Principal-internal joint resonance of an axially moving conductive beam between parallel conductors

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Journal of Vibration and Shock ›› 2022, Vol. 41 ›› Issue (3) : 287-298.

LI Xiaojing1,2, HU Yuda1,2

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Abstract

The principle-internal resonance of an axially moving conductive beam in the magnetic field induced by parallel wires is investigated. Based on the theory of electromagnetic field and Hamilton principle, the nonlinear vibration equation of the beam under external excitation and magnetic field is derived. For a conductive beam with one side clamped and the other side hinged, the approximate analytical solution and the amplitude frequency response equations for the nonlinear equation are derived by the multiple-scale method, and the stability of the steady-state solutions are also analyzed. Through numerical examples, the corresponding amplitude curves of the first two order vibration modes varying with different frequency tuning parameters, external excitation force, axial velocity and current intensity are obtained. The results show that the first and the second-order response are both excited, and different multi-solution regions are found. The number of steady-state solutions of the first and second-order amplitudes changes simultaneously in the multi-solution regions, and the number depends on the external excitation force, moving velocity and current intensity value.

Key words

magneto-elastic / conductive beam / axially moving / principal- internal resonance / multiple-scale method / Galerkin method

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LI Xiaojing1,2, HU Yuda1,2. Principal-internal joint resonance of an axially moving conductive beam between parallel conductors[J]. Journal of Vibration and Shock, 2022, 41(3): 287-298

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