载流简支微梁在磁场中的磁弹性随机振动  

Magneto-elastc random vibration of a current carrying simply supported micro-beam in a magnetic field

作　　者：王平[1,2,3] 王东贤[1,2] 姚杰 Wang Ping;Wang Dongxian;Yao Jie(College of Sciences,Yanshan University,066004,Qinhuangdao,China;Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures of Hebei Province,066004,Qinhuangdao,China;The State Key Laboratory of Nonlinear Continuum Mechanics(LNM),100080,Beijing,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]中国科学院力学研究所非线性力学国家重点实验室(LNM),北京100080

出　　处：《应用力学学报》2020年第6期2567-2573,I0017,I0018,共9页Chinese Journal of Applied Mechanics

基　　金：河北自然科学基金(A2016203101);河北省高等学校科学技术研究青年基金资助;北京大学湍流与复杂系统国家重点实验室开放课题资助。

摘　　要：研究了简支微梁在磁场中的随机振动。基于修正的偶应力理论及磁弹性理论建立了外加磁场情况下载流微梁的运动方程,导出了微梁的磁弹性随机振动方程。利用模态分析法分别得到了外加磁场情况下通入平稳和非平稳随机电流时微梁的随机位移响应的均值、功率谱密度函数等数字特征。对通入平稳随机电流的简支微梁进行了算例分析,并绘制了在不同随机电流、磁场强度和本征长度下的位移响应功率谱密度图。计算结果表明,耦合项的存在使得振动响应能量发生了很大的变化,对微梁的疲劳寿命也会产生显著的影响,通过改变随机电流和磁场强度来改变振动能量的分布规律,进而可以达到控制微梁随机振动的目的。The random vibration of simply supported micro-beam in magnetic field is studied in this paper. Based on the modified couple stress theory and magneto-elastic theory, the motion equations of downloading micro-beam in the external magnetic field is established, and the magneto-elastic random vibration equations of micro-beam is derived. The mean value of the random displacement response and the power spectral density function of the beamunder the condition of external magnetic field are obtained by using the modal analysis method. An example of a simply supported micro-beam with steady random current is giving, and the power spectral density diagram of displacement response under different random current, magnetic field strength and intrinsic length are drawn. The results show that the random vibration of the micro-beam can be controlled by controlling the intensity of the random current and magnetic field.

关 键 词：随机振动 简支微梁 磁弹性理论 功率谱密度函数 

分 类 号：O324[理学—一般力学与力学基础]