轴向运动导电板磁弹性非线性动力学及分岔特性

研究磁场环境中轴向运动导电薄板磁弹性动力学及分岔特性。考虑几何非线性因素,在给出薄板运动的动能、应变能及外力虚功的基础上,应用哈密顿变分原理,得到磁场中轴向运动薄板的非线性磁弹性振动方程,并给出洛伦兹电磁力的确定形式。针对横向磁场环境中条形板共振特性进行分析,应用多尺度法和奇异性理论,得到稳态运动下的分岔响应方程以及普适开折对应的转迁集。通过算例,分别得到以磁感应强度、轴向运动速度和激励力为分岔控制参数的分岔图、最大李雅普诺夫指数图和庞加莱映射图等计算结果,讨论不同分岔参数对系统呈现的倍周期和混沌运动的影响。结果表明,通过相应参数的改变可实现对系统复杂动力学行为的控制。

Magneto-elastic nonlinear dynamics and bifurcation of axially moving current-conducting plate

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.