Magnetic Field Of Current-carrying Plate And Shell Of Non-stationary Random Vibration Analysis

The magneto-elastic random vibration problems of the current carrying thin platesand the cylindrical shells in a magnetic field are studied in this paper. It mainly studies therandom vibration problems of a current rectangular thin plate or a cylindrical shellswitching on non-stationary random current or smooth white noise random current in alongitudinal or transverse magnetic field.According to the theory of plates and shells, the magneto-elastic theory and therandom vibration theory of continuum, the magneto-elastic random vibration equations ofthe plate and cylindrical shell in different magnetic fields are derived. Then one part of thecoupling term of the Lorentz force is assumed as the linear damping to the plate or shell,and the other as the non-stationary random uniform distribution load. And the digitalfeatures as like the mean of the random displacement response, power spectral densityfunction and autocorrelation function of the plate and cylindrical shell with non-stationaryrandom current or the white noise random current in the different magnetic fields.In view of the specific examples, the thin plate and shell switching on thenon-stationary random current or ideal white noise stationary random current are put in thelongitudinal and transverse magnetic field respectively. The power spectrum densityfunction and the mean square value function of the displacement response are calculatedrespectively. The maps of the displacement power spectral density, the velocity powerspectral density and the acceleration power spectrum density are drawn by using Matlabsoftware. The influences of the magnetic field intensity, the input current and the thicknessof the plate and the shell to random response are discussed. It is known that the greater themagnetic field intensity, the greater the damping and the smaller the random displacementresponse. It is also known that the different direction of magnetic field intensity and thetype of the current both can influence the random displacement responses of the plate andthe shell.