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| Magneto-elastic nonlinear dynamics and bifurcation of axially moving current-conducting plate |
| Received:September 14, 2012 Revised:April 25, 2013 |
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| DOI：10.7511/jslx201402007 |
| KeyWord:magneto-elastic thin plate axially moving bifurcation chaotic motion resonance |
| Author | Institution |
| 胡宇达 |
燕山大学 河北省重型装备与大型结构力学可靠性重点实验室, 秦皇岛 |
| 胡朋 |
燕山大学 河北省重型装备与大型结构力学可靠性重点实验室, 秦皇岛 |
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| Abstract: |
| Magneto-elastic dynamic behavior of the axially moving current-conducting thin plate in a magnetic field is investigated in this paper.Based on the expressions of total kinetic energy,strain energy and virtual work done by external force of the thin plate,method of Hamilton principle has been used to get the nonlinear magneto-elastic vibration equations of axially moving thin plate while considering geometric nonlinear.In addition,we give the electromagnetic forces expressions of the axially moving current conducting thin plate in a magnetic field.In order to analyze the resonance of a strip thin plate in the transverse magnetic field,multiple-scale method and singularity theory are employed to derive the bifurcation-response equation and the corresponding transition variety of universal unfolding.Numerical simulation is carried out to plot the bifurcation diagrams,corresponding maximum Lyapunov exponent diagrams and Poincaré map with respect to the bifurcation parameters such as magnetic induction intensity,axial speed and external force.The influences of different bifurcation parameters on period doubling motion and chaotic motion of resonance system are analyzed.The results show that the complex dynamic behaviors of resonance system can be controlled by changing the corresponding parameters. |