磁场中轴向运动铁磁梁固有振动与内共振的理论及数值模拟研究

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (18) : 190-198.

论文

崔雪1，孔祥清1，胡宇达2

作者信息 +

Theoretical investigation and numerical simulation of the natural vibration and internal resonance of an axially moving ferromagnetic beam in magnetic field

CUI Xue1, KONG Xiangqing1, HU Yuda2

Author information +

文章历史 +

摘要

本文研究了在磁场环境中做轴向运动铁磁梁的非线性双向固有频率和内共振问题。给出了梁的动能、势能以及洛伦兹力和磁体力偶的表达式，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。利用多尺度法求解耦合方程，得到双向振动固有频率表达式。进一步研究梁两个振动方向的固有频率接近1:1时的内共振问题，得到了相互耦合的特征方程。通过算例，得到了梁固有频率与振动时间、磁感应强度和轴向速度的曲线图和系统发生内共振时共振幅值的能量交换时程响应图。在此基础上，利用ABAQUS有限元分析软件计算了梁的前十二阶振动模态和对应的固有频率，数值模拟结果与理论值吻合较好。

Abstract

The nonlinear two-way natural frequency and internal resonance of a ferromagnetic beam moving axially in a magnetic field are studied. The expressions of kinetic energy, potential energy, Lorentz force and magnetic couple of the beam are given. The magnetoelastic two-way coupling nonlinear vibration equation of the axially moving ferromagnetic beam in the magnetic field is derived according to the Hamilton principle. The multi-scale method is used to solve the coupling equation, and the expression of the natural frequency of bidirectional vibration is obtained. Further study the internal resonance of the beam when the natural frequencies of the two vibration directions are close to 1:1, and get the characteristic equations of mutual coupling. Through examples, the curves of the natural frequency of the beam with vibration time, magnetic induction intensity and axial velocity and the time history response diagram of energy exchange of resonance amplitude when the system has internal resonance are obtained. On this basis, the first twelve vibration modes and corresponding natural frequencies of the beam are calculated by using ABAQUS finite element analysis software. The numerical simulation results are in good agreement with the theoretical values.

导出引用

崔雪1，孔祥清1，胡宇达2. 磁场中轴向运动铁磁梁固有振动与内共振的理论及数值模拟研究[J]. 振动与冲击, 2023, 42(18): 190-198

CUI Xue1, KONG Xiangqing1, HU Yuda2. Theoretical investigation and numerical simulation of the natural vibration and internal resonance of an axially moving ferromagnetic beam in magnetic field[J]. Journal of Vibration and Shock, 2023, 42(18): 190-198

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