摘要
针对磁场环境中轴向运动导电导磁梁磁弹性耦合振动的理论建模问题进行研究.基于Timoshenko(铁木辛柯)梁理论并考虑几何非线性因素,给出轴向运动弹性梁在横向双向振动下的形变势能、动能计算式以及电磁力和机械力的虚功表达式.应用Hamilton(哈密顿)变分原理,推得磁场中轴向运动Timoshenko梁的非线性磁弹性耦合振动方程,并给出了简化形式的Euler-Bernoulli(欧拉-伯努利)梁磁弹性振动方程.根据电磁理论和相应的电磁本构关系,得到载流导电弹性梁所受电磁力的表达式,基于磁偶极子-电流环路模型给出铁磁弹性梁所受磁体力和磁体力偶的表述形式.通过算例,分析了轴向运动导电弹性梁的奇点分布及其稳定性问题.
The magneto-elastic coupled vibration theoretical model for axially moving conduc- tive and magnetic beams in magnetic field environment was studied. Based on the Timoshenko beam theory and with the geometric nonlinearity considered, the expressions for the deforma- tion potential energy, kinetic energy, electromagnetic force and the virtual work of mechanical force of the elastic beam in axial motion and lateral bidirectional vibration were gained. Then the Hamilton variational principle was applied to get the nonlinear magneto-elastic coupled vi- bration equations for the axially moving Timoshenko beam in a magnetic field, and get those for the simplified Euler-Bernoulli beam. Based on the electromagnetic theory and the constitutive relation of the corresponding electromagnetism, the expressions for the electromagnetic force of the current-conducting elastic beam, and for the magnet force and magnet force couple of the magneto-elastic beam based on the magnetic dipole-current loop model, were derived. Through the numerical example, the singularity distribution and stability of the conductive and elastic beam in axial movement were analyzed.
出处
《应用数学和力学》
CSCD
北大核心
2015年第1期70-77,共8页
Applied Mathematics and Mechanics
基金
国家自然科学基金(11472239)
河北省高等学校科学技术研究重点项目(ZD20131055)~~
关键词
导电导磁梁
磁弹性
振动
轴向运动
HAMILTON原理
conductive and magnetic beam
magneto-elastic
vibration
axially moving
Hamilton principle
