电磁场中导电梁式板非线性振动的分岔

Study on Nonlinear Vibration Bifurcation of Conductive Beam Plate in Magneto Fields

在给出薄板的电磁弹性运动基本方程及电磁力表达式的基础上,得到了横向磁场和机械载荷共同作用下梁式薄板的振动方程,应用Calerkin法将簿板的振动方程化为Duffing方程,用多尺度法得到二阶主共振的分岔方程,最后用奇异性理论得出分岔方程的转迁集并得出了分岔图。

Based on the nonlinear electro-magneto-elastic equations of thin plate and the expression of the electromagnetic forces, the vibration equations of the thin beam plate applied mechanical loadings in a uniform transverse magnetic field are obtained .By using the Calerkin＇s method, the vibration equations of the conductive beam plate is changed to a Duffing equation. And the second principal resonance bifurcation equation is given by means of the multiscale method. Finally the transition varieties and the bifurcation diagram are given by means of singularity analysis.