磁场中轴向运动导电梁弯曲自由振动分析

研究磁场环境下轴向运动导电梁的弯曲自由振动．首先给出系统的动能、势能以及电磁力表达式，进而应用哈密顿变分原理，推得磁场中轴向运动导电梁的磁弹性弯曲振动方程．在位移函数设定基础上，应用伽辽金积分法分别推出三种不同边界约束条件下，轴向运动梁的磁弹性自由振动微分方程和频率方程，得到固有频率表达式．通过算例，得到了弹性梁固有振动频率的变化规律曲线图，分析了轴向运动速度、磁感应强度和边界条件对固有振动频率和临界值的影响．

Analysis of Bending Free Vibration of Conductive Beam with Axis Motion in Magnetic Field

The paper is focused on the bending free vibration of conductive beam with axis motion in magnetic field. Firstly, the expressions of kinetic energy, potential energy and electromagnetic force of the system were provided separately. By applying the Hamilton variational principle, the magneto-elastic bending vibration equation of the beam with axis motion in magnetic field was formulated. Base on the already-set displacement function, by applying the Galerkin integral method, magnetic-elastic free vibration differential equation and frequency equation of the axial movement beam for three different boundary constraints were derived. The expressions of natural frequencies were obtained. The numerical example further provided the curves of natural vibration frequencies of the elastic beam. The influences of the axial motion velocity, magnetic strength and boundary conditions on the natural vibration frequency and the critical value were also analyzed.