磁场环境下导电圆形薄板的磁弹性强迫振动

研究了电磁场环境下机械载荷作用圆形导电薄板的磁弹性强迫振动问题。首先给出了圆形薄板的磁弹性轴对称振动方程,并依据麦克斯韦方程,得到了相应的电磁场方程和电磁力表达式,在此基础上,对横向恒定磁场中周边固支和周边简支边界约束圆板的振动问题进行了分析。基于位移函数的设定,应用伽辽金法,推得了导电圆板的磁弹性强迫振动微分方程。通过数值计算,得到了两种边界约束条件下圆板磁弹性振动的幅频和相频曲线图,并对结果进行了分析,讨论了磁感应强度和板厚等参数对系统振动特性的影响。

FORCED VIBRATION OF A THIN ROUND CONDUCTIVE PLATE IN MAGNETIC FIELD

Magnetoelastic forced vibration of a thin round plate subjected to mechanical loading in magnetic field is studied. Based on axisymmetric vibration equations, electromagnetic field equations and electromagnetic forces derived form Maxwell’s equations, the vibration problem of a round plate with clamped and simple support boundary is analyzed in the uniform magnetic field. With the aid of displacement mode hypothesis, the differential forced vibration equation is obtained by using of Galerkin method. By numerical method, the amplitude-frequency resonance and phase-frequency are gained, and the influences of magnetic induction as well as plate thickness on vibration characteristics are discussed.