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| Bifurcation and chaos of a rotating circular plate in magnetic field |
| Received:September 26, 2015 Revised:March 09, 2016 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201701002 |
| KeyWord:magneto-elastic circular plate Bessel bifurcation chaos |
| 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 |
| 朴江民 |
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: |
| Numerical simulation was used to research the bifurcation and the chaos of rotating circular plate in magnetic field.Firstly,based on the thin plate theory and Maxwell Equations,the expressions of kinetic energy,potential energy,virtual work by external force and electromagnetic force were derived.Using Hamilton's principle,the nonlinear non-axisymmetric magnetoelastic vibration differential equations for vibration of the rotating circular plate in the magnetic field were investigated.Secondly,the Galerkin method and Bessel mode shape function were used to derive the ordinary differential equations for axisymmetric transverse vibration.Finally,the primary resonance of the circular plat fixed boundary was studied.Considering the first order mode shape function,the results such as bifurcation diagrams and Poincare map were obtained under the control parameters of magnetic induction,transverse force magnitude and frequency respectively.The influence of bifurcation parameters on the bifurcation and chaos of system was discussed.The results show that the bifurcation parameters affect the stability of the system,and with the system experiences a complicated process from chaos to multi periodic motion to chaos as these parameters vary. |
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