导电薄板在纵向磁场中的谐波共振分析

基于Maxwell方程及Kirchhoff薄板基本假设,导出了导电薄板的非线性磁弹性振动方程、电动力学方程和电磁力表达式。在此基础上,研究了纵向磁场中横向机械动载作用下条形薄板的非线性谐波共振问题。针对两端简支边界条件情况,应用伽辽金法进行积分,导出了关于振动位移和电场强度函数的磁弹性耦合振动微分方程组。利用多尺度法进行求解,得到了共振下的幅频响应方程,并对定常解的稳定性进行了分析,得到了解的稳定性判定条件。通过数值计算,得到了共振振幅随调谐参数、激励力幅值和磁感应强度的变化规律曲线图,以及系统振动位移和电场强度的时程响应图,分析了电磁、机械等参量对共振现象及解的稳定性的影响。

Harmonic resonance of current-conducting thin plate in longitudinal magnetic field

Based on the Maxwell equation and Kirchhoff assumption of thin plate,nonlinear magneto-elastic vibration equation,electrodynamics equation,electromagnetic forces expressions of current-conducting thin plate are deduced.Furthermore,nonlinear harmonic resonance of thin strip-plate under lateral mechanical motive load in longitudinal magnetic field is studied.Considering the thin plate simply supported on two opposite sides,the magneto-elastic coupled vibration differential equations about function of displacement of vibration and electric field intensity are obtained by the method of Galerkin.Then,the amplitude-frequency re-sponse equation under resonance is derived by using method of multiple scales,and the stability of stable solution is analyzed;the discriminant of stable solutions is obtained.Through the numerical calculation,characteristic curves of amplitude changing with detuning parameter,the excitation amplitude and the magnetic intensity,and also the time history response plot of systemic dis-placement of vibration and electric field intensity are obtained.At last,the influence of electric-magnetic and mechanic parameter on resonance phenomenon and stability of solution are analyzed.