载流线圈中导电圆板的磁弹性固有振动  

MAGNETOELASTIC NATURAL VIBRATION OF CONDUCTIVE CIRCULAR PLATE IN CURRENT-CARRYING COILS

作　　者：徐浩然 胡宇达[1,2] 李文平[3] XU HaoRan;HU YuDa;LI WenPing(School of Civil Engineering and Mechanics,Yanshan University,Qinhuangdao 066004,China;Key Laboratory of Mechanical Reliability for Heavy Equipment and Large Structures of Hebei Province y Yanshan University,Qinhuangdao 066004,China;School of Vehicles and Energy,Yanshan University,Qinhuangdao 066004,China)

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 [3]燕山大学车辆与能源学院,秦皇岛066004

出　　处：《机械强度》2019年第6期1271-1277,共7页Journal of Mechanical Strength

基　　金：国家自然科学基金项目(11472239);河北省自然科学基金项目(A2015203023);秦皇岛市科学技术研究与发展计划项目(201601B016)资助~~

摘　　要：针对处于平行共轴三线圈和球形载流线圈产生磁场中的导电圆板,基于Kirchhoff薄板理论,给出磁场中圆板的磁弹性横向振动基本方程。根据电磁理论,导出线圈产生均匀磁场区域中圆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法,得到圆板的磁弹性轴对称振动微分方程及固有频率的表达式。通过算例,绘制了周边夹支和简支两种边界条件下圆板的磁弹性固有振动特性曲线图,分析了两种边界条件下固有频率、阻尼比、电磁力矩随线圈载流强度、线圈匝数和板厚等参数的变化规律。As for the conductive plate in magnetic field generated by current-carrying three parallel coaxial circular coils and spherical coils,based on the Kirchhoff plate theory,the magnetoelastic transverse vibration equation of the plate in magnetic field was given.According to electromagnetic theory,the expressions of electromagnetic forces acting on circular plate in uniformly distributed region of the magnetic field generated by current-carrying coils were derived.By setting of a displacement function and using of Galerkin method,the magnetoelastic axisymmetric vibration differential equation of the plate and the expression of the natural frequency were obtained.By calculation examples,the curves of magnetoelastic natural vibration characteristics of the circular plate with clamped boundary condition and simply supported boundary condition were drawn.The analysis on laws of the natural frequency,damping ratio and electromagnetic moment varying with current intensity,turns of coils and plate thickness is presented finally.

关 键 词：圆板 磁弹性 固有振动 载流线圈 电磁力 

分 类 号：O321[理学—一般力学与力学基础] O442[理学—力学]