旋转运动导电圆板电磁弹性耦合振动方程  

Electromagnetic elastic coupling vibration equations of a conductive rotating circular plate

作　　者：胡宇达[1,2] 李哲[1,2] Hu Yuda Li Zhe(School of Civil Engineering and Mechanics, Yanshan University,Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures of Hebei Province, Yanshan Universit)

机构地区：[1]燕山大学建筑工程与力学学院,秦皇岛066004 [2]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,秦皇岛066004

出　　处：《应用力学学报》2017年第1期38-42,共5页Chinese Journal of Applied Mechanics

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);河北省研究生创新资助项目(2016SJBS023)

摘　　要：针对磁场环境中旋转运动导电圆板的电磁弹性耦合振动理论建模问题进行研究。在考虑几何非线性效应下,给出了旋转运动圆板的形变势能、动能及变分表达式。应用哈密顿变分原理,推得磁场中旋转运动导电圆板的磁弹性耦合非线性振动方程。根据麦克斯威尔电磁场方程及相应的电磁本构关系,并基于磁弹性基本假设,推得磁场环境中旋转运动圆板所受的电磁力表达式和磁弹性二维电动力学方程。通过算例,分析了横向磁场中旋转运动圆板的轴对称振动问题,得到了圆板的固有振动频率随转速、磁感应强度的变化规律,并对结果进行了分析。Modeling of a conductive rotating thin circular plate in magnetic field based on the electromagnetic elastic coupling vibration theory is investigated. Considering the geometric nonlinear effects, the deformation potential energy, kinetic energy and the variation expressions of the rotating circular plate are obtained. Applying the Hamilton variational principle, the magneto-elastic coupling nonlinear vibration equations of the conductive rotating thin circular plate in magnetic field are derived. According to the Maxwell＇s equations and the corresponding electromagnetic constitutive relation, the expressions of the electromagnetic force undergone by the conductive rotating thin circular plate in magnetic field and the magneto elastic two-dimensional electrodynamics equation are derived based on the magneto elastic basic hypothesis. Through an example, the axisymmetric vibration problem of the rotating thin circular plate in transverse magnetic field is analyzed. The change curves of the natural vibration frequency of the circular plate changing with the rotating velocity, the magnetic induction intensity are obtained. Finally, the results are analyzed.

关 键 词：电磁弹性 圆板 振动方程 旋转运动 哈密顿原理 

分 类 号：O322[理学—一般力学与力学基础] O442[理学—力学]