轴向运动导电薄板磁弹性耦合动力学理论模型

针对磁场环境中轴向运动导电薄板的动力学理论建模问题进行研究，得到较为完备的磁弹性耦合振动基本方程及相应的补充关系式。在考虑几何非线性效应下，给出薄板运动的动能、应变能以及外力虚功的表达式。应用哈密顿变分原理，推得磁场中轴向运动薄板的非线性磁弹性耦合振动方程，并得到力和位移满足的边界条件。基于麦克斯威尔电磁场方程，并考虑相应的电磁本构关系和电磁边界条件，推得任意磁场环境中轴向运动导电薄板满足的电动力学方程和所受电磁力表达式。分别针对纵向磁场环境、横向磁场环境、条形板等具体情形，给出了振动方程、电动力学方程和电磁力的简化形式。所得结果，可为此类问题的进一步求解和分析提供理论参考。

MAGNETO-ELASTIC COUPLED DYNAMICS THEORETICAL MODEL OF AXIALLY MOVING CURRENT-CONDUCTING THIN PLATE

The problem of dynamics theoretical modeling for axially moving current-conducting thin plate in magnetic field is investigated and the basic magneto-elastic coupled vibration equations and corresponding relational expressions were derived. Kinetic energy, strain energy and virtual work done by external force of the thin plate are obtained when geometric nonlinearity was taken into account. The nonlinear magneto-elastic coupled vibration equations of an axially moving thin plate in magnetic field were deduced by using Hamilton principle, and boundary conditions of force and displacement were also obtained. Based on the Maxwell equations, the corresponding electromagnetic constitutive relations and boundary conditions, the electrodynamics equations and electromagnetic forces expressions of axially moving current-conducting thin plate in general magnetic field were derived. In particular, the expressions of vibration equations, electrodynamics equations and electromagnetic forces were simplified in terms of longitudinal, transverse magnetic field and strip thin plate. The results are expected to be a theoretical reference for further analysis of this case.