分析载流圆板在磁场中的磁弹性随机振动问题。根据薄板、薄壳体的磁弹性运动方程和连续体的随机振动理论,导出在磁场环境中圆板的磁弹性随机振动方程。对磁场中的载流圆板进行随机响应分析,得到圆板位移响应的自相关函数、功率谱密度函数及均值函数等数字特征。通过具体算例,对处于外加磁场中通入平稳随机电流的导电圆板,计算其位移响应的功率谱密度函数。
The magnetic-elastic random vibration problem of a current-carrying circular plate in a magnetic field is studied. Based on the magneto-elastic theory and the random vibration theory of a continue system with distributed parameters, the magneto-elastic random vibration equation of a current carrying circular plate in a magnetic field was derived. The stochastic response analysis of the circular plate in a magnetic field was finished. The auto-correlation function, power spectral density function and the mean function of the random displacement response of the circular plate in a magnetic field were obtained. In a specific example, the power spectral density function of the displacement response of the circular plate with stationary random current was calculated.