载流导线间轴向运动导电梁的参数-主共振

研究轴向运动导电梁在载流导线产生的周期变化磁场中的参数-主共振问题。给出载流导线间导电梁处的磁感应强度、梁的应变能、动能及所受电磁力表达式,推得轴向运动导电梁的磁弹性横向振动微分方程。应用伽辽金积分法,得到导电梁无量纲化的非线性参数-主共振微分方程。利用多尺度法求解方程,得到系统关于非线性参数-主共振联合方程的近似解析解。通过计算,得到了轴向运动导电梁共振幅值随调谐参数变化的幅频图,共振系统的动相平面轨迹图,以及在变化调谐参数下的时程图和相图。结果表明,相关参数的改变对系统的共振幅值及稳定性影响明显。

Parametric and primary resonance of an axially moving conductive beam between current-carrying wires

The parametric and primary resonance of an axially moving conductive beam in the magnetic field induced by current-carrying wires was investigated.Based on the magnetic inductive intensity between current-carrying wires,the strain energy and kinetic energy of the beam,the expressions of the electromagnetic force loading on the current-carrying beam,and the magneto-elastic transverse vibration differential equation of the axially moving conductive beam were derived.The non-dimensional nonlinear parametric and primary resonance differential equation of the axially moving beam was obtained by means of Galerkin method.The approximate analytical solution of the nonlinear parametric and primary resonance differential equation was derived by the multiple-scale method.Through calculation,the corresponding amplitude frequency response curves with different frequency parameters,the dynamic phase trajectory graph of resonance,as well as the time history response diagrams and phase plots with changing frequency parameters were obtained.The results show that the change of relevant parameters has an obvious influence on the resonance amplitude and stability of system.