磁场中导电旋转圆板的磁弹性非线性共振

发布时间：2019-03-21 12:05

【摘要】：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。
[Abstract]:The magnetoelastic nonlinear resonance of a rotating circular thin plate subjected to mechanical loads in a magnetic field is studied. According to Hamiltonian principle, the magnetoelastic nonlinear vibration equation of rotating circular plate in magnetic field is derived, and the expression of electromagnetic force on rotating plate is given based on electromagnetic theory. By setting the displacement function and applying Galerkin integral method, the magneto-elastic axisymmetric vibration differential equation of rotating conductive circular plate in transverse magnetic field is obtained. The average method is used to solve the nonlinear principal resonance problem of the system, and the amplitude-frequency response equation under steady-state motion is obtained. Through numerical calculation, the amplitude-frequency characteristic curve of circular plate and the curve of amplitude with magnetic induction intensity, rotational speed, excitation force and other parameters are obtained under the condition of fixed-support boundary, and the curves of amplitude change with magnetic induction intensity, rotational speed and excitation force are obtained. The influence of different parameters on the resonance amplitude and nonlinear characteristics of the rotating plate is analyzed.
【作者单位】：燕山大学河北省重型装备与大型结构力学可靠性重点实验室;
【基金】：国家自然科学基金(11472239) 河北省自然科学基金(A2015203023) 河北省高等学校科学技术研究重点项目(ZD20131055)
【分类号】：O322

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