As an essential model of magnetoelastic interaction between magneticfield and mechanical deformation, the study on magnetoelastic buckling phenomenonof soft ferromagnetic plates in a magnetic environment has been conducted. One ofthe key steps for the theoretical prediction of the critical magnetic field is how toformulate lnagnetic force exerted on the magnetized medium. Till today, the the-oretical predictions, from theoretical models in publications, of the magnetoelasticbuckling of ferromagnetic cantilevered beam-plate in transverse magnetic field are allhigher than their experimental data. Sometimes, the discrepancy between them isas high as 100%. In this paper, the macroscope formulation of the magnetic forcesis strictly obtained from the microscope Amperion current model. After that, a newtheoretical model is established to describe the magnetoelastic buckling phenomenonof ferromagnetic thin plates with geometrically nonlinear deformation in a nonuni-form transverse magnetic field. The numerical method for quantitative analysis isemployed by combining the finite elemental method for magnetic fields and the finitedifference method for deformation of plates. The numerical results obtained from thisnew theoretical model show that the theoretical predictions of critical values of thebuckling magnetic field for the ferromagnetic cantilevered beam-plate are in excellentagreement with their experimental data. By the way, the region of applicability tothe Moon-Pao’s model, or the couple model, is checked by quantitative results.
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