Effect of the magnetic field of a current-carrying conductor on the vibrations of magnetoelastic plate structures

Document Type : Article


1 Department of Mechanical Engineering, Islamic Azad University, Karaj Branch, Karaj, Iran

2 Department of Mechanical Engineering, Islamic Azad University, Shabestar Branch, Shabestar, Iran

3 Department of Vehicle Engineering, Technology and Engineering Research Center, Standard Research Institute, Iran


The aim of this study was to investigate the vibration behavior of soft magnetoelastic plates mounted close to rectangular conductors conducting current. New relationships are derived for electromagnetic interaction forces with magnetoelastic plates by taking into consideration the general form of Maxwell's equations and Lorentz forces. By using von-Kámán strain-displacement relations and Hamilton's principle, we derive the nonlinear differential equations for the plate based on classical first-order shear deformation theory. It is investigated numerically how different parameters affect the resonance features of these plates by discretizing the nonlinear equations using the Galerkin method. It has been demonstrated that the intensity of the magnetic field and electric current has a profound effect on the vibration behavior of the plates. Through these effects, energy is lost in the plate, which, as a result, results in a decrease in oscillation amplitude over time.


1. She, S., Chen, Y., He, Y., et al. "Optimal design of bremote field eddy current testing probe for ferromagnetic pipeline inspection", Measurement, 168, pp. 33- 45 (2021).
2. Yuan, F., Yu, Y., Wang, W., et al. "Pulsed eddy current array design and electromagnetic imaging for defects detection in metallic materials", Nondestructive Testing and Evaluation, 56, pp. 1-19 (2021).
3. Kassanos, P., Rosa, B.G., Keshavarz, M., et al. "From wearables to implantables-clinical drive and technical challenges", Wearable Sensors, 8, pp. 29-84 (2021).
4. Madina, B. and Gumilyov, L.N. "Determination of the most effective location of environmental hardenings in concrete cooling tower under far-source seismic using linear spectral dynamic analysis results", Journal of Research in Science, Engineering and Technology, 29(1), pp. 22-24 (2020).
5. Assadi, A., Najaf, H., and Nazemizadeh, M. "Sizedependent vibration of single-crystalline rectangular nanoplates with cubic anisotropy considering surface stress and nonlocal elasticity effects", Thin-Walled Structures, 170, 108518 (2022).
6. Liang, X., Dong, C., Chen, H., et al. "A review of thin-film magnetoelastic materials for magnetoelectric applications", Sensors, 20(5), 1532 (2020).
7. Minaev, A.J. and Korovkin, J.V. "Vibration studies of a magnetoelastic material", in IOP Conference Series: Materials Science and Engineering. IOP Publishing, 91 (2020).
8. Ren, L., Yu, K., and Tan, Y. "Applications and advances of magnetoelastic sensors in biomedical engineering: A review", Materials, 12(7), 1135 (2019).
9. Xu, X., Han, Q., and Chu, F. "Nonlinear vibration of a rotating cantilever beam in a surrounding magnetic field", International Journal of Non-Linear Mechanics, 95, pp. 59-72 (2017).
10. Youhe, Z. and Xiaojing, Z. "A theoretical model of magnetoelastic bucking for soft ferromagnetic thin plates", Acta Mechanica Sinica, 12(3), pp. 213-224 (1996).
11. Wu, B. and Destrade, M. "Wrinkling of soft magnetoactive plates", International Journal of Solids and Structures, 208, pp. 13-30 (2021).
12. Molaei, S., Ghorbani, N., Dashtiahangar, F., et al. "FDCNet: Presentation of the fuzzy CNN and fractal feature extraction for detection and classification of tumors", Computational Intelligence and Neuroscience, 2022, 7543429 (2022). 
13. Karami, S. and Saeedi Dehaghani, A. "Sensitivity analysis of electromagnetic stimulation of oil wells using simulation technique and Box-Behnken design", Scientia Iranica, 29(3), pp. 1377-1390 (2022).
14. Hasanyan, D.J., Librescu, L., and Ambur, D.R. "Buckling and postbuckling of magnetoelastic  at plates carrying an electric current", International Journal of Solids and Structures, 43(16), pp. 4971-4996 (2006).
15. Xue, C., Pan, E., Han, Q., et al. "Non-linear principal resonance of an orthotropic and magnetoelastic rectangular plate", International Journal of Non-Linear Mechanics, 46(5), pp. 703-710 (2011).
16. Zheng, X., Zhang, J., and Zhou, Y. "Dynamic stability of a cantilever conductive plate in transverse impulsive magnetic field", International Journal of Solids and Structures, 42(8), pp. 2417-2430 (2005).
17. Li, J. "Magneto-elastic combination resonances analysis of current-conducting thin plate", Applied Mathematics and Mechanics, 29(8), pp. 1053-1066 (2008).
18. Hu, Y., Cao, T., and Xie, M. "Magnetic-structure coupling dynamic model of a ferromagnetic plate parallel moving in air-gap magnetic field", Acta Mechanica Sinica, 38(10), pp. 1-11 (2022).
19. Murodillayevich, N.F., Sharibayevich, A.B., and Artikbayevich, A.M. "Mathematical model and computational algorithm of vibration processes of thin magnetoelastic plates with complex form", International Conference on Information Science and Communications Technologies (ICISCT). IEEE (2021).
20. Hu, Y. and Xu, H. "Nonaxisymmetric magnetoelastic coupling natural vibration analysis of annular plates in an induced nonuniform magnetic field", Nonlinear Dynamics, 7, pp. 1-31 (2022).
21. Xu, H., Hu, Y., and Hao, Y. "Magnetoelastic nonlinear free vibration of an annular plate under a nonuniform magnetic field of the long straight current-carrying wire. ZAMM", Journal of Applied Mathematics and Mechanics, 102(6), 202000299 (2022).
22. Vlasov, V.S., Kirushev, M.S., Shavrov, V.G., et al. "Forced nonlinear precession of the second-order magnetization in a magnetoelastic material", Journal of Communications Technology and Electronics, 64(1), pp. 41-51 (2019).
23. Pourreza, T., Alijani, A., Maleki, V.A., et al. "The effect of magnetic field on buckling and nonlinear vibrations of Graphene nanosheets based on nonlocal elasticity theory", International Journal of Nano Dimension, 13(1), pp. 54-70 (2022).
24. Wang, Y.S. and Shih, Y.S. "Analysis of the vibration of a cracked ferromagnetic rectangular plate in a transverse magnetic field", Journal of Vibration and Control, 7, 10775463221081181 (2022).
25. Li, J., Hu, Y., and Wang, Y. "The magneto-elastic internal resonances of rectangular conductive thin plate with different size ratios", Journal of Mechanics, 34(5), pp. 711-723 (2018).
26. Kedzia, P., Magnucki, K., Smyczynski, M., et al. "An influence of homogeneity of magnetic field on stability of a rectangular plate", International Journal of Structural Stability and Dynamics, 19(05), pp. 34- 56 (2019).
27. Zhang, C., Wang, L., Eyvazian, A., et al. "Analytical solution for static and dynamic analysis of FGP cylinders integrated with FG-GPLs patches exposed to longitudinal magnetic field", Engineering with Computers, 56, pp. 1-19 (2021).
28. Hosseinian, A. and Firouz-Abadi, R. "Vibrations and stability analysis of double current-carrying strips interacting with magnetic field", Acta Mechanica, 232(1), pp. 229-245 (2021).
29. Firouz-Abadi, R.D. and Hosseinian, A.R. "Resonance frequencies and stability of a current-carrying suspended nanobeam in a longitudinal magnetic field", Theoretical and Applied Mechanics Letters, 2(3), 031012 (2012).
30. Pourreza, T., Alijani, A., Maleki, V.A., et al. "Nonlinear vibration of nanosheets subjected to electromagnetic fields and electrical current", Advances in Nano Research, 10(5), pp. 481-491 (2021).
31. Kletsel, M., Barukin, A., and Talipov, O. "About the biot-savart-laplace law and its use for calculations in high-voltage AC installations", Electrotechnical Inspection, 93(11), pp. 129-132 (2017).
32. Ghaderloo, R.A., Sirat, A.P., and Shoulaie, A., A High Frequency Active Clamp Forward Converter with Coreless Transformer, arXiv preprint arXiv:2307, 12804 (2023). https://doi.org/10.48550/arXiv.2307.12804.
33. Assadi, A. and Najaf, H. "Nonlinear static bending of single-crystalline circular nanoplates with cubic material anisotropy", Archive of Applied Mechanics, 90(4), pp. 847-868 (2020).
34. Tahmasebi, E., Ashrafi Khorasani, N., and Imam, A. "Nonlinear vibration behavior of a carry current ferromagnetic beam plate under magnetic fields and thermal loads", Journal of Vibration and Control, 26(15-16), pp. 1276-1285 (2020).
35. Alim A., Ngakan K., Naresh B., et al. "Multi project scheduling and material planning using lagrangian relaxation algorithm", Industrial Engineering & ManagementSystems, 20(4), pp. 580-587 (2021). 
36. Hu, Y.-D. and Xu, H.-R. "Nonlinear natural vibration of a circular plate in the non-uniform induced magnetic field", Archive of Applied Mechanics, 91(6), pp. 2513- 2533 (2021).