【摘要】 基于哈密顿变分原理，建立机械载荷和磁化产生的谐变磁力共同作用下铁磁板的非线性磁弹性振动方程。针对两长边简支约束边界条件，利用伽辽金积分法得到变量分离后的横向振动微分方程。应用多尺度法和李雅普诺夫稳定性理论求解电磁激发下的1阶主共振问题，得到稳态响应下的幅频方程和定常解的稳定性判据。通过算例，得到铁磁板的幅频特性、振幅-磁场强度幅值和振幅-速度的变化曲线图。曲线分析结果表明，稳定解部分的振幅随磁场强度幅值的增大而增大；非线性刚度随速度的增大而增大，硬弹簧特性增强，非线性特征更为显著。更多还原

【Abstract】 Based on Hamilton principle, the nonlinear magneto-elastic vibration equation of ferromagnetic plate is established under the combined action of mechanical load and harmonic magnetic force induced by magnetization. For the boundary conditions with two long simply supported edges, the transverse vibration differential equations after variables separation is obtained by Galerkin method. The multi-scale method and Lyapunov stability theory are used to solve the first-order principal resonance problem under electromagnetic excitation, the amplitude-frequency equation and the stability criterion of the steady-state solutions are obtained. Through numerical examples, the amplitude-frequency characteristic curves, the amplitude-magnetic field intensity curves and the amplitude-velocity variation curves of the ferromagnetic plate are obtained. The results show that the amplitude of stable solutions increases with the increase of magnetic field intensity amplitude. The nonlinear stiffness increases with the increase of the velocity, the hard-spring characteristics are enhanced and the nonlinear characteristics are more significant.更多还原