轴向运动导电条形板的磁弹性主-内联合共振  

Magnetoelastic primary-internal combined resonance of axially moving conductive strip plate

作　　者：胡宇达[1,2] 刘超[1,2] Hu Yuda;Liu Chao(School of Civil Engineering and Mechanics,Yanshan University,066004,Qinhuangdao,China;Key Laboratory of Mechanical Reliability for Heavy Equipment and Large Structures of Hebei Province,Yanshan University,066004,Qinhuangdao,China)

机构地区：[1]燕山大学建筑工程与力学学院,秦皇岛066004 [2]燕山大学河北省重型装备与大型结构力学可靠性重点实验室,秦皇岛066004

出　　处：《应用力学学报》2020年第6期2480-2488,I0012,共10页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11472239);河北省自然科学基金(A2020203007)。

摘　　要：研究轴向运动导电条形板的磁弹性1∶3主-内联合共振问题。以轴向运动导电条形板为研究对象,建立磁场中导电条形板的力学模型。利用哈密顿原理建立轴向运动导电条形板的振动方程。当夹支-铰支轴向运动导电条形板发生共振现象时,针对约束边界条件,通过对位移模态函数的设定,利用Galerkin积分法得到了双自由度非线性振动微分方程组。采用多尺度法得到了轴向运动导电条形板在主-内联合共振状态下的幅频响应方程组。通过算例分析,得到了关于一阶共振幅值和二阶共振幅值变化规律曲线图,讨论了磁场强度、轴向速度、外部激振力幅值和轴力对系统振动的影响。结果表明:系统发生主-内联合共振时,一阶共振和二阶共振均被激发,且幅值解呈现多值性和跳跃现象,表现出复杂的非线性特征。The magnetoelastic 1:3 principal-internal resonance of an axially moving conductive strip plate is studied. In this paper, the mechanical model of conductive strip in magnetic field is established by taking the axially moving conductive strip as the research object. The vibration equations of axially moving conductive strip plate are established by using the Hamilton principle. When the resonance of the clamped-hinged axially moving conductive strip occurs, the Galerkin integral method is used to obtain the two-degree-of-freedom nonlinear vibration differential equations by the setting of displacement modal function for the constrained boundary conditions. The amplitude-frequency response equations for the axially moving conductive strip plate in principal-internal resonance state are obtained by using the multi-scale method. The curves of first-order and second-order resonance amplitudes are obtained by numerical example analysis. The effects of magnetic field strength, axial velocity, amplitude of external excitation force and axial force on the system vibration are discussed. Results show that when the principal-internal joint resonance occurs, the first-order and the second-order resonance are both excited, and the amplitude solution is multivalued and presents jumping phenomenon, which shows complex nonlinear characteristics.

关 键 词：轴向运动 导电板 主-内联合共振 磁场 多尺度法 

分 类 号：O322[理学—一般力学与力学基础] O442[理学—力学]