磁场中旋转圆环板的气磁弹性动力稳定性

研究磁场作用下导电旋转圆形环板受气动载荷的磁弹性行波动力学特性问题。应用哈密顿原理推导出磁场作用下旋转运动圆板的磁弹性振动控制方程，给出电磁力和气动载荷的表达式。根据边界条件设定行波特性振型函数，应用伽辽金积分推得行波动力学特征方程。通过算例，得到磁场中旋转运动圆环板在不同空气动力载荷作用下的前、后行波振动频率变化曲线和不同阶模态下的临界转速值，分析了气磁弹性条件对不同阶模态振动频率和阻尼的影响，分别讨论了基于振动频率和阻尼的临界转速变化规律及动力失稳特性。结果表明，磁场、空气动力载荷、转速等参数对旋转圆板的行波振动有显著影响。

MAGNETOELASTIC DYNAMICS STABILITY ANALYSIS OF A ROTATING ANNULAR PLATE SUBJECTED TO AERODYNAMIC LOAD

The traveling wave dynamics characteristics of a conductive rotating annular plate subjected to aerodynamic load in a magnetic field was investigated. Firstly, the aeroelastic vibration control equation of a rotating annular plate in magnetic field was derived according to the Hamilton's principle. Then, the mode shape function was set based on the boundary conditions. The vibration frequency changes of the forward and backward traveling waves of the rotating annular plate were investigated. The critical speed of occurring standing wave instability in each mode were captured by the Galerkin integral method. Also, with the changes of magnetic intensity and aerodynamics load, the corresponding vibration modes and magneto-aero damping are changed. The vibration frequency of the rotating annular plate also changed with the changing of aerodynamic load in the same magnetic field. The impact on the critical speed of the changing of aerodynamic load in each vibration mode was also studied. The results showed that the traveling wave vibration would be affected obviously by the magnetic field, speed, aerodynamic load and other parameters.