轴向运动导电薄板的磁弹性振动  

Magneto-elastic vibration of an axially moving current-conducting thin plate

作　　者：胡宇达[1] 孙建涛[1] 杜国君[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,河北秦皇岛066004

出　　处：《振动与冲击》2013年第13期34-38,共5页Journal of Vibration and Shock

基　　金：河北省自然科学基金资助项目(E2010001254;E2011203176)

摘　　要：针对磁场环境中轴向运动导电薄板的磁弹性振动问题进行研究。在给出薄板运动的动能、应变能以及电磁力虚功表达式的基础上,应用哈密顿变分原理,推得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,得到薄板所受电磁力的表达式。针对横向磁场中矩形板的自由振动问题,通过位移函数的设定并应用伽辽金积分法,得到三种边界约束条件下轴向运动薄板的磁弹性振动微分方程。通过数值算例,给出了不同边界条件下矩形板的磁弹性振动特性曲线图,分析了轴向运动速度和磁感应强度等参量对薄板固有振动频率的影响,讨论了临界速度的变化规律。The problem of magneto-elastic vibration of an axially moving current-conducting thin plate in magnetic field was 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 in magnetic field were deduced by using Hamilton principle.Based on Maxwell equations,and the corresponding electromagnetic constitutive relations,the electromagnetic forces expressions of the thin plate were derived.Based on the displacement mode hypothesis of the rectangular thin plate free vibration in transverse magnetic field,by using of Galerkin method,the corresponding magneto-elastic vibration differential equations of the axially moving thin plate under three different boundary conditions were obtained.With numerical examples,the magneto-elastic vibration characteristic curves of the rectangular thin plate under different boundary conditions were obtained.The influences of axially moving velocity and magnetic induction intensity etc.parameters on the natural frequencies of the plate were analyzed,the variation law of the critical velocity was also discussed.

关 键 词：磁弹性 矩形板 轴向运动 固有频率 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]