磁场中旋转运动圆板磁弹性超谐-组合共振

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (12) : 167-173.

论文

磁场中旋转运动圆板磁弹性超谐-组合共振

胡宇达1,2，秦晓北1,2

作者信息 +

Magnetoelastic ultraharmoniccombination resonance of a rotating circle plate in magnetic field

HU Yuda1,2 ，QIN Xiaobei1,2

Author information +

文章历史 +

摘要

针对磁场中的旋转运动导电圆板，基于弹性理论和电磁原理，给出旋转圆板的动能、应变能和电磁力表达式。应用Hamilton原理，推得了几何非线性下圆板的磁弹性横向振动方程。针对横向磁场中双频外载作用下圆板的轴对称振动问题进行分析，利用辽金积分法得到夹支约束下旋转板的无量纲化振动微分方程。应用多尺度法求解非线性方程，得到超谐-组合联合共振下系统的幅频响应方程，并对稳态解的稳定性进行分析，得出稳定解的判定条件。通过算例，给出了旋转运动圆板共振幅值随频率参数、磁场及力幅的变化规律曲线图，分析了转速、磁场等参量对共振稳态解的影响；通过分析所绘制动相平面图上奇点附近相轨迹的变化趋向，进一步阐明了稳态解的多值性和稳定性。

Abstract

Aiming at a rotating conductive circle plate in magnetic field, based on the theory of elastic and electromagnetic principle, the kinetic energy, strain energy and electromagnetic forced expressions of rotating plate were obtained. Applied the Hamilton theory, the electroelastic transverse vibration equation of circular plate under the condition of geometric nonlinear was set up. The axisymmetric problem of a circular plate under the dualfrequency excitations in a transverse magnetic field was analyzed, and the nondimensional differential equation of vibration of the rotating plate was obtained by the Galerkin integral method. The multiscale method was used to solve the nonlinear equation, and the amplitude frequency response equation of the system with ultraharmoniccombination resonance was received, and the stability of steady solution was analyzed. An example was given to show the curves of the resonance amplitude of the rotating circular plate with frequency parameters, magnetic field and force amplitude, and the effects of rotational speed and magnetic field on the steadystate solution were analyzed; by analyzing the trend of the phase trajectory near the singularity on the plot of the moving phase, the multivalue and stability of the steady state solution were further elucidated.

导出引用

胡宇达1,2，秦晓北1,2. 磁场中旋转运动圆板磁弹性超谐-组合共振[J]. 振动与冲击, 2018, 37(12): 167-173

HU Yuda1,2,QIN Xiaobei1,2 . Magnetoelastic ultraharmoniccombination resonance of a rotating circle plate in magnetic field[J]. Journal of Vibration and Shock, 2018, 37(12): 167-173

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