双平行导线间轴向运动导电梁的动力稳定性

Dynamic stability of axially moving conductive beam between two parallel wires

针对双平行导线间的轴向运动导电梁,给出系统的动能和势能表达式。基于电磁场理论得到双平行导线间运动梁处磁场及所受电磁力表达式。应用哈密顿变分原理,导出轴向运动导电梁的磁弹性振动方程,并应用伽辽金积分法导出铰支约束下轴向运动梁的磁弹性振动常微分方程。根据奇点分析方法,给出磁弹性动力系统稳定性划分条件。通过算例,给出关于不同参量关系的奇点类型及其稳定性划分域,阐明了运动速度、导电载流强度、导线位置等参量对系统动力稳定性的影响。

According to the conductive beam between two parallel wires,the kineticenergy and potential energy expressions of the system were given.Based on the electromagnetic field theory,the magnetic induction intensity and electro-magnetic force expressions of conductive beam between two parallel wires were obtained.The magneto-elastic vibration equation of axially moving conductive beam was deduced by the use of Hamiltonian principle,and the magneto-elastic vibration ordinary differential equation of axially moving beamwith hinged constraintwas obtained by the Galerkin integral method.According to the singularity analysis method,the stability conditions of magnetoelastic dynamic system were given.Through the example,the singularity types and stability fields of different parameters are given,and the influence of the parameters such as the velocity,current carrying strength and the position of the wire was investigated on the dynamic stability of the system.