微尺度载流纳米板在磁场中的磁弹性随机振动
Magnetoelastic random vibration of micro-scale current-carrying nanoplates in a magnetic field
摘要
研究了四边简支矩形微板在磁场及随机电流作用下的磁弹性随机振动问题。应用非局部弹性理论和板壳磁弹性理论建立外加磁场中载流微板的运动方程,导出了微板的磁弹性随机振动方程; 采用模态分析法对其进行了位移响应分析,得到了在通入平稳和非平稳随机电流时微板的随机位移响应的均值、功率谱密度函数等数字特征。针对具体算例,在通入平稳随机电流的情形下,得到了位移响应的功率谱密度函数,并绘出了板中心点的位移响应功率谱密度图。结果表明:耦合项对振动响应带宽有很大的影响,当考虑耦合项时,振动能量主要分布在0～20 Hz带宽范围内,且随着随机电流和磁场强度的增加,振动能量集中分布带宽变窄。根据此性质可以有效地降低振动的发生或减少振动的破坏,对微结构系统的结构检测和故障诊断等问题起到参考作用。
Abstract
The magnetoelastic random vibration of a simply supported rectangular micro-plate with four sides under the action of magnetic field and random current is studied.The non-local elastic theory and the plate-shell magnetoelastic theory are used to establish the motion equation of the current-carrying micro-plate in an external magnetic field,and the magnetoelastic random vibration equation of the micro-plate is derived; the displacement response is analyzed by the modal analysis method,and the numerical characteristics such as the mean value of the random displacement response of the micro-plate and the power spectral density function when the steady and non-stationary random current are applied.For a specific example,in the case of a steady random current,the power spectral density function of the displacement response is obtained,and the displacement response power spectral density diagram of the center point of the plate is drawn.The results show that the coupling term has a great influence on the vibration response bandwidth.When considering the coupling term,it is mainly distributed in the range of 0-20 Hz.With the increase of random current and magnetic field strength,the bandwidth of the concentrated distribution of vibration energy becomes narrower.According to this property,it can effectively reduce the occurrence of vibration or reduce the damage of vibration,and play a reference role in structure detection and fault diagnosis of the micro-structure system.关键词
微板/磁弹性/随机振动/功率谱密度函数引用本文复制引用
王佳悦1,2, 王平1,2.微尺度载流纳米板在磁场中的磁弹性随机振动[EB/OL].(2023-11-09)[2026-04-05].https://chinaxiv.org/abs/202311.00197.学科分类
电工基础理论/力学/物理学
评论