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Magnetic-structure coupling dynamic model of a ferromagnetic plate parallel moving in air-gap magnetic field

气隙磁场作用**行运动铁磁板磁固耦合动力学模型

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Abstract

Aiming at the air-gap magnetic field excited by wall armatures, Laplace’s partial differential equation of air-gap magnetic potential is achieved by means of the electromagnetic field theory. According to the magnetic boundary conditions and the method of separation of variables, the magnetic potential of the air-gap magnetic field is obtained. Based on the magnetization force model and Lorentz force of ferromagnetic thin-walled structures, and introducing the electromagnetic constitutive relations and boundary conditions, the calculation model of electromagnetic force of the soft ferromagnetic thin plate moving in air-gap magnetic field is established. Considering geometric nonlinearity, expressions of strain energy and kinetic energy of the elastic thin plate and the work of forces are given, respectively. The magnetic-structure coupling nonlinear vibration equations of ferromagnetic thin plate parallel moving in the air-gap magnetic field excited by armatures are obtained by using the Hamilton principle, which can be of the characterization of the system dynamics model with electro-magneto-velocity-mechanical interaction. Through numerical examples, primary resonance characteristics of the strip thin plate under the action of air-gap magnetic force are obtained. The results show that the two stable amplitude values will increase as amplitude of magnetic potential increases and thickness of air-gap decreases, and the amplitude’s multi-valued region will change due to the varieties of magnetic potential, air-gap and velocity. The model established in this paper is a theoretical reference for investigation on the multi-field coupling dynamic behaviors of structures moving in complex electromagnetic fields.

摘要

针对壁面电枢激发气隙磁场问题, 基于电磁场理论给出气隙域磁势满足的拉普拉斯偏微分方程; 根据磁边界条件并应用分 离变量法求解二维拉普拉斯方程, 得到气隙域磁势通解. 基于铁磁薄壁体的磁化力模型和洛伦兹力表述式, 考虑电磁本构关系和边 界条件, 建立气隙磁场中面内运动软铁磁薄板的电磁力计算模型. 考虑几何非线性条件, 给出弹性薄板的应变能、动能和力所做功 的表达式. 根据哈密顿变分原理, 建立电枢激发气隙磁场环境中**行运动铁磁性薄板的磁固耦合非线性振动方程组, 得出描述系统 力、电、磁、速度等多参量相互耦合的动力学理论模型. 通过算例, 得出气隙磁力作用下条形薄板的主共振特征规律, 结果表明: 磁势幅值的增大和气隙厚度的减小都会使两个稳定振幅值增大, 磁势、气隙和速度量的改变均会使振幅的多解区域范围发生变化. 所建模型可为研究复杂电磁场环境中运动结构的多场耦合动力学行为提供理论参考.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12172321 and 11472239) and the Hebei Provincial Natural Science Foundation of China (Grant No. A2020203007).

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Authors and Affiliations

  1. School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao, 066004, China

    Yuda Hu  (胡宇达), Tianxiao Cao  (曹天笑) & Mengxue **e  (解梦雪)

  2. Hebei Key Laboratory of Mechanical Reliability for Heavy Equipment and Large Structures, Yanshan University, Qinhuangdao, 066004, China

    Yuda Hu  (胡宇达), Tianxiao Cao  (曹天笑) & Mengxue **e  (解梦雪)

Authors
  1. Yuda Hu  (胡宇达)
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  2. Tianxiao Cao  (曹天笑)
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  3. Mengxue **e  (解梦雪)
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Corresponding author

Correspondence to Yuda Hu  (胡宇达).

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Author contributions

Yuda Hu performed conceptualization, methodology, and investigation. Tianxiao Cao designed computer programs and contributed to visualization. Mengxue **e wrote the manuscript.

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Hu, Y., Cao, T. & **e, M. Magnetic-structure coupling dynamic model of a ferromagnetic plate parallel moving in air-gap magnetic field. Acta Mech. Sin. 38, 522084 (2022). https://doi.org/10.1007/s10409-022-22084-x

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