Principal and internal resonance of rectangular conductive thin plate in transverse magnetic field

Li, Jing; Hu, Yuda

doi:10.1016/j.taml.2018.04.004

Cited by 3 publications

(1 citation statement)

References 18 publications

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“…and the need to achieve 1:3 internal resonance requires that the value of ω 1 /ω 2 is close to 1/3. Taking b/a = 2, the condition can be satisfied [47]. The object of this study is a rectangular thin plate, whose material is soft ferromagnetic.…”

Section: Example Analysismentioning

confidence: 99%

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

Kang,

Wang,

Lei

et al. 2024

TECM

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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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Section: Example Analysismentioning

confidence: 99%