横向常磁场中铁磁圆板的主共振特性与静载效应

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摘要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方程进行一阶和二阶近似求解，得到主共振下系统幅频响应方程。通过算例，给出了系统幅频特性曲线图、振幅随磁场强度和激励力变化的曲线图，分析了板厚、磁场强度、激励力对系统共振振幅的影响，并对比了一阶近似和二阶近似计算结果的不同。结果表明，共振区域内振幅显著增加，磁场强度较小时一阶近似与二阶近似计算结果相近，而磁场强度较大时，二阶近似计算结果更加准确。

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关键词 ：铁磁圆板, 常磁场, 磁弹性, 主共振, 多尺度法

Abstract：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.

Key words： ferromagnetic circular plate constant magnetic field magnetoelasticity principal resonance multiscale method

收稿日期: 2019-01-15 出版日期: 2021-01-15

引用本文:

马冰冰1,2，胡宇达1,2. 横向常磁场中铁磁圆板的主共振特性与静载效应[J]. 振动与冲击, 2021, 40(1): 308-316.
MA Bingbing 1,2 HU Yuda 1,2. Principal resonance characteristics and static load effect of a ferromagnetic circular plate in a transverse constant magnetic field. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(1): 308-316.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2021/V40/I1/308

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