磁场中轴向运动载流梁磁弹性主共振分析

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振动与冲击 ›› 2016, Vol. 35 ›› Issue (23) : 65-73.

论文

磁场中轴向运动载流梁磁弹性主共振分析

王杰，胡宇达

作者信息 +

ANALYSIS OF MAGNEOT-ELASTIC PRINCIPAL RESONANCE OF AXIALLY MOVING CURRENT-CARRING BEAMS IN MAGNETIC FIELD

Wang Jie， Hu yu-da

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文章历史 +

摘要

研究磁场环境中轴向运动载流梁的磁弹性共振问题。考虑几何非线性，给出梁在力、运动、电磁作用下的动能、应变能以及电磁力的表达式。应用哈密顿变分原理，推得磁场中轴向运动载流梁的磁弹性振动方程。针对两端简支边界条件，假设三阶模态形函数，通过伽辽金积分推得梁的磁弹性振动微分方程。应用多尺度法，得到外激励力和外加电流作用下系统的主共振幅频响应方程。数值分析了磁感应强度、外加电流、轴向速度和外激励力对系统共振幅值的影响。结果表明，在振幅-磁感应强度响应图中，随着调谐参数的增大，共振曲线逐渐内缩最终上部封闭，外加电流使此变化过程中的临界分离点向右“偏移”。

Abstract

The magneto-elastic resonance of axially moving current-carrying beams in magnetic field was investigated. With the geometric nonlinearity and the interaction in force, motion, electric and magnetic considered, the expressions of kinetic energy, strain energy and electro-magnetic force was derived. Then the Hamilton princile was applied to the vibration equation of the axially moving current-carrying beam in magnetic field. According to the simply supported boundary condition and assuming the third-order modal shape function, the magneto-elastic vibration differential equation of beams was obtained through the application of Galerkin integral method. Based on the method of multiple-scale, the principal resonance amplitude-frequency response equation of external excitation and applied current interaction system were gained. Influence of the magnetic field strength, the applied current, axial velocity, external motivation on the amplitude of system resonance was analyzed. The results show that in the curve of amplitude-intensity of magnetic field, with the increase of tuning parameters resonance, the curve gradually retracted and its upper final closed, the critical separation point "shifted" to the right by the applied current in this process.

导出引用

王杰，胡宇达. 磁场中轴向运动载流梁磁弹性主共振分析[J]. 振动与冲击, 2016, 35(23): 65-73

Wang Jie， Hu yu-da. ANALYSIS OF MAGNEOT-ELASTIC PRINCIPAL RESONANCE OF AXIALLY MOVING CURRENT-CARRING BEAMS IN MAGNETIC FIELD[J]. Journal of Vibration and Shock, 2016, 35(23): 65-73

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