导电矩形薄板的磁弹性超谐-内联合共振  

The combined resonance of superharmonic resonance and internalresonance of conductive rectangular thin plate

作　　者：李晶[1,2] 胡宇达[2] 高崇一[1] LI Jing;HU Yuda;GAO Chongyi(Key Laboratory of Intelligent Equipment Digital Design and Process Simulation of Hebei Province,Tangshan University,063000 Tangshan,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]唐山学院河北省智能装备数字化设计及过程仿真重点实验室,唐山063000 [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》2024年第3期673-681,共9页Chinese Journal of Applied Mechanics

基　　金：河北省自然科学基金资助项目(No.A2020203007);河北省教育厅科学技术研究项目(No.BJ2019209);唐山市科技创新团队培养计划项目(No.21130205D);唐山市人才资助项目(No.A202203031)。

摘　　要：研究横向磁场中矩形薄板在外激励作用下的超谐波共振和1∶3内共振的联合共振问题。针对一边固定三边简支的矩形薄板,利用Galerkin积分法得到两自由度非线性振动微分方程组。采用多尺度法求解,得到前两阶模态的幅频响应方程组。通过算例,得到系统发生超谐-内联合共振时前两阶响应幅值与各参数关系的曲线图,讨论了外激励幅值、磁场强度等参数对系统振动的影响。结果表明,考虑内共振时高阶模态被间接激发,系统存在着能量的交换,调节磁场强度可控制系统的共振。The combined resonance of superharmonic resonance and 1∶3 internal resonance of a rectangular thin plate in transverse magnetic field is studied.For the rectangular thin plate with one side fixed and three sides simply supported,the two degree of freedom nonlinear vibration differential equations are obtained by the Galerkin method.Then the multiple-scale method is employed to solve equations,and amplitude frequency response equations of the first two modes are obtained.Through calculation examples,the relationship between the first two order response amplitudes and parameters when superharmonic internal resonance occurs in system is obtained,in which the influence of parameters e.g.,external excitation amplitude and magnetic field intensity on the vibration of system is discussed.The results show that the high-order modes are indirectly excited when internal resonance is considered,and there is energy exchange in the system,and the resonance of system can be controlled by changing the magnetic field intensity.

关 键 词：磁弹性 矩形薄板 超谐波共振 内共振 多尺度法 

分 类 号：O442[理学—电磁学] O322[理学—物理]