23: 201–217
Xie Huicai, Fang Guofong, Wang Deman. Magnetoelastic buckling of in-plane circular coil.Acta Mechanica Sinica (Chinese Edition), 1991, 23(6): 706–711
Wang Zhangqi. Magnetoelastic buckling of beam-plate with consideration of effect of dimension size.J Applied Mech (Chinese Edition), 1991, 8(4)
Miya K, Tagaki T, Audo F. Finite-element analysis of magnetoelastic buckling of ferromagnetic beam-plate.ASME J Appl Mech, 1980, 47: 377–382
Popelar CR, Bast CO. An experimental study of the magneto-elastic postbuckling behavior of a beam.Experimental Mechanics, 1972, 12: 537–542
van de Ven AAF. Magnetoelastic buckling of thin plates in a uniform transverse magnetic field.J. Elasticity, 1978, 8: 279–312
Peach MO, Chrastopherson NS, Dalrgymple JM et al. Magnetoelastic buckling: Why theory and experiment disagree?Experimental Mechanics, 1987, 27: 65–69
Chao Chang-qi. Electrodynamics. Beijing: People's Education House, 1979
Zheng Xiao-jing. Theory of Large Deflection of Circular Plates and Its Applications. Changchun: Publication House of Science and Technology of Jilin, 1990 (in Chinese)
Zhou Youhe, Zheng Xiaojing. Some developments and problems in magnetoelastic buckling of thin plates.Advances in Mechanics, 1995, 25 (4): 525–536 (in Chinese)
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This project was supported in part by the National Natural Science Foundation of China and the Foundation of the SEdC of China for Returned Chinese Scholars from Abroad.
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Youhe, Z., Xiaojing, Z. A theoretical model of magnetoelastic bucking for soft ferromagnetic thin plates. Acta Mech Sinica 12, 213–224 (1996). https://doi.org/10.1007/BF02486808
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DOI: https://doi.org/10.1007/BF02486808