横向磁场中轴向运动铁磁梁的磁弹性主共振

研究在外激励力与磁场作用下轴向运动铁磁梁的磁弹性非线性主共振问题．基于弹性理论和电磁理论，给出梁的动能和弹性势能表达式，根据哈密顿原理，推导出磁场中轴向运动铁磁梁的磁弹性双向耦合非线性振动方程．通过伽辽金积分法进行离散，得出两端简支边界条件下铁磁梁磁弹性非线性强迫振动方程．应用多尺度法对方程进行求解，得出幅频响应方程．最后通过算例，给出铁磁梁的幅频特性曲线、振幅-磁感应强度和振幅-外激励力曲线并进行分析．结果显示，在幅频响应曲线中铁磁梁的轴向运动速度、外激励力、轴向拉力越大，共振振幅越大；而磁感应强度越大，振幅越小．

Magnetoelastic Primary Resonance of Axial Moving Ferromagnetic Beams

The magnetoelastic nonlinear primary resonance problem of axially moving ferromagnetic beams under external excitation force and magnetic field is studied. Based on the elastic theory and electromagnetic theory, the expressions of the kinetic energy and the elastic potential energy of the beam are given. According to the Hamiltonian principle, the magnetoelastic bidirectional coupled nonlinear vibration equation of the axially moving ferromagnetic beam in the magnetic field is derived. The magnetoelastic nonlinear forced vibration equation of the ferromagnetic beam is obtained by the Galerkin integral method. The multi-scale method is used to solve the equation to obtain the amplitude-frequency response equation. Finally, an example is given to show the amplitude-frequency characteristic curve, amplitude-magnetic induction intensity and amplitude-external excitation force curve of the ferromagnetic beam. The results show that increase of the axial movement speed, or the external excitation force, or the axial tensile force of the ferromagnetic beam in the amplitude-frequency response curve, leads to the increase of the resonance amplitude; and increase of the magnetic induction intensity leads to decrease of the amplitude.