挥舞旋转运动薄板磁弹性振动分析

Magnetoelastic Vibration Analysis of Flapping Thin Plate

基于非线性薄板理论假设,建立了旋转运动柔性薄板在横向磁场环境下的振动方程。应用Maxwell电磁定律得出导电薄板的电磁本构关系,得到了Lorentz力的表达公式。在考虑了薄板横向变形引起的轴向缩短基础上,使用Hamilton原理推导出在磁场中旋转运动薄板的变分方程,并使用Galerkin法对方程进行离散,研究了旋转运动、磁场强度以及薄板长宽比对薄板振动的影响。

Based on the assumption of nonlinear thin plate theory,the vibration equation of rotating flexible thin plate in magnetic field is established.The electromagnetic relation of the conducting thin plate and the expression formula of Lorentz force is obtained by Maxwell’s law.Considering the axial shortening caused by the transverse deformation of the thin plate,the equation of the rotating thin plate in the magnetic field is derived by Hamilton principle.The equation is discretized by Galerkin method.The effects of rotating motion,magnetic field strength and length width ratio of plate on vibration of the thin plate are studied.