摘要
基于麦克斯韦方程和弹性动力学理论,导出了纵向磁场中导电薄板的非线性磁弹性耦合振动方程和电动力学方程,运用伽辽金法推得了两对边简支导电条形板的达芬型振动方程。针对亚谐波共振问题,应用多尺度法进行求解,得到了相应的近似解析解和幅频响应方程以及非平凡解存在条件。应用李雅普诺夫稳定性理论,对解的稳定性进行了分析,得到了稳态解稳定性的判别式。通过数值计算,得到了非平凡解存在域、振幅特性变化曲线图及动相平面轨迹图,分析了电磁、机械等参量对系统共振特性的影响。
Based on the Maxwell equations and elastic dynamics theory,the electrodynamics equation and the nonlinear magneto-elastic coupling vibration equation of a current-conducting thin plate in a longitudinal magnetic field are deduced.By Galerkin method,the Duffing type vibration equation of the current-conducting strip plate with its two opposite sides simply supported is obtained.To the subharmonic resonance,the method of Multiple Scales is used to solve the equations.The corresponding approximately analytical solution,the amplitude-frequency response equation and the existential condition of nontrivial solutions are derived.According to Lyapunov stability theory,the stability of the solution is analyzed,and the discriminant of steady solutions is obtained.By numerical calculations,the existential region of nontrivial solutions,amplitude characteristic curves and phase trajectories in a moving phase plane are obtained.The effects of electro-magnetic and mechanical parameters on system resonance characteristics are analyzed.
出处
《工程力学》
EI
CSCD
北大核心
2011年第2期223-228,共6页
Engineering Mechanics
基金
河北省自然科学基金项目(E2010001254)
关键词
磁弹性
导电薄板
亚谐波共振
磁场
多尺度法
magnetoelasticity
current-conducting thin plate
subharmonic resonance
magnetic field
method of multiple scales
