磁场中简支矩形薄板的非线性稳态随机振动  

Nonlinear stationary random vibration of a rectangular thin plate in a magnetic field

作　　者：涂建新[1] 王知人[1] 王平[2,3] 

机构地区：[1]燕山大学理学院,秦皇岛066004 [2]燕山大学建筑工程与力学学院,秦皇岛066004 [3]中国科学院力学研究所国家非线性力学重点实验室,北京100080

出　　处：《振动与冲击》2015年第8期36-40,共5页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(11172024);河北省自然科学基金资助项目(A2012203140)

摘　　要：根据电动力学理论、板壳磁弹性理论和结构随机振动理论,导出电磁场中矩形薄板的磁弹性非线性随机振动方程,然后利用伽辽金法对四边简支矩形薄板的非线性随机振动方程进行整理,得到伊藤型状态方程;在外界激励是平稳高斯白噪声的条件下,利用稳态的FPK方程法求解得到薄板的稳态随机振动位移和速度响应的多个数字特征;通过具体数值算例分析,讨论了电磁参数对各数字特征的影响。According to the theory of electrodynamics,the magneto-elastic theory of plates and shells,and the theory of structure＇s random vibration,the magneto-elastic nonlinear random vibration equation of a plate simply supported in an electromagnetic field was derived.And then,the nonlinear random vibration equation was changed into an ITO equation using Galerkin method.The statistical characteristics of the displacement and velocity responses of the plate＇s stationary random vibration were obtained by using FPK equations method when the external excitation was stationary Gauss white noise.The influences of the parameters of the electromagnetic field on the statistical characteristics were discussed with numerical examples.

关 键 词：磁弹性 非线性 随机振动 矩形薄板 

分 类 号：O326[理学—一般力学与力学基础]