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

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (18) : 190-198.

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

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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.

Key words

Ferromagnetic beam / Natural frequency / internal resonance / Finite element

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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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