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Simultaneous resonance of an axially moving ferromagnetic thin plate under a line load in a time-varying magnetic field

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Abstract

In this paper, the simultaneous resonance of a ferromagnetic thin plate in a time-varying magnetic field, having axial speed and being subjected to a periodic line load, is studied. Based on the large deflection theory of thin plates and electromagnetic field theory, the nonlinear vibration differential equation of the plate is obtained by using the Hamilton’s principle and the Galerkin method. Then the boundary condition in which the longer opposite sides are clamped and hinged is considered. The dimensionless nonlinear differential equations are solved by using the method of multiple scales, and the analytical solution is given. In addition, the stability analysis is also carried out by using Lyapunov stability theory. Through numerical analysis, the variation curves of system resonance amplitude with frequency tuning parameter, magnetic field strength and external excitation amplitude are obtained. Different parameters that have significant effects on the response of the system, such as the thickness, the axial velocity, the magnetic field intensity, the position, and the frequency of external excitation, are considered and analyzed. The results show that the system has multiple solution regions and obvious nonlinear coupled characteristics.

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Acknowledgement

This work was supported by the National Natural Science Foundation of China (Nos. 12172321 and 11472239), the Hebei Provincial Natural Science Foundation of China (Grant No. A2020203007), and the Hebei Provincial Graduate Innovation Foundation of China (Grant No. CXZZBS2022146).

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Authors and Affiliations

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

    Mengxue Xie, Yuda Hu & Haoran Xu

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

    Mengxue Xie, Yuda Hu & Haoran Xu

Authors
  1. Mengxue Xie
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  2. Yuda Hu
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  3. Haoran Xu
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Corresponding author

Correspondence to Yuda Hu.

Additional information

Supported by: National Natural Science Foundation of China under Grant Nos. 12172321 and 11472239, Hebei Provincial Natural Science Foundation of China under Grant No. A2020203007, and Hebei Provincial Graduate Innovation Foundation of China under Grant No. CXZZBS2022146

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Xie, M., Hu, Y. & Xu, H. Simultaneous resonance of an axially moving ferromagnetic thin plate under a line load in a time-varying magnetic field. Earthq. Eng. Eng. Vib. 22, 951–963 (2023). https://doi.org/10.1007/s11803-023-2215-7

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  • DOI: https://doi.org/10.1007/s11803-023-2215-7

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