横向常磁场中铁磁圆板的主共振特性与静载效应

针对横向常磁场中铁磁圆板的主共振问题进行研究.基于电磁基本理论,得到薄板在常磁场中所受的磁体力和洛伦兹力,应用哈密顿变分原理,推导出磁场中铁磁圆板磁弹性耦合横向振动微分方程.常磁场中铁磁圆板受到的磁体力为静载荷,根据伽辽金法得到周边夹支边界条件下铁磁圆板在静载荷作用下的初挠度,进一步应用多尺度法对周期载荷作用下的非线性...

Principal resonance characteristics and static load effect of a ferromagnetic circular plate in a transverse constant magnetic field

The principal resonance of a ferromagnetic circular plate in transverse constant magnetic field was studied.Based on the theory of electromagnetism,the magnet force and Lorentz force acting on a circular plate in a constant magnetic field were obtained.Applying Hamiltonian variational principle,the differential equation of magnetoelastic transverse vibration of ferromagnetic circular plate in magnetic field was derived.The magnet force acting on a ferromagnetic circular plate in a constant magnetic field is a static load.The initial deflection of a ferromagnetic circular plate under static load and clamped boundary was obtained by Galerkin method.The first and second order approximate solutions of the nonlinear equations under periodic loads were obtained by multiscale method,and the amplitude-frequency response equations of the principal resonance were obtained.Through numerical examples,the amplitude-frequency curves,the curves of amplitude varying with magnetic field intensity and excitation force were obtained.The effects of plate thickness,magnetic field intensity and excitation force on resonance amplitude were analyzed,and the differences between two approximations were compared.The results show that the amplitude increases significantly in the resonance region,and the first-order approximation is similar to the second-order approximation when the magnetic field intensity is low,while the second-order approximation is more accurate when the magnetic field intensity is high.