不可移简支几何非线性铁磁梁式板的磁弹性屈曲与后屈曲分析

Analysis for Magnetoelastic Buckling and Post buckling of Ferromagnetic Beam Plates with Simply Supported and Unmovable Ends

采用基于薄板挠曲变形的广义变分原理导出的磁力计算公式和运用电磁弹性耦合的非线性数值计算程序，定量分析了不可移简支几何非线性铁磁梁式板的屈曲与后屈曲路径，给出了非线性静态解的分叉图象．然后对于在斜磁场作用下这一铁磁板的磁弹性弯曲与失稳情形，得到了梁由两个半波的挠曲构形演变为单半波挠曲构形的跳跃失稳临界磁场与失稳后的路径等；并且随着倾斜磁场的倾角增大，简支梁式板磁弹性的临界磁场值随之增加．这一结果表明简支梁式板的磁弹性系统对安装偏差之类的缺陷是不敏感的．

Based on the general expression of magnetic force from the variational principle of ferromagnetic plates, and the numerical programme of nonlinear magnetoelastic interaction, this paper is to quatitatively analyze the magnetoelastic buckling/instability and the path of post buckling for a simply supported and unmovable beam plate with geometrical nonliearity, and give the bifurcation pattern of static solutions of the nonlinear problem. After that, the characteristic of the snapping/jumping phenomenon for the plate in oblique magnetic fields is shown to be that the plate jumps from the configuration of bending deflection with two semi wave state to that with single semi wave state. The critical magnetic field of this jumping phenomenon increases with increasing of the incident angle of the oblique magnetic field, which tells us that the critical magnetic field is not sensitive to the imperfect of misalignment of the plate in transverse magnetic field.