Magneto-Elastic Combination Resonances Analysis of Current-Conducting Thin Plate

HU Yu-da; LI Jing

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Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(8): 954-966

HU Yu-da, LI Jing. Magneto-Elastic Combination Resonances Analysis of Current-Conducting Thin Plate[J]. Applied Mathematics and Mechanics, 2008, 29(8): 954-966.

Citation:

HU Yu-da, LI Jing. Magneto-Elastic Combination Resonances Analysis of Current-Conducting Thin Plate[J]. Applied Mathematics and Mechanics, 2008, 29(8): 954-966.

Citation:

HU Yu-da, LI Jing. Magneto-Elastic Combination Resonances Analysis of Current-Conducting Thin Plate[J]. Applied Mathematics and Mechanics, 2008, 29(8): 954-966.

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Magneto-Elastic Combination Resonances Analysis of Current-Conducting Thin Plate

HU Yu-da¹,
LI Jing^1,2

1.
School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao, Hebei 066004, P. R. China;

Received Date: 2007-09-04
Rev Recd Date: 2008-07-15
Publish Date: 2008-08-15

Abstract

Abstract

Based on Maxwell the nonlinear magneto-elastic vibration equations of a thin plate were derived.The electrodynamic equations and of electromagnetic forces were also derived.In addition,the magneto-elastic combination resonances and stabilities of the thin beam-plate subjected to mechanical loadings in a constant magnetic filed were studied.by means of the Galerldn Method,the corresponding nonlinear vibration differential equatios were derived.The amplitude frequency response equation of the system in steady motion was obtained by the method of multiple scales.The exatation condition of combination resonances was analyzed.Based on the Liapunov stability theory,the stabilities of steady solutions were analyzed and the critical conditions of stability were also obtained.Through the numerical calculation,the curves which resonance-amplifades changing with detuning parameters,excitation amplitudes and magnetic intensity in the fast and the second order modality were obtained respectively.The time history response plots,the phase charts,the Poincare mapping charts and the spectrum plots of vibraiaons were also obtained.The effeet of electso-mangetic and mechanical parameters for the stabilities of solutions and the bifurcattion are further analyzed.Some complex dynamic performances such as the period-doubling motion and the quasi-period motion were discussed.
- magneto-elastic,
- current-conducting thin plate,
- combination resonance,
- stability,
- method of multiple scales

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References(17)

References

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