磁场中轴向运动载流梁磁弹性主共振分析

Magneto-elastic primary resonance of axially moving current-carrying beams in magnetic fieid

研究磁场环境中轴向运动载流梁的磁弹性共振问题;考虑几何非线性,给出梁在力、运动、电磁作用下的动能、应变能以及电磁力的表达式。应用哈密顿变分原理,推得磁场中轴向运动载流梁的磁弹性振动方程。针对两端简支边界条件,假设三阶模态形函数,通过伽辽金积分推得梁的磁弹性振动微分方程;应用多尺度法,得到外激励力和外加电流作用下系统的主共振幅频响应方程;数值分析了磁感应强度、外加电流、轴向速度和外激励力对系统共振幅值的影响。结果表明,在振幅-磁感应强度响应图中,随着调谐参数的增大,共振曲线逐渐内缩最终上部封闭,外加电流使此变化过程中的临界分离点向右"偏移"。

The magneto-elastic resonance of axially moving current-carrying beams in magnetic field was investigated.Considering the geometric nonlinearity and the interaction among force,motion,electric action and magnetic one,the expressions of kinetic energy,strain energy and electro-magnetic force were derived.Then with Hamilton princile,the vibration equation of an axially moving current-carrying beam in magnetic field was deduced.According to the simply supported boundary condition and assuming three orders modal shape functions,the magneto-elastic vibration differential equations of the beam were obtained through applying Galerkin integral method.Based on the method of multi-scale,the primary resonance amplitude-frequency response equations under external excitation and current of the system were gained.The influences of magnetic field strength,applied current,axial velocity,external motion on the amplitude of the system resonance were analyzed.The results showed that in the response plot of amplitude-intensity of magnetic field,with increase in tuning parameters,the resonance curve gradually retracts and its upper finally closes,the critical separation point in this varying process is shifted to the right due to the applied current.