Joint Resonance Analysis in Multiple Modes of Soft Ferromagnetic Rectangular Thin Plate

Authors

  • Xiaofang Kang School of Civil Engineering, Anhui Jianzhu University, Hefei, 230601, China
  • Xinzong Wang School of Civil Engineering, Anhui Jianzhu University, Hefei, 230601, China
  • Qingguan Lei School of Civil Engineering, Anhui Jianzhu University, Hefei, 230601, China
  • Zhengxing Zhu School of Civil Engineering, Anhui Jianzhu University, Hefei, 230601, China
  • Ziyi Sheng School of Civil Engineering, Anhui Jianzhu University, Hefei, 230601, China
  • Fuyi Zhang School of Civil Engineering, Anhui Jianzhu University, Hefei, 230601, China

DOI:

https://doi.org/10.13052/ejcm2642-2085.3311

Keywords:

Principal and internal resonance, soft ferromagnetic rectangular thin plate, Galerkin’s method, multiscale method

Abstract

In this article, the nonlinear principal and internal resonance properties of a soft ferromagnetic rectangular thin plate are investigated in a magnetic field environment. The nonlinear partial differential equation of motion of a soft ferromagnetic rectangular thin plate is derived under the effect of homogeneous simple harmonic excitation. The system of nonlinear differential equations with multiple degrees of freedom is established by the assumed one-sided fixed trilateral simply support condition using the Galerkin’s method. The system of nonlinear differential equations is solved by the multiscale method to obtain the response of two modes under the simple harmonic force at the principal and internal resonance. The numerical results of the system response show that when the frequency of the simple harmonic force is close to one of the modes (first-order or second-order mode) causing it to resonate, the other mode will also resonate internally. The magnetic field can have an inhibiting effect on the resonant response of the system and also affect the kinematic state of the system. The internal resonance provides a mechanism for transferring energy from a high mode to a lower mode.

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Author Biographies

Xiaofang Kang, School of Civil Engineering, Anhui Jianzhu University, Hefei, 230601, China

Xiaofang Kang received the B.S. degree in Engineering Management from Anhui Jianzhu University, Hefei, China, in 2009 and the M.S. degree in Engineering Mechanics from Hefei University of Technology, Hefei, China, in 2012. He received the Ph.D. degree in Structural Engineering from Hefei University of Technology, Hefei, China, in 2016. He research interests include Structural vibration control and energy harvesting.

Xinzong Wang, School of Civil Engineering, Anhui Jianzhu University, Hefei, 230601, China

Xinzong Wang received the B.S. degree in Civil Engineering from Wuxi Taihu University, Wuxi, China, in 2019. He is currently working toward the M.S. degree in Structural Engineering with the School of Civil Engineering, Anhui Jianzhu University, Hefei, China. He research interests include Structural vibration control and Nonlinear Vibration Analysis.

Qingguan Lei, School of Civil Engineering, Anhui Jianzhu University, Hefei, 230601, China

Qingguan Lei received the B.S. degree in Water Resources and Hydropower Engineering from Hefei University of Technology, Hefei, China, in 1985 and the M.S. degree in Structural Engineering from Hefei University of Technology, Hefei, China, in 1991. He research interests include Structural vibration control and energy harvesting.

Zhengxing Zhu, School of Civil Engineering, Anhui Jianzhu University, Hefei, 230601, China

Zhengxing Zhu received the B.S. degree in Civil Engineering from Suzhou University, Suzhou, China, in 2020. He is currently working toward the M.S. degree in Structural Engineering with the School of Civil Engineering, Anhui Jianzhu University, Hefei, China. The main research direction is engineering disaster prevention and reduction.

Ziyi Sheng, School of Civil Engineering, Anhui Jianzhu University, Hefei, 230601, China

Ziyi Sheng is currently working toward the B.S. degree in Civil Engineering with the School of Civil Engineering, Anhui Jianzhu University, Hefei, China. The main research direction is engineering disaster prevention and reduction.

Fuyi Zhang, School of Civil Engineering, Anhui Jianzhu University, Hefei, 230601, China

Fuyi Zhang is currently studying for a bachelor’s degree in civil engineering at the School of Civil Engineering, Anhui Jianzhu University, Hefei, China. He mainly studies structural reliability and use safety. The main research direction is engineering disaster prevention and reduction.

References

M. A. Abazid, “The Nonlocal Strain Gradient Theory for Hygrothermo-Electromagnetic Effects on Buckling, Vibration and Wave Propagation in Piezoelectromagnetic Nanoplates,” International Journal of Applied Mechanics, vol. 11, no. 7, pp. 31, 2019.

F. X. Duthoit, T. S. Hahm and L. Wang, “Electromagnetic nonlinear gyrokinetics with polarization drift,” Advanced Materials Research, vol. 21, no. 8, pp. 1–11, 2014.

T. Rabenimanana, V. Walter and M. Kacem, “Functionalization of electrostatic nonlinearities to overcome mode aliasing limitations in the sensitivity of mass microsensors based on energy localization,” Applied Physics Letters, vol. 117, no. 3, pp. 6, 2020.

T. C. Adorno, D. M. Gitman, A. E. Shabad and A. A. Shishmarev, “Quantum Electromagnetic Nonlinearity Affecting Charges and Dipole Moments,” Russian Physics Journal, vol. 59, no. 11, pp. 1775–1787, 2017.

R. Y. Li, H. Q. Zhang, H. Q. Gao, Z. Wu and C. X. Guo, “An improved extreme learning machine algorithm for transient electromagnetic nonlinear inversion,” Computers & Geosciences, vol. 156, pp. 104877, 2021.

V. Balasubramanian, A. Bernamonti, J. de Boer et al., “Inhomogeneous thermalization in strongly coupled field theories,” Physical Review B: Condensed Matter & Materials Physics, vol. 111, no. 23, pp. 231602, 2013.

L. Cheng, Y. Yang, F. L. Jiang and C. Li, “Experimental investigation and FEM analysis of laser cladding assisted by coupled field of electric and magnetic,” Materials Research Express, vol. 6, no. 1, pp. 016516, 2019.

Y. L. Lv, K. Guo, L. M. He, L. C. Shi and Y. Cao, “Effect of Frequency on Dehydration Efficiency under the Electromagnetic Coupling Field,” Journal of Chemical Engineering of Japan, vol. 53, no. 2, pp. 49–57, 2020.

S. A. Zhou, “Magnetoelastic theory of type-II superconductors in the mixed state,” Physical Review, vol. 50, no. 1, pp. 354–361, 1994.

O. Tsyplyatyev, P. Kopietz, Y. Tsui et al., “Many-body theory of magnetoelasticity in one dimension,” Physical Review B, vol. 95, no. 4, 2017.

Z. Yin, H. D. Gao and G. Lin, “An efficient semi-analytical static and free vibration analysis of laminated and sandwich beams based on linear elasticity theory,” The Journal of Strain Analysis for Engineering Design, vol. 57, no. 8, pp. 631–646, 2022.

S. B. Medvedev and V. N. Grebenev, “Hamiltonian structure and conservation laws of two-dimensional linear elasticity theory,” ZAMM - Journal of Applied Mathematics and Mechanics, vol. 96, no. 10, pp. 1175–1183, 2016.

S. I. Kruglov, “Dyonic and magnetized black holes based on nonlinear electrodynamics,” European Physical Journal C: Particles and Fields, vol. 80, no. 3, 2020.

B. K. Datta, “MagnetoElastic Wave Propagation in a Linear Viscoelastic Solid Medium,” Proceedings of Indian National Science Academy, vol. 52, no. 6A, 2015.

D. V. Rastyagaev, E. A. Palkin, D. S. Lukin, A. S. Kryukovsky and E. V. Ipatov, “Application of the Diffraction-Ray Theory to the Problems of Propagation of Electromagnetic Waves in the Ionospheric Plasma,” Radiophysics and Quantum Electronics, vol. 64, no. 8–9, pp. 533–544, 2022.

P. Bradley, “A dense voltage-mode Josephson memory cell insensitive to systematic variations in critical current density,” IEEE Transactions on Magnetics, vol. 21, no. 2, pp. 729–732, 1985.

V. V. Fadin, M. I. Aleutdinova and O. A. Kulikova, “Average contact temperature and morphological details of the worn surface of copper based materials under high current density sliding against steel,” AIP Conference Proceedings, vol. 1783, no. 1, pp. 020051, 2016.

W. P. Zhang, J. Y. Chen and X. J. Luo, “Effects of impressed current density on corrosion induced cracking of concrete cover,” Construction and Building Materials, vol. 204, pp. 213–223, 2019.

M. Malikan, V. A. Eremeyev, “Flexomagnetic response of buckled piezomagnetic composite nanoplates,” Compos. Struct, vol. 267, pp. 113932, 2021.

M. Malikan, V. A. Eremeyev, “On dynamic modeling of piezomagnetic flexoma-gnetic microstructures based on Lord–Shulman thermoelastic model,” Arch Appl Mech, vol. 93, pp. 181–196, 2023.

M. Malikan, V. A. Eremeyev, “On a flexomagnetic behavior of composite structures,” Int J Eng Sci, vol. 175, pp. 103671, 2022.

M. Malikan, V. A. Eremeyev, “Flexomagneticity in buckled shear deformable hard-magnetic soft structures,” Contin. Mech. Thermodyn, pp. 1–16, 2021.

H. Altenbach, O. Morachkovsky, K. Naumenko and D. Lavinsky, “Inelastic deformation of conductive bodies in electromagnetic fields,” Continuum Mechanics and Thermodynam, vol. 28, no. 5, pp. 1421–1433, 2016.

S. O. Gladkov, “Theory of Electromagnetic Radiation by Inertially Moving Conductive Bodies,” Journal of Communications Technology and Electronics, vol. 66, no. 6, pp. 690–693, 2021.

T. J. Yin, X. J. Jiang and W. Qin, “A magnetic field-directed self-assembly solid contact for construction of an all-solid-state polymeric membrane Ca2+

-selective electrode,” Analytica Chimica Acta, vol. 56, no. 989, pp. 15–20, 2017.

M. Martinez-Santiesteban Francisco, D. Swanson Scott, C. Noll Douglas and J. Anderson David, “Magnetic field perturbation of neural recording and stimulating microelectrodes,” Physics in Medicine & Biology, vol. 52, no. 8, pp. 2073–2088, 2007.

Y. Kim and X. H. Zhao, “Magnetic Soft Materials and Robots,” Chemical Reviews, vol. 122, no. 5, pp. 5317–5364, 2022.

W. J. Yang, J. J. Liu, X. F. Yu et al., “The Preparation of High Saturation Magnetization and Low Coercivity Feco Soft Magnetic Thin Films via Controlling the Thickness and Deposition Temperature,” Materials, vol. 15, no. 20, pp. 7191–7191, 2022.

J. W. Zheng, D. N. Zheng, L. Qiao et al., “High permeability and low core loss Fe-based soft magnetic composites with Co-Ba composite ferrite insulation layer obtained by sol-gel method,” Journal of Alloys and Compounds, vol. 893, 2022.

Anil K. Bastola and Mokarram Hossain, “The shape – morphing performance of magnetoactive soft materials,” Materials & Design, vol. 893, pp. 110172, 2021.

K. Niitsu, “Temperature dependence of magnetic exchange stiffness in iron and nickel,” Journal of Physics D: Applied Physics, vol. 53, no. 39, 2020.

K. G. Suresh, R. Srinivasan, G. Karunakaran et al., “Microwave-assisted combustion synthesis of soft ferromagnetic spinel MFe2

O4 (M =

Ni, Mg, Zn) nanoparticles using Citrus limon fruit extract as a fuel,” Applied Physics A, vol. 127, no. 7, 2021.

E. Sobhani and M. Avcar, “Natural frequency analysis of imperfect GNPRN conical shell, cylindrical shell, and annular plate structures resting on Winkler-Pasternak Foundations under arbitrary boundary conditions,” Eng Anal Bound Elem, vol. 144, pp. 145–164, 2022.

L. Hadji and M. Avcar, “Free Vibration Analysis of FG Porous Sandwich Plates under V-arious Boundary Conditions,” J. Appl. Comput. Mech, vol. 7, no. 2, pp. 505–519, 2021.

O. Civalek and M. Avcar, “Free vibration and buckling analyses of CNT reinforced laminated non-rectangular plates by discrete singular convolution method,” Engineering with Computers, vol. 38, pp. 489–521, 2022.

P. Van Vinh, M. Avcar, M. O. Belarbi et al., “A new higher-order mixed four-node quadrilateral finite element for static bending analysis of functionally graded plates,” Structures, vol. 47, pp. 1595–1612, 2023.

A. Daikh, M. Belarbi, D. Ahmed et al., “Static analysis of functionally graded plate structures resting on variable elastic foundation under various boundary conditions,” Acta Mech, vol. 234, pp. 775–806, 2023.

V. A. Krysko, A. Awrejcewicz and I. V. Papkova, “Chaotic vibrations of size-dependent flexible rectangular plates,” Chaos, vol. 31, no. 4, pp. 043119–043119, 2021.

P. Li, Z. X. Wang, D. C. Zhang and Y. R. Yang, “On bifurcations and chaos of a forced rectangular plate with large deflection loaded by subsonic airflow,” Thin-Walled Structures, vol. 161, 2021.

K. L. Wang and C. F. Wei, “New Analytical Approach for Nonlinear Fractal K(p,q) Model,” Fractals: Complex Geometry, Patterns, and Scaling in Nature and Society, vol. 29, no. 5, 2021.

L. Ma, M. H. Yao, W. Zhang and D. X. Cao, “Bifurcation and dynamic behavior analysis of a rotating cantilever plate in subsonic airflow,” Applied Mathematics and Mechanics (English Edition), vol. 41, pp. 1–20, 2020.

J. J. Qing, S. S. Zhou, J. M. Wu and M. Y. Shao, “Primary and secondary resonance responses of fractional viscoelastic PET membranes,” Communications in Nonlinear Science and Numerical Simulation, vol. 116, 2023.

C. X. Xue, E. Pan, Q. K. Han, S. Y. Zhang and H. J. Chu, “Non-linear principal resonance of an orthotropic and magnetoelastic rectangular plate,” International Journal of Non-Linear Mechanics, vol. 46, no. 5, pp. 703–710, 2011.

Z. Y. Cao and Y. H. Pao, “Vibration theory of plates and shells,” Beijing: China Railway Publishing House, 1983.

J. Wang and R. X. Wu, “The Extended Galerkin Method for Approximate Solutions of Nonlinear Vibration Equations,” Applied sciences, vol. 12, no. 6, pp. 2979, 2022.

A. H. Nayfeh and S. A. Emam, “Non-linear response of buckled beams to 1:1 and 3:1 internal resonances,” Int. J. Nonlin. Mech, vol. 52, pp. 12–25, 2013.

J. Li and Y. D. Hu, “Principal and internal resonance of rectangular conductive thin plate in transverse magnetic field,” Theoretical & Applied Mechanics Letters, vol. 8, no. 4, pp. 257–266, 2018.

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Published

2024-03-27

How to Cite

Kang, X., Wang, X., Lei, Q., Zhu, Z., Sheng, Z., & Zhang, F. (2024). Joint Resonance Analysis in Multiple Modes of Soft Ferromagnetic Rectangular Thin Plate. European Journal of Computational Mechanics, 33(01), 1–30. https://doi.org/10.13052/ejcm2642-2085.3311

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Original Article