线载和弹性支承作用面内运动薄板磁固耦合双重共振  

Double Resonance of Magnetism-Solid Coupling of in-Plane Moving Thin Plates With Linear Loads and Elastic Supports

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

机构地区：[1]燕山大学建筑工程与力学学院,河北秦皇岛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,河北秦皇岛066004

出　　处：《应用数学和力学》2021年第7期713-722,共10页Applied Mathematics and Mechanics

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

摘　　要：针对磁场环境中具有线载荷和弹性支承作用的面内运动薄板,给出了系统的势能、动能及电磁力表达式,应用Hamilton变分原理,推得面内运动条形板的磁固耦合非线性振动方程.考虑边界为夹支-铰支的约束条件,利用变量分离法和Galerkin积分法,得到了含简谐线载力和电磁阻尼力项的两自由度非线性振动微分方程组.应用多尺度法对主-内联合共振问题进行解析求解,得到了双重联合共振下系统的一阶状态方程和共振响应特征方程.通过算例,得到了面内运动薄板的一阶和二阶共振幅值变化规律曲线图,分析了不同作用量和载荷位置对系统振动特性的影响.结果表明:系统发生主-内双重共振时,解的多值性和跳跃现象明显,弹性支承和线载荷位置对共振现象影响显著;一阶和二阶的共振多值解区域同时出现同时消失,体现了明显的内共振特征.For the in-plane moving thin plates with linear loads and elastic supports in magnetic field,the potential energy,the kinetic energy and the electromagnetic force expressions of the system were given.Based on the Hamiltonian variational principle,the magnetism-solid coupling nonlinear vibration equation for the in-plane moving strip plate was deduced.For the clamped-hinged boundary condition,the variable separation method and the Galerkin method were employed to obtain the 2DOF nonlinear vibration differential equations containing the simple harmonic linear load and the electromagnetic damping force terms.The multiscale method was used to analytically solve the principal-internal resonance problem,and the 1st-order state equation and the resonance response characteristic equation for the system under the double joint resonance were obtained.Through numerical examples,the 1st-and 2nd-order resonance amplitude curves of the in-plane moving thin plate were obtained.The effects of different parameters and load positions on vibration characteristics of the system were analyzed.The results show that,for the principal-internal resonance occurring in the system,the multivaluedness and jumping phenomenon of the solution are obvious,and the effects of the elastic support and the linear load position on the resonance are significant.Additionally,the 1st-and 2nd-order resonance multivalued solution areas appear and disappear simultaneously,which reflects obvious internal resonance characteristics.

关 键 词：薄板 磁固耦合共振 面内运动 线载荷 弹性支承 多尺度法 

分 类 号：O322[理学—一般力学与力学基础] O442[理学—力学]