In this paper, the simultaneous resonance of a ferromagnetic thin plate in a time-varying magnetic field, having axial speed and being subjected to a periodic line load, is studied. Based on the large deflection theory of thin plates and electromagnetic field theory, the nonlinear vibration differential equation of the plate is obtained by using the Hamilton’s principle and the Galerkin method. Then the boundary condition in which the longer opposite sides are clamped and hinged is considered. The dimensionless nonlinear differential equations are solved by using the method of multiple scales, and the analytical solution is given. In addition, the stability analysis is also carried out by using Lyapunov stability theory. Through numerical analysis, the variation curves of system resonance amplitude with frequency tuning parameter, magnetic field strength and external excitation amplitude are obtained. Different parameters that have significant effects on the response of the system, such as the thickness, the axial velocity, the magnetic field intensity, the position, and the frequency of external excitation, are considered and analyzed. The results show that the system has multiple solution regions and obvious nonlinear coupled characteristics.

本文研究了具有轴向速度并承受周期线载荷的铁磁薄板在时变磁场中的同时谐振。基于薄板大挠度理论和电磁场理论，利用哈密顿原理和伽辽金法，得到了薄板的非线性振动微分方程。然后考虑较长相对边被夹紧和铰接的边界条件。采用多尺度方法求解无量纲非线性微分方程，并给出解析解。此外，还利用Lyapunov稳定性理论进行了稳定性分析。通过数值分析，得到系统谐振幅值随频率调谐参数的变化曲线，获得磁场强度和外部激励幅度。考虑并分析了对系统响应有显着影响的不同参数，例如厚度、轴向速度、磁场强度、外部激励的位置和频率。结果表明，系统具有多个解域和明显的非线性耦合特性。