磁场中导电矩形薄板1∶3内共振下的超谐波动力学响应  

Superharmonic Dynamic Response of Rectangular Conductive Thin Plate Under 1∶3 Internal Resonance in Magnetic Field

作　　者：李晶[1,2,3] 高崇一 LI Jing;GAO Chongyi(Key Lab of Intelligent Equipment Digital Design and Process Simulation of Hebei Province,Tangshan University,Tangshan 063000,China;Key Lab of Microstructure Material Physics of Tangshan City,Tangshan University,Tangshan 063000,China;Department of Fundamental Sciences Teaching,Tangshan University,Tangshan 063000,China;School of Mechanical and Electrical Engineering,Tangshan University,Tangshan 063000,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,河北唐山063000 [2]唐山学院唐山市微结构材料物理重点实验室,河北唐山063000 [3]唐山学院基础教学部,河北唐山063000 [4]唐山学院机电工程学院,河北唐山063000

出　　处：《唐山学院学报》2024年第3期1-7,77,共8页Journal of Tangshan University

基　　金：河北省自然科学基金资助项目(A2020203007);唐山市科技创新团队培养计划项目(21130205D);唐山市人才资助项目(A202203031);2023唐山学院博士创新基金项目(tsxybc-202301)。

摘　　要：针对横向恒定磁场中一边固定三边简支的导电矩形薄板,研究1∶3内共振条件下系统发生超谐波共振时的动力学响应。利用伽辽金法得到两自由度非线性振动微分方程组,并通过数值计算得到系统发生超谐-内联合共振时前两阶模态的响应图。结果表明,内共振的存在使得高阶模态被间接激发,不同参数下系统呈现出混沌、概周期运动等复杂动力学响应,可以通过调节磁场强度控制系统振动。In this paper,the dynamic response of the rectangular thin plate with one side fixed and three sides simply supported in a transverse constant magnetic field is studied at its superharmonic resonance under 1∶3 internal resonance.The two degrees of freedom nonlinear vibration differential equations are derived by the Galerkin method.Through numerical calculation,the response diagrams of the first two modes of the system are obtained under superharmonic internal resonance.The results show that the high-order modes are indirectly excited by internal resonance.Under different parameters,the system presents complex dynamic responses such as chaos and quasi-periodic motion,and the vibration of the system can be controlled by adjusting the magnetic field intensity.

关 键 词：磁弹性 矩形薄板 内共振 超谐波共振 

分 类 号：TM151[电气工程—电工理论与新技术] O322[理学—一般力学与力学基础]