Nonlinear Coupled Magneto-elastic Theory In Ferromagnetic Materials And The Application In Giant Magnetostrictive Smart Materials

Along with the development of modern high and new technology realm, ferromagnetic materials play more and more important rules in modern industry. For example, there are many ferromagnetic materials in electric machines (such as generators and transformer) which are convenient in electrical energy production and transportation. However, there still exist a series of complicated unsolved problems in these equipments. One of them is generators and transformer's vibration and noise problem. The investigative results by engineers show that a main reason about the vibration and noise of electric machine is because of the vibration and noise of the silicon steel sheets in its cores, so the essential problem of the vibration of electric machines is the mechanical deformation of ferromagnetic materials induced by electromagnetic field. During operation, sinusoidal alternating magnetic fields established inside the cores would cause magnetic forces and then cause the vibrations of silicon steel sheets and make noise. If only considering the effect of magnetic forces, it is hard to explain the frequency multiplication phenomenon in dynamic response. Thus, the magnetostrictive phenomenon of ferromagnetic materials under magnetic field becomes a hot research topic. In conclusion, a key problem of the researches of vibration and noise in electric machines is presenting a deformation model of ferromagnetic materials by magnetic forces and magentostriction under complex magnetic fields. The present study about nonlinear magneto-elastic coupling of ferromagnetic materials is based on above considerations in this paper.Firstly, this paper deal with the local coupling theory of ferromagnetic materials, namely the nonlinear magneto-mechanics coupling constitutive relations. For better describing the complex behavior of ferromagnetic materials, a nonlinear constitutive model is developed in this paper, which can reflect the effect of pre-stress (or residual stress) on the magnetostrictive strain and magnetization curves. And the comparison between the theoretical prediction and the experimental results verifies that the new model can more effectively characterize the magnetic, magnetoelastic (magnetostrictive and inverse magnetostrictive) and elastic properties, including saturation effect, stress dependence andΔE effect, than the previous models. It is noticed that the constitutive relation with proper simplification is suitable for giant magnetostrictive materials. Secondly, what we study is the global coupling theory of ferromagnetic materials, that is, the magnetic forces and the geometry of the magnetic field problem changes due to deformation. Based on the variation of total magnetic energy, a magnetic force formula is presented. This formula is consistent with the formula that depict two typical experiments by Zhou and Zheng. To consider from a continuum mechanics standpoint, we give a nonlinear magnetoelstic coupling theory frame combined with the global coupling and local coupling and some basic equationes of mechanics and magnetic. This frame is of great significance for the research of deformation of ferromagnetic materials, not only in theoretical analysis but also in numerical calculation, besides, with simplification it can be applied to giant magnetostrictive materials.Based on this new established theory frame, we also do some researches on the application of vibration control of giant magnetostrictive materials, such as, Terfenol-D rod actuator and laminated structures actuator. The numerical results show that the nonlinear control model based on the nonlinear magnetoelastic coupling theory has great advantage compared with the linear control model based on piezomagnetic model.In a word, we build up a nonlinear magnetoelastic coupling theory frame, which is very important for the researches of deformation of ferromagnetic materials, not only in theoretical analysis but also in numerical calculation. In addition, this simplified frame is still proper for giant magnetostrictive materials. The work of this paper has shown a promising future of mechanical methods in the research on magnetoelastic coupling of ferromagnetic materials and thus lay a good study on the electro-magneto-thermo-mechanical multi-field coupling problems.