周边夹支旋转运动圆板磁弹性谐波共振分析  

Electro-magnetic elastic harmonic resonance analysis of a periphery fixed rotating circular plate

作　　者：胡宇达[1,2] 秦晓北 姚臻臻[3] 

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]新疆工程学院基础教研部,乌鲁木齐830000

出　　处：《应用力学学报》2018年第4期709-714,共6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(A2015203023);新疆工程学院科研基金项目(2014xgy141612)

摘　　要：针对磁场环境下做旋转运动导电圆形薄板的谐波共振问题进行分析。通过位移函数的设定及伽辽金法的运用,得到了周边夹支约束下旋转运动导电圆板的磁弹性轴对称非线性振动微分方程。采用多尺度法对旋转圆板的磁弹性超谐波共振和亚谐波共振进行求解,得到了两种共振情况下的幅频响应方程。通过数值算例,得到了共振幅值随不同参数变化的响应曲线图以及时程图、相轨迹图、庞加莱映射图等计算结果并进行了分析。结果表明:系统的旋转速度、磁场强度、激励力等参量对系统的谐波共振的共振幅值、运动形态有显著影响,并能使系统幅值解实现单值到多值的变化,同时体现了复杂的非线性特性。The harmonic resonances for a conductive rotating circular plate in magnetic field are investigated. According to the vibration equation of the rotating circular plate in magnetic field, the dimensionless equation is derived through the displacement function and application of Galerkin method. The multi-scales method is applied to solve the harmonic resonance and sub-harmonic resonance of rotating plate, and the amplitude-frequency response equations are obtained. By a numerical example, the response curves with different parameters and the corresponding response curve, waveform graph, phase plot and Poincare map are obtained and analyzed. According to the results, the parameters such as rotating speed, magnetic induction and excitation force have a significant influence on the harmonic resonance and movement forms, and make the solution of system change from single solution to multiple solutions. Meanwhile the system shows the complex non-linear characteristics.

关 键 词：旋转运动圆板 磁弹性 谐波共振 多尺度法 

分 类 号：O322[理学—一般力学与力学基础] O442[理学—力学]