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

被引：0
作者：
Cui X. [1 ]
Kong X. [1 ]
Hu Y. [2 ]
机构：
[1] College of Civil Engineering, Liaoning University of Technology, Jinzhou
[2] School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao
来源：
Zhendong yu Chongji/Journal of Vibration and Shock | 2023年 / 42卷 / 18期
关键词：
ferromagnetic beam; finite element; internal resonance; natural frequency;
D O I：
10.13465/j.cnki.jvs.2023.018.021
中图分类号：
学科分类号：
摘要：
The nonlinear two-way natural frequency and internal resonance of a ferromagnetic beam moving axially in a magnetic field were studied. The expressions of kinetic energy, potential energy, Lorentz force and magnetic force couple of the beam were given. The magnetoelastic two-way coupling nonlinear vibration equation of the axially moving ferromagnetic beam in the magnetic field was derived according to the Hamilton principle. The multi-scale method was used to solve the coupled equation, and the natural frequency of the bidirectional vibration was obtained. The internal resonance of the beam with the natural frequencies of the two vibration directions close to 1 : 1, was analysed, and the characteristic equations of mutual coupling were achieved. Through calculation examples, the curves of the natural frequency of the beam against the vibration time, magnetic induction intensity and axial velocity were presented and the time history response diagram of the energy exchange of resonance amplitude during the system' s internal resonance was obtained. On this basis, the first twelve vibration modes and corresponding natural frequencies of the beam were calculated by using ABAQUS finite element analysis software. The numerical simulation results are in good agreement with the theoretical values. © 2023 Chinese Vibration Engineering Society. All rights reserved.
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页码：190 / 198
页数：8
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