研究磁场作用下导电旋转圆形薄板的行波动力学特性问题.根据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,根据边界条件设定行波特性振型函数,应用伽辽金积分得到了行波动力学特征方程.通过算例分析旋转运动圆板在磁场作用下的前、后行波振动频率变化和各阶模态的临界转速与振动失稳问题,并得到了圆形薄板临界转速对应各阶模态的变化规律,分析了不同磁场强度对各阶模态振动频率的影响曲线和不同振动模态阻尼的变化曲线,以及相同磁场作用下旋转圆板厚度变化对振动频率和临界转速的影响曲线.结果表明:磁场、转速、板厚等参数对旋转圆板的行波振动有显著影响.%The dynamical characteristics of the traveling waves of a conductive rotating circular plate in magnetic fields are investigated.Firstly,the governing vibration equation of a thin circular rotating plate in magnetic field is derived based on Hamilton's principle.Then,the traveling wave dynamical equation is derived through assuming proper mode shape function according to the boundary condition and using Galerkin method.The variation of the vibration frequency of the forward traveling wave and the backward traveling wave,the critical rotational speed and the instability of each mode are then investigated with some examples.The relation curves between the magnetic strength and the vibration frequency as well as the damping of each mode,the relation curve between the thickness of the plate and its vibration frequency as well as the critical speed are also presented.The results show that the traveling wave vibration would be affected significantly by the magnetic field,the speed,the thickness and other system parameters.
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