Nonlinear Random Vibration Of A Sandwich Plate In A Magnetic Field

The sandwich plates and sandwich shells is a new style of structural member. Thesandwich has more advantage than ordinary single-layer board, such as high rigidity, lightmass, vibration and noise reduction, sound insulation and so on. Hence the sandwich plateis applied widely to aeronautic and shipbuilding and some industry.This paper studies the nonlinear random vibration of rectangular sandwich plate inthe magnetic filed. This paper analyzes, in detail, the nonlinear random vibration offour-edge simple supported rectangular sandwich plate and four-edge fixed rectangularsandwich plate in transverse magnetic field and in longitudinal magnetic field. Based onthe magnetic elastic theory of plate and shell, according to the bending vibration theory ofsandwich plate and the random vibration theory of continuum system, the nonlinearrandom vibration equation of four-edge simple supported rectangular sandwich plate andthe nonlinear random vibration equation of four-edge fixed rectangular sandwich plate intransverse magnetic field and in longitudinal magnetic field are obtained. The precedingequations are simplified by using Galerkin Principle, and then the displacement responsevariance and probability density and the velocity response variance and probability densityare solved through the FPK equation method. Take four-edge simple supported rectangularsandwich plate and four-edge fixed rectangular sandwich plate in transverse magneticfield as examples. Passing analysis of examples and drawing by Matlab program, get thefigure of displacement response variance and probability density, and the figure ofvelocity response variance and probability density. Then the author analyzes the effects ofdifferent parameters on the variance and probability density. Through the change ofmagnetic field and mechanical field and thickness of sandwich plate, we could wellcontrol variance and probability density occurring large displacement of random vibrationof sandwich plate.