磁场中轴向运动导电薄板的强迫振动分析  

Forced vibration of axially moving current-conducting thin plate in magnetic field

作　　者：胡宇达[1] 孙建涛[1] 

机构地区：[1]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》2013年第3期339-343,472,共5页Chinese Journal of Applied Mechanics

基　　金：河北省自然科学基金(E2010001254)

摘　　要：对磁场环境中轴向运动导电薄板的磁弹性强迫振动问题进行了研究。在给出薄板运动的动能、应变能、电磁力虚功的基础上,应用哈密顿变分原理推得了磁场中轴向运动矩形薄板的磁弹性振动方程;基于麦克斯威尔电磁场方程并考虑相应的电磁关系式,得到了薄板所受电磁力的表达式。针对横向磁场中矩形板的强迫振动问题,通过位移函数的设定并应用伽辽金积分法,分别得到了对边简支-对边自由、对边夹支-对边自由两种边界约束条件下轴向运动薄板的磁弹性强迫振动微分方程。通过数值算例,给出了横向磁场中均布动载作用下对边夹支对边自由边界约束条件下轴向运动矩形板的振幅放大因子随频率、轴向速度、磁感应强度的变化规律曲线图。结果表明:频率比和轴向运动速度的改变,均使振幅放大因子在共振区出现了峰值,外加磁场则起到了电磁阻尼的作用。The magneto-elastic forced vibration of an axially moving current-conducting thin plate in magnetic field is investigated.Based on the expressions of kinetic energy,strain energy and virtual work done by electromagnetic forces,the magneto-elastic vibration equations of an axially moving rectangular thin plate are deduced by using Hamilton principle.Based on the Maxwell equations and the corresponding electromagnetic constitutive relations,electromagnetic forces expressions of thin plate are derived out.Based on displacement mode hypothesis,by using Galerkin method,the corresponding magneto-elastic forced vibration differential equations of axially moving thin plate with the two opposite edges simply supported or clamped and the other two edges free,are obtained.By the numerical examples,the curves of amplitude amplifying factor,axially moving velocity and magnetic induction intensity of axially moving thin rectangular plate with the two opposite edges clamped and the other two edges free under uniform loading in the transverse magnetic field are obtained.The results show the variations of frequency ratio and axially moving velocity lead to the peak value of amplitude amplifying factor in the resonance region,the applied magnetic field plays a role of damping.

关 键 词：磁弹性 强迫振动 矩形板 轴向运动 哈密顿原理 

分 类 号：O322[理学—一般力学与力学基础]