摘要
针对四边固支矩形薄板,以连续体的随机振动理论及板壳磁弹性基本理论为基础,导出了在外加磁场中通入非平稳随机电流情形下矩形薄板的磁弹性随机振动方程。将洛伦兹力耦合项中的一部份假设为薄板的一种阻尼,另一部分假设为非平稳随机均匀分布载荷,分别得到了外加磁场中通入非平稳随机电流时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,在通以非平稳随机电流的情形下,计算了其位移响应的功率谱密度函数和均方值函数,并绘出了板中心点的位移响应功率谱密度图、速度功率谱密度图及加速度功率谱密度图,并讨论了磁场强度及洛伦兹力耦合项对在非平稳随机电流下的随机位移响应的影响。
The magneto-elastic random vibration equation of a fixed rectangular plate in a magnetic field with non-stationary random current was derived based on magneto-elastic theory and the theory of of random vibration of continuous. The random displacement response of the plate was analyzed on the assumptions that one part of the coupled part of the Lorentz force is a kind of damping and the other part is random distributing load. The mathematical expectation, the auto-correlation function, the power spectral density function of the random displacement response of the plate with non-stationary random current were obtained. As an example, the power spectral density function and the mean square value function of the displacement response of a fixed plate with non-stationary random current were calculated. The diagrams of the power spectral density of the displacement response, velocity and acceleration at center point of the plate were shown here. The changes of the diagrams of the power spectral density indicated the effects of the coupled parts of the Lorentz force to the random displacement response.
出处
《机械强度》
CAS
CSCD
北大核心
2014年第5期676-681,共6页
Journal of Mechanical Strength
基金
河北省自然科学基金(A2012203140)
2013年非线性力学国家重点实验室开放基金资助~~
关键词
非平稳随机电流
磁弹性
随机振动
功率谱密度函数
Non-stationary random current
Magneto-elastic
Random vibration
Power spectral density function
