A GENERAL EXPRESSION OF MAGNETIC FORCE FOR SOFT FERROMAGNETIC-PLATES IN COMPLEX MAGNETIC-FIELDS

The experiments of ferromagnetic plates in different magnetic environm ents exhibit two distinct phenomena, i.e. the magnetoelastic instabili ty of a ferromagnetic plate in transverse magnetic fields, and the inc rease of natural frequency of a ferromagnetic plate with low susceptib ility in an inplane magnetic field. Although these two typical phenome na can be predicted separately by two kinds of theoretical models in w hich the magnetic forces are formulated by totally different expressio ns, no theoretical model has been found to commonly describe them. Thi s makes it difficult to predict theoretically magnetoelastic interacti on of a ferromagnetic structure in complex magnetic environment. A var iational principle, here, is proposed to establish the governing equat ions of magnetoelastic interaction for soft ferromagnetic thin plate s tructures under complex magnetic fields. The functional is chosen as t he summation of the magnetic energy and the strain energy as well as t he external work from applied magnetic fields. From manipulations of t he variational principle, the governing equations of the magnetic fiel d and mechanical deformation together with an expression of equivalent magnetic force exerted on the ferromagnetic plates are obtained. It i s shown that this theoretical model can commonly characterize the expe rimental phenomena of the magnetoelastic interaction aforementioned. ( C) 1997 Elsevier Science Ltd.