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2 Journal of Theoretical and Applied Mechanics

2 2019

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Magneto-elastic internal resonance of an axially moving conductive beam in the magnetic field

Wang Jie, Hu Yuda, Su Yu, Gong Liangfei, Zhang Qingnan

Journal of Theoretical and Applied Mechanics

2019

Vol. 57 nr 1

179--191

The Hamiltonian principle is applied to the nonlinear vibration equation of an axially moving conductive beam in the magnetic field with consideration of the axial velocity, axial tension, electromagnetic coupling effect and complex boundary conditions. Nonlinear vibration characteristics of the free vibrating beam under 1:3 internal resonances are studied based on our approach. For beams with one end fixed and the other simply supported, the nonlinear vibration equation is dispersed by the Galerkin method, and the vibration equations are solved by the multiple-scales method. As a result, the coupled relations between the first-order and second-order vibration modes are obtained in the internal resonance system. Firstly, the influence of initial conditions, axial velocity and the external magnetic field strength on the vibration modes is analysed in detail. Secondly, direct numerical calculation on the vibration equations is carried out in order to evaluate the accuracy of the perturbation approach. It is found that through numerical calculations, in the undamped system, the vibration modes are more sensitive to the initial value of vibration amplitude. The amplitude changes of the first-order and second-order modes resulting from the increase of the initial amplitude value of the vibration modes respectively are very special, and present a “reversal behaviour”. Lastly, in the damped system, the vibration modes exhibit a trend of coupling attenuation with time. Its decay rate increases when the applied magnetic field strength becomes stronger.

Magneto-elastic combined multidimensional resonance of a rotating circular plate in a double-direction magnetic field

Li Zhe, Hu Yu Da, Li Wen Qiang

Journal of Theoretical and Applied Mechanics

2019

Vol. 57 nr 4

883--895

Magneto-elastic nonlinear non-axisymmetric resonance is investigated for a rotating annular plate in a double-direction magnetic field. According to transverse and longitudinal magneto- -elastic non-axisymmetric vibration equations of the thin annular plate, and considering the influence of the static load term, non-axisymmetric vibration differential equations by combined parametric and forced excitations are obtained through application of the Galerkin method. Then, the method of multiple scales is applied to solve differential vibration equations. By numerical computations, the influence of magnetic induction intensity, inner and outer diameters, excitation and radial forces on transverse and longitudinal resonance characteristics are analyzed.