旋转运动导电圆环板磁弹性参数-谐波联合共振  

Magneto-elastic combination multidimensional resonance of a rotating annular plate in magnetic field

作　　者：李哲[1,2] 胡宇达[1,2] 彭艳[3] Li Zhe;Hu Yuda;Peng Yan(School of Civil Engineering and Mechanics,Yanshan University,066004,Qinhuangdao,China;Hebei Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures,Yanshan University,066004,Qinhuangdao,China;School of Mechanical Engineering,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 [3]燕山大学机械工程学院,秦皇岛066004

出　　处：《应用力学学报》2021年第3期1176-1184,共9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);燕山大学博士基金(BL19001);秦皇岛市科学技术研究与发展计划(201902A025)。

摘　　要：针对双向磁场中旋转运动圆环板非线性非轴对称参数-谐波联合共振问题进行研究。在非线性轴向和径向振动方程的基础上,给出了旋转圆环板的位移表达式。通过分离变量法对位移函数进行了设定,分析求解了方程中的静载荷项。应用伽辽金积分法,得到了内部固定外部自由边界约束条件下旋转运动圆环板的振动方程组。运用多尺度法对系统的非线性参数-谐波联合共振问题进行了求解,得到了稳态运动下的幅频响应方程。通过数值计算,得到了不同方向磁感应强度和外激励以及几何参数变化时系统共振幅值变化规律曲线图,分析了参数变化对系统非线性动力学行为的影响。结果表明:随着纵向磁感应强度增加,系统联合共振幅值及多值解个数减少。The nonlinear non-axisymmetric resonance for a thin annular plate in transverse and longitudinal magnetic fields is investigated.The expressions for displacements of the transverse and longitudinal vibrations are assumed to solve the equations containing static load term.The vibration equations of rotating circular plate with fixed internal and external free boundary constraints are obtained through the application of the Galerkin method.Then,the method of multiple scales is applied to solve the nonlinear parameter-harmonic combination resonance,and the amplitude-frequency response equations of steady-state motion are obtained.By the numerical computations,the curves of vibration amplitude of the system versus different parameters are obtained,and the influence of parameters on nonlinear dynamic behaviors of the system is analyzed.The results show that when the parameters or initial conditions change,the amplitude-frequency response curves of the system and multi-valued properties change significantly.

关 键 词：圆环板 非轴对称 谐波共振 参数振动 多尺度法 

分 类 号：O322[理学—一般力学与力学基础] O442[理学—力学]