电磁与周期载荷作用下导电薄板的稳定性分析  

A Stability Analysis of Current-conducting Thin Plate under Electromagnetism and Periodic Load

作　　者：李晶[1] 周小利[2] 

机构地区：[1]唐山学院基础教学部,河北唐山063000 [2]河北工程大学土木工程学院,河北邯郸056038

出　　处：《唐山学院学报》2014年第3期8-11,共4页Journal of Tangshan University

基　　金：河北省自然科学基金项目(E2010001254)

摘　　要：基于麦克斯威尔方程,给出导电薄板的非线性磁弹性振动方程,以及磁场环境下的电动力学方程和电磁力表达式。在此基础上,应用伽辽金法导出相应的非线性振动微分方程组,研究横向恒定磁场中周期载荷作用下梁式薄板的稳定性问题。根据李雅普诺夫近似稳定性理论,对稳态解的稳定性进行分析,得到稳定性的判定条件。通过对算例特征值的求解对振动的稳定性进行分析。Based on the Maxwell equations,the authors of this paper work out the nonlinear mag-neto elastic vibration equation of the thin conductive plate,the dynamic equation and the electro-magnetic force expression in the field environment.On this basis,nonlinear vibration differential equations are derived by using Galerkin method to study the stability of beam sheets under the pe-riodic load of transverse constant magnetic field.According to Lyapunov’s stability theory of ap-proximation,the authors study the stability of steady-state solutions,get the decision conditions of stability and analyze the stability of numerical examples according to their eigenvalues.

关 键 词：磁弹性 导电薄板 周期载荷 组合共振 稳定性 特征值 

分 类 号：O322[理学—一般力学与力学基础]