Dynamic behaviors of conductive circular plate in time-varying magnetic fields

Gao, Yuanwen; Xu, Bibo

doi:10.1016/s0894-9166(10)60008-0

Cited by 6 publications

(3 citation statements)

References 16 publications

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“…In single-mode and threemode cases, the relationship between amplitude and parameters was also obtained. Eshaghi et al [18,19] provided free vibration of circular plate in time-varying magnetic field, and analyzed the dynamic response and stability. Razavi et al [20,21] conducted nonlinear oscillation and buckling of electromagnetic elastic rectangular plates under simply supported boundary, obtained analytical solutions and numerical results of nonlinear frequency ratio.…”

Section: Introductionmentioning

confidence: 99%

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Magnetoelastic nonlinear free vibration of an annular plate under a nonuniform magnetic field of the long straight current‐carrying wire

Hao

2022

Z Angew Math Mech

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In this article, the magnetoelastic nonlinear free vibration of a thin conductive annular plate under the nonuniform toroidal magnetic field is investigated, where the magnetic field is generated by a long straight current-carrying wire.Based on electromagnetic theory, expressions of the nonuniform magnetic field, electromagnetic forces are deduced. The nonlinear free vibration equation of plate is derived by using the Hamilton principle. Considering different boundary conditions, the axisymmetric vibration differential equation is achieved by the Galerkin method. The method of multiple scales is employed to obtain the second-order approximate analytical solutions and natural frequency. In numerical calculation, the characteristics of nonlinear natural vibration and singular points varying with different parameters, for example, current intensity and plate size, are presented, respectively. The results indicate that, with the increase of current, natural frequency increases and then stabilizes in the inner-clamped and out-free (C-F) boundary, but decreases and stabilizes in the cases of the inner-clamped and out-clamped (C-C) boundary or inner-simply and out-simply (S-S) boundary. Moreover, when wire current is off, natural frequency maintains a constant, where the equilibrium solution of the system is a center. In addition, for all boundary conditions, natural frequency increases significantly with increase of internal radius and thickness, but decreases with the increase of outer radius.

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Section: Introductionmentioning

confidence: 99%

“…Eshaghi et al. [18, 19] provided free vibration of circular plate in time‐varying magnetic field, and analyzed the dynamic response and stability. Razavi et al.…”

Section: Introductionmentioning

confidence: 99%

Magnetoelastic nonlinear free vibration of an annular plate under a nonuniform magnetic field of the long straight current‐carrying wire

Hao

2022

Z Angew Math Mech

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“…Pratiher et al [5,6] investigated the parametric vibration and stability of cantilever beam in time-varying magnetic field. Based on the T-method, Gao and Xu [7] investigated the eddy currents and electromagnetic forces of conductive circular plate in timevarying magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Strongly Nonlinear Subharmonic Resonance and Chaotic Motion of Axially Moving Thin Plate in Magnetic Field

Jinzhi

2015

Journal of Computational and Nonlinear Dynamics

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In this paper, the nonlinear vibration and chaotic motion of the axially moving currentconducting thin plate under external harmonic force in magnetic field is studied. Improved multiple-scale method is employed to derive the strongly nonlinear subharmonic resonance bifurcation-response equation of the strip thin plate in transverse magnetic field. By using the singularity theory, the corresponding transition variety and bifurcation, which contain two parameters of the universal unfolding for this nonlinear system, are obtained. Numerical simulations are carried out to plot the bifurcation diagrams, corresponding maximum Lyapunov exponent diagrams, and dynamical response diagrams with respect to the bifurcation parameters such as magnetic induction intensity, axial tension, external load, external excited frequency, and axial speed. The influences of different bifurcation parameters on period motion, period times motion, and chaotic motion behaviors of subharmonic resonance system are analyzed. The results show that the complex dynamic behaviors of resonance system can be controlled by changing the corresponding parameters.

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Nonlinear free vibration analysis of the rectangular conductive elastic plate in magnetic field based on homotopy perturbation method

Gu,

Shi

2024

Z Angew Math Mech

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This article tries to investigate the nonlinear free vibrations of the rectangular conductive elastic plate in uniform magnetic fields under the classic plate theory considering nonlinear strain‐displacement. The formulation of the governing equations integrates the electromagnetic forces arising from the motion of the plate. The nonlinear motion equations are dimensionless, which takes the effect of in‐plane inertia into account. The equations are solved by the Galerkin method and homotopy perturbation method (HPM). The effectiveness of the solution is verified. According to the solutions by HPM, the effects of the initial conditions, length‐to‐thickness ratio, and magnetic induction intensity on the nonlinear free vibrations behavior of conductive elastic plates are discussed.

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Dynamic behaviors of conductive circular plate in time-varying magnetic fields

Cited by 6 publications

References 16 publications

Magnetoelastic nonlinear free vibration of an annular plate under a nonuniform magnetic field of the long straight current‐carrying wire

Magnetoelastic nonlinear free vibration of an annular plate under a nonuniform magnetic field of the long straight current‐carrying wire

Strongly Nonlinear Subharmonic Resonance and Chaotic Motion of Axially Moving Thin Plate in Magnetic Field

Nonlinear free vibration analysis of the rectangular conductive elastic plate in magnetic field based on homotopy perturbation method

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