软铁磁矩形薄板非线性运动的扩展伽辽金法近似分析  

Approximate analysis of nonlinear motion of soft ferromagnetic rectangular thin plate by extended Galerkin method

作　　者：王奥 陈东 曹立染 WANG Ao;CHEN Dong;CAO Liran(School of Civil Engineering,Anhui Jianzhu University,Hefei 230601,China)

机构地区：[1]安徽建筑大学土木工程学院,安徽合肥230601

出　　处：《陕西理工大学学报（自然科学版）》2023年第6期87-92,共6页Journal of Shaanxi University of Technology:Natural Science Edition

基　　金：安徽省教育厅高校自然科学研究项目(KJ2021A0608)。

摘　　要：研究了磁场环境下,四边简支的软铁磁矩形薄板的非线性运动行为。采用磁偶极子模型,考虑因涡电流而在板的中面受到的分布力,推导出软铁磁矩形薄板的非线性运动偏微分方程;利用分离变量法及伽辽金法,将系统运动偏微分方程转化为Duffing方程的一般式。对一个运动周期内的加权运动方程进行积分,以消除变形函数中的谐波。对一般的伽辽金方法进行扩展,从而得到非线性微分方程的频率近似解。The nonlinear motion behavior of a soft ferromagnetic rectangular thin plate simply supported on four sides in a magnetic field is studied.Using the magnetic dipole model,the nonlinear motion partial differential equation of the soft ferromagnetic rectangular thin plate is deduced considering the distributed force on the mid-plane of the plate due to eddy currents;using the separation variable method and the Galerkin method,the partial differential equation of system motion is transformed into the general formula of Duffing equation.The general Galerkin method is extended by integrating the weighted motion equations over a motion cycle to eliminate harmonics in the deformation function,resulting in frequency approximate solutions to nonlinear differential equations.

关 键 词：软铁磁矩形薄板 磁场 扩展伽辽金方法 非线性运动 频率近似解 

分 类 号：O322[理学—一般力学与力学基础]