摘要
研究轴向运动载流梁在两平行导线产生磁场中的主共振问题。给出两平行导线间载流梁处磁感应强度及所受电磁力表达式,推得轴向运动载流梁的横向振动微分方程。应用伽辽金积分法,得到轴向运动梁无量纲化的非线性振动微分方程。采用多尺度法进行求解,得到系统关于前两阶模态非线性方程的近似解析解以及主共振幅频响应方程。通过算例,得到了轴向运动载流梁共振幅值随调谐参数、载流电流密度、导线电流和位置的变化关系曲线图。结果表明,各相关物理和几何参数的改变对系统共振特征有较大影响,且非线性振动特征较为明显。
The magneto-elastic primary resonance of an axially moving current-carrying beam is investigated,where the beam move between two parallel and infinite long straight current-carrying wires.According to the principles of an electromagnetic field,the expressions of the electromagnetic force loading on the current-carrying beam is developed.Based on the Hamiltonian principle,the transverse vibration control equations of an axially moving current-carrying beam is derived.The non-dimensional nonlinear differential equation of an axially moving beam is obtained by means of Galerkin method.The approximate analytical solution of first two-order modal nonlinear equation and the primary resonance-amplitude-frequency response equation are derived by means of the multiple scales method.Through computational examples,the resonance amplitude of the axially moving current-carrying beam varying with frequency parameters,current-carrying density,current of wire,and the position variation relationship are obtained.The results show that there is an obvious nonlinear behavior and a great influence on the resonance characteristics of the system when the relevant physical and geometric parameters are changed.
作者
胡宇达
张明冉
HU Yu-da;ZHANG Ming-ran(School of Civil Engineering and Mechanics,Yanshan University,Qinhuangdao,Hebei 066004,China;Key Laboratory of Mechanical Reliability for Heavy Equipment and Large Structures of Hebei Province,Yanshan University,Qinhuangdao,Hebei 066004,China)
出处
《工程力学》
EI
CSCD
北大核心
2018年第10期238-248,共11页
Engineering Mechanics
基金
国家自然科学基金项目(11472239)
河北省自然科学基金项目(A2015203023)
关键词
载流梁
轴向运动
主共振
平行导线
多尺度法
current-carrying beam
axially moving
primary resonance
two parallel wires
multi-scale method
作者简介
通讯作者:胡宇达(1968―),男,黑龙江人,教授,博士,博导,主要从事非线性动力学、电磁弹性力学研究(E-mail:huyuda03@163.com).;张明冉(1992―),女,内蒙古人,硕士生,主要从事结构磁弹性振动研究(E-mail:zlxiaoranran@163.com).
