Parametric and primary resonance of an axially moving conductive beam between current-carrying wires

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Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (14) : 1-10.

HU Yuda1,2,ZHANG Mingran1,2

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Abstract

The parametric and primary resonance of an axially moving conductive beam in the magnetic field induced by current-carrying wires was investigated.Based on the magnetic inductive intensity between current-carrying wires, the strain energy and kinetic energy of the beam, the expressions of the electromagnetic force loading on the current-carrying beam, and the magneto-elastic transverse vibration differential equation of the axially moving conductive beam were derived.The non-dimensional nonlinear parametric and primary resonance differential equation of the axially moving beam was obtained by means of Galerkin method.The approximate analytical solution of the nonlinear parametric and primary resonance differential equation was derived by the multiple-scale method.Through calculation, the corresponding amplitude frequency response curves with different frequency parameters, the dynamic phase trajectory graph of resonance ,as well as the time history response diagrams and phase plots with changing frequency parameters were obtained.The results show that the change of relevant parameters has an obvious influence on the resonance amplitude and stability of system.

Key words

magneto-elastic / axially moving beam / primary resonance / parametric resonance / current-carrying wires / multi-scale method

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HU Yuda1,2,ZHANG Mingran1,2. Parametric and primary resonance of an axially moving conductive beam between current-carrying wires[J]. Journal of Vibration and Shock, 2019, 38(14): 1-10

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