电磁与周期载荷作用下导电薄板的稳定性分析

摘要

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.%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。