磁弹性耦合效应引起的铁磁直杆磁场中振动频率的改变  

Changes of Natural Frequency of a Ferromagnetic Rod in Magnetic Field Due to Magnetoelastic Interaction

作　　者：王省哲[1] 郭兴明 

机构地区：[1]兰州大学西部灾害与环境力学教育部重点实验室兰州大学土木工程与力学学院,兰州730000

出　　处：《应用数学和力学》2008年第8期927-935,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10502022);教育部新世纪优秀人才支持计划资助项目(NCET-050878)

摘　　要：基于磁弹性广义变分原理和Hamilton原理,对处于外加磁场中的软铁磁体,建立了磁弹性动力学理论模型.分别通过关于铁磁杆磁标势和弹性位移的变分运算,获得了包含磁场和弹性变形的所有基本方程,并给出描述磁弹性耦合作用的磁体力和磁面力.采用摄动技术和Galerkin方法,将所建立的磁弹性理论模型用于外加磁场中铁磁直杆的振动分析.结果表明,由于磁弹性耦合效应,外加磁场将对铁磁杆的振动频率产生影响:当铁磁杆的振动位移沿着磁场方向时,其频率减小并出现磁弹性屈曲失稳;当铁磁杆的振动位移垂直于磁场方向时,其频率将会增大.理论模型能够很好地解释已有实验观测的振动频率改变现象.Based on magnetoelastie generalized variational principle and Hamilton＇ s principle, a dynamic theoretical model characterizing the magnetoelastic interaction of a soft ferromagnetic medium in an applied magnetic field is developed. From variational manipulation respectively on magnetic scale potential and elastic displacement, the all fundamental equations for the magnetic field and mechanical deformation, as well as the the magnetic body force and magnetic traction for describing magnetoelastic interaction, were derived. The theoretical model was applied to a ferromagnetic rod vibrating in an applied magnetic field by means of perturbation technique and Galerkin method. The results show that the magnetic field will change the natural frequencies of the ferromagnetic rod by decrease as the bending motion along the applied magnetic field where the magnetoelastic buckling will take place,but by increase when bending motion of the rod is perpendicular to the field. The prediction by the model qualitatively agrees with the natural frequency changes of the ferromagnetic rod observed in the experiment.

关 键 词：铁磁杆 磁弹性相互作用 广义变分原理 振动频率 摄动方法 

分 类 号：O344[理学—固体力学]