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

Xu, Hang; Hu, Yuda; Hao, Ying

doi:10.1002/zamm.202000299

Cited by 3 publications

(2 citation statements)

References 22 publications

(47 reference statements)

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“…The account of nonlinearity in magnetoelasticity usually is limited by the nonlinearity of the interaction between the elastic medium and the electromagnetic field [18,19] and the nonlinearity associated with thermal stresses [20].…”

Section: Introductionmentioning

confidence: 99%

Spatially localized nonlinear magnetoelastic waves in an electrically conductive micropolar medium

Ерофеев

Malkhanov

2023

Z Angew Math Mech

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A nonlinear model of an electrically conductive micropolar medium interacting with an external magnetic field is proposed. The deformable state of such a medium is described by two asymmetric tensors: tensor of deformations and bending‐torsion tensor. Both tensors consider both linear and nonlinear terms in rotation and displacement gradients (geometric nonlinearity). The components of the bending‐torsion tensor which have the same indices, describe torsional deformations, while the rest describe bending deformations. The stress state of the medium is described by two asymmetric tensors: stresses tensor and moment stresses tensor. It is assumed, as is customary in magnetoelasticity, that the action of an electromagnetic field on a strain field occurs through Lorentz forces. From the system of Maxwell's equations follow the equations for electric and magnetic induction, which together with electromagnetic equations of state, should be added to the group of equations which describe the dynamics of a micropolar medium. In the frames of the proposed model, a one‐dimensional nonlinear magnetoelastic shear‐rotation wave is considered. In the equations of dynamics, a nonlinear term is considered. This term makes the most significant contribution to wave processes. It is shown that two factors will influence the wave propagation: dispersion and nonlinearity. Nonlinearity leads to the emergence of new harmonics in the wave, which contributes to the appearance of sharp drops in the moving wave profile. Dispersion, on the contrary, smoothed out differences due to differences in phase velocities of harmonic component waves. The combined action of these factors can lead to the formation of stationary waves that propagate at a constant speed without changing shape. Only those cases where a constant component is absent in the deformation wave are physically realizable. Stationary waves can be either periodic or aperiodic. The latter are spatially localized waves—solitons. It is shown that the behavior of “subsonic” and “supersonic” solitons will be qualitatively different.

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Section: Introductionmentioning

confidence: 99%

Spatially localized nonlinear magnetoelastic waves in an electrically conductive micropolar medium

Ерофеев

Malkhanov

2023

Z Angew Math Mech

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“…They nally obtained an analytical secondapproximation solution using multiple scales followed by the expressions for the rst three nondimensional natural frequencies of the plate. Xu et al [21] studied the magnetoelastic nonlinear free vibration of thin conductive annular plates under a nonuniform magnetic eld generated by a long wire carrying current. Their results indicated that with an increase in the current, the natural frequency would be notably enhanced and then stabilized in the inner-clamped and out-clamped boundaries; however, it would be reduced and stabilized in the inner-simple and out-simple boundaries.…”

Section: Introductionmentioning

confidence: 99%

Effect of magnetic field of conductor with current on vibrations of magneto-elastic plate Structures

et al. 2023

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The main objective of this study is to investigate the vibration behavior of soft magnetoelastic plates mounted close to the rectangular conductors conducting current that can be e ciently applicable in structures. New relationships are derived for electromagnetic interaction forces with magnetoelastic plates using the general form of Maxwell's equations and Lorentz forces. Based on von-K am an strain-displacement relations and Hamilton's principle, nonlinear di erential equations are further derived for the plate through classical rst-order shear deformation theory. This research numerically investigates how di erent parameters a ect the resonance features of these plates by discretizing the nonlinear equations based on Galerkin method. The obtained results demonstrate that the intensity of the magnetic eld and electric current profoundly a ects the vibration behavior of the plates. Through these e ects, loss of energy will happen in the plate which in turn results in a decrease in the oscillation amplitude over time.

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

Cited by 3 publications

References 22 publications

Spatially localized nonlinear magnetoelastic waves in an electrically conductive micropolar medium

Spatially localized nonlinear magnetoelastic waves in an electrically conductive micropolar medium

Effect of magnetic field of conductor with current on vibrations of magneto-elastic plate Structures

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

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