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| Principal resonance characteristics and static load effect of a ferromagnetic circular plate in a transverse constant magnetic field |
| MA Bingbing 1,2 HU Yuda 1,2 |
1. School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao Hebei 066004, China
2. Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures of Hebei Province, Yanshan University, Qinhuangdao Hebei 066004, China |
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Abstract The principal resonance of a ferromagnetic circular plate in transverse constant magnetic field was studied. Based on the theory of electromagnetism, the magnet force and Lorentz force acting on a circular plate in a constant magnetic field were obtained.Applying Hamiltonian variational principle, the differential equation of magnetoelastic transverse vibration of ferromagnetic circular plate in magnetic field was derived.The magnet force acting on a ferromagnetic circular plate in a constant magnetic field is a static load. The initial deflection of a ferromagnetic circular plate under static load and clamped boundary was obtained by Galerkin method. The first and second order approximate solutions of the nonlinear equations under periodic loads were obtained by multiscale method, and the amplitude-frequency response equations of the principal resonance were obtained. Through numerical examples, the amplitude-frequency curves, the curves of amplitude varying with magnetic field intensity and excitation force were obtained. The effects of plate thickness, magnetic field intensity and excitation force on resonance amplitude were analyzed, and the differences between two approximations were compared.The results show that the amplitude increases significantly in the resonance region, and the first-order approximation is similar to the second-order approximation when the magnetic field intensity is low, while the second-order approximation is more accurate when the magnetic field intensity is high.
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Received: 15 January 2019
Published: 15 January 2021
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