磁场中矩形薄板的非线性内共振响应

摘要

The author of this paper has deduced the magnetoelastic vibration equation of the rec-tangular thin plate in transverse magnetic field.With Galerkin and through displacement mode expansion,the author has also acquired the differential equations of the two-DOF internal reso-nance nonlinear vibration in relation to a rectangular thin plate with one side fixed and three other sides simply supported.The author has obtained the two-order mode time history response dia-gram and phase plan under the internal vibration of the system through the analysis of samples and with numerical method,and discussed the initial value of the system and the influence of magnetic field intensity on the vibration.The results show that the system exhibits the character-istics of obvious nonlinear internal resonance.%给出了横向磁场作用下矩形薄板的磁弹性振动方程，针对一边固定、三边简支的矩形薄板，通过位移模态展开，并利用Galerkin法得到两自由度内共振非线性振动微分方程组。算例分析中，利用数值方法得到了系统内共振时两阶模态的时间历程响应图和相平面图，并分别讨论了系统初值及磁场强度对系统振动的影响。结果表明，系统呈现明显的非线性内共振特征。