中国物理B ›› 2017, Vol. 26 ›› Issue (9): 94302-094302.doi: 10.1088/1674-1056/26/9/094302
• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇 下一篇
Magneto-elastic dynamics and bifurcation of rotating annular plate
Yu-Da Hu(胡宇达), Jiang-Min Piao(朴江民), Wen-Qiang Li(李文强)
- 1 School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao 066004, China;
2 Key Laboratory of Mechanical Reliability for Heavy Equipment and Large Structures of Hebei Provincial, Yanshan University, Qinhuangdao 066004, China
Magneto-elastic dynamics and bifurcation of rotating annular plate
Yu-Da Hu(胡宇达)1,2, Jiang-Min Piao(朴江民)1,2, Wen-Qiang Li(李文强)1,2
- 1 School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao 066004, China;
2 Key Laboratory of Mechanical Reliability for Heavy Equipment and Large Structures of Hebei Provincial, Yanshan University, Qinhuangdao 066004, China
摘要：
In this paper, magneto-elastic dynamic behavior, bifurcation, and chaos of a rotating annular thin plate with various boundary conditions are investigated. Based on the thin plate theory and the Maxwell equations, the magneto-elastic dynamic equations of rotating annular plate are derived by means of Hamilton's principle. Bessel function as a mode shape function and the Galerkin method are used to achieve the transverse vibration differential equation of the rotating annular plate with different boundary conditions. By numerical analysis, the bifurcation diagrams with magnetic induction, amplitude and frequency of transverse excitation force as the control parameters are respectively plotted under different boundary conditions such as clamped supported sides, simply supported sides, and clamped-one-side combined with simply-another-side. Poincaré maps, time history charts, power spectrum charts, and phase diagrams are obtained under certain conditions, and the influence of the bifurcation parameters on the bifurcation and chaos of the system is discussed. The results show that the motion of the system is a complicated and repeated process from multi-periodic motion to quasi-period motion to chaotic motion, which is accompanied by intermittent chaos, when the bifurcation parameters change. If the amplitude of transverse excitation force is bigger or magnetic induction intensity is smaller or boundary constraints level is lower, the system can be more prone to chaos.
中图分类号: (Vibrations of membranes and plates)
- 43.40.Dx