磁场中导电旋转圆板的磁弹性非线性共振

摘要

The nonlinear resonance of a conductive rotating thin circular plate subjected to mechanical loads in a magnetic field was investigated.The nonlinear vibration equation,related to the spinning round plate,was derived according to the Hamilton principle.Based on electromagnetic theory,the expressions of electromagnetic forces were derived.According to the set of a displacement function,the magnetoelastic forced vibration differential equation of the round plate was obtained through the application of the Galerkin integral method.By means of an averaging method,the amplitude-frequency response equation in a steady state was established.The amplitude frequency characteristic curves and the relationship curves of an amplitude that changes with the magnetic induction intensity,the speed of rotation and the excitation force of the plate with a fixed boundary condition were obtained according to the numerical calculation.The influence of different parameters on the amplitude and nonlinear characteristics of the spinning plate was analyzed finally.%研究旋转运动圆形薄板在磁场中受到机械载荷作用时的磁弹性非线性共振问题。根据哈密顿原理推导出旋转运动圆板在磁场中的磁弹性非线性振动方程，基于电磁理论给出了旋转板所受电磁力的表达式；通过位移函数的设定并应用伽辽金积分法，得到横向磁场中旋转导电圆板的磁弹性轴对称振动微分方程。应用平均法对系统非线性主共振问题进行求解，得到稳态运动下的幅频响应方程。通过数值计算，得到固支边界条件下圆板的幅频特性曲线以及振幅随磁感应强度、转速、激励力等参数的变化规律曲线图，分析了不同参数对旋转板共振幅值及非线性特性的影响。