Study on primary resonance and bifurcation of a conductive circular plate rotating in air-magnetic fields

Hu, Yuda; Li, W. Q.

doi:10.1007/s11071-018-4217-y

Cited by 15 publications

(4 citation statements)

References 24 publications

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“…Then according to the Hamiltonian principle, based on research about magnetoelastic vibration of circular plate structure in Refs. [16,17], considering the excited non-uniform magnetic field, after organizing and arranging, the transverse magnetoelastic nonlinear axisymmetric equation about deflection 𝑤 is obtained as:…”

Section: Magnetoelastic Vibration Equation Of Annular Plate In Toroid...mentioning

confidence: 99%

“…Then according to the Hamiltonian principle, based on research about magnetoelastic vibration of circular plate structure in Refs. [16, 17], considering the excited non‐uniform magnetic field, after organizing and arranging, the transverse magnetoelastic nonlinear axisymmetric equation about deflection w is obtained as:

\begin{matrix} D_{M} (\frac{\partial^{4} w}{\partial r^{4}} + \frac{2}{r} \frac{\partial^{3} w}{\partial r^{3}} - \frac{1}{r^{2}} \frac{\partial^{2} w}{\partial r^{2}} + \frac{1}{r^{3}} \frac{\partial w}{\partial r}) - D_{N} [\frac{1}{2 r} {((), \frac{\partial w}{\partial r})}^{3} + \frac{3}{2} {((), \frac{\partial w}{\partial r})}^{2} \frac{\partial^{2} w}{\partial r^{2}}] + σ_{0} h {((), \frac{μ_{0} I}{2 π r})}^{2} \cdot \frac{\partial w}{\partial t} \\ - \frac{σ_{0} h^{3}}{12} {((), \frac{μ_{0} I}{2 π r})}^{2} \cdot [\frac{\partial^{3} w}{\partial r^{2} \partial t} - \frac{1}{r} \frac{\partial^{2} w}{\partial r \partial t}] + ρ h \frac{{normald}^{2} w}{d t^{2}} - \frac{ρ h^{3}}{12} [\frac{1}{r} \frac{d^{2}}{d t^{2}} (\frac{\partial w}{\partial r}) + \frac{d^{2}}{d t^{2}} (\frac{\partial^{2} w}{\partial r^{2...}})] \end{matrix}

…”

Section: Magnetoelastic Vibration Equation Of Annular Plate In Toroid...mentioning

confidence: 99%

“…For soft ferromagnetic circular plates with clamped support condition in transverse magnetic field, the buckling problem is reported by Jabbari et al [15], who noted that transverse shear stress can be ignored, thereby simplifying the problem and obtaining better results. For magneto-aeroelastic forced oscillation, Hu et al [16,17] modeled circular plate rotating in air-magnetic fields, which studies bifurcation, chaotic motion and modal interaction. Through bifurcation diagram, maximum Lyapunov exponent and system response, the dynamic behavior of system under different parameters was studied.…”

Section: Introductionmentioning

confidence: 99%

“…For magneto‐aeroelastic forced oscillation, Hu et al. [16, 17] modeled circular plate rotating in air–magnetic fields, which studies bifurcation, chaotic motion and modal interaction. Through bifurcation diagram, maximum Lyapunov exponent and system response, the dynamic behavior of system under different parameters was studied.…”

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: Magnetoelastic Vibration Equation Of Annular Plate In Toroid...mentioning

confidence: 99%

\begin{matrix} D_{M} (\frac{\partial^{4} w}{\partial r^{4}} + \frac{2}{r} \frac{\partial^{3} w}{\partial r^{3}} - \frac{1}{r^{2}} \frac{\partial^{2} w}{\partial r^{2}} + \frac{1}{r^{3}} \frac{\partial w}{\partial r}) - D_{N} [\frac{1}{2 r} {((), \frac{\partial w}{\partial r})}^{3} + \frac{3}{2} {((), \frac{\partial w}{\partial r})}^{2} \frac{\partial^{2} w}{\partial r^{2}}] + σ_{0} h {((), \frac{μ_{0} I}{2 π r})}^{2} \cdot \frac{\partial w}{\partial t} \\ - \frac{σ_{0} h^{3}}{12} {((), \frac{μ_{0} I}{2 π r})}^{2} \cdot [\frac{\partial^{3} w}{\partial r^{2} \partial t} - \frac{1}{r} \frac{\partial^{2} w}{\partial r \partial t}] + ρ h \frac{{normald}^{2} w}{d t^{2}} - \frac{ρ h^{3}}{12} [\frac{1}{r} \frac{d^{2}}{d t^{2}} (\frac{\partial w}{\partial r}) + \frac{d^{2}}{d t^{2}} (\frac{\partial^{2} w}{\partial r^{2...}})] \end{matrix}

…”

Section: Magnetoelastic Vibration Equation Of Annular Plate In Toroid...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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Axisymmetric Nonlinear Free Vibration of a Conductive Annular Plate Under Toroidal Magnetic Field

2022

NODYCON Conference Proceedings Series

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Magnetoelastic combined resonance and stability analysis of a ferromagnetic circular plate in alternating magnetic field

2019

Appl. Math. Mech.-Engl. Ed.

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Study on primary resonance and bifurcation of a conductive circular plate rotating in air-magnetic fields

Cited by 15 publications

References 24 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

Axisymmetric Nonlinear Free Vibration of a Conductive Annular Plate Under Toroidal Magnetic Field

Magnetoelastic combined resonance and stability analysis of a ferromagnetic circular plate in alternating magnetic field

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