Combination Resonances of Axially Moving Current-conducting Strip Plate in Transverse Magnetic Field

Abstract

Abstract:

Based on expressions of total kinetic energy, potential energy and electromagnetic force, the nonlinear magneto-elastic vibration equations of an axially moving current-conducting thin plate in magnetic field were deduced by using Hamilton principle. According to displacement mode hypothesis, by using the Galerkin method, a duffing magneto-elastic vibration equation of axially moving strip plate with two opposite edges simply supported in transverse magnetic field was obtained. Combination resonance amplitude-frequency equation was derived by means of the multiple-scale method, and the critical condition of stability of steady-state solution was also given. By several numerical examples, the variation curves of the amplitude for different axial speeds, magnetic induction intensities, external excitations and axial tensions were obtained respectively, then time history plot and phase plot were also obtained. The influences of different parameters on the resonance amplitudes and nonlinear characteristic behaviors were investigated, and the quasi-periodic, chaotic motion of axially moving system were further discussed.

Key words: magneto-elastic, combination resonance, current-conducting thin plate, axially moving, magnetic field

摘要：

给出了磁场中轴向运动条形导电薄板的动能、应变能以及电磁力表达形式，应用哈密顿变分原理,推导出了轴向运动导电板的非线性磁弹性振动微分方程。通过位移函数的设定并应用伽辽金积分法，得到横向磁场中对边简支边界约束轴向运动条形板的达芬型磁弹性振动方程。利用多尺度法进行求解，得到组合共振发生时确定共振幅值的幅频响应方程，并给出定常稳定解的判定条件。通过数值算例，得到轴向运动速度、磁感应强度、激励力和轴向拉力等参量不同时的振幅变化规律曲线图以及系统振动的时程响应图和相图，分析了不同参量对共振幅值和非线性特征的影响,并对系统呈现的概周期和混沌运动行为变化规律进行了分析。

关键词: 磁弹性, 组合共振, 导电薄板, 轴向运动, 磁场

CLC Number:

O322
O442

Hu Yuda, Hu Shoupeng, Zhang Yiying. Combination Resonances of Axially Moving Current-conducting Strip Plate in Transverse Magnetic Field[J]. China Mechanical Engineering, 2014, 25(7): 882-887.

胡宇达, 胡首鹏, 张翼颖. 横向磁场中轴向运动条形导电板的组合共振[J]. 中国机械工程, 2014, 25(7): 882-887.

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