旋转圆环动态特性的行波解

A traveling wave approach for dynamic characters of rotating circular rings

基于固体弹性介质中的行波理论,对旋转圆环的固有频率进行了计算。以扩张弯曲梁微元体的运动方程为基础,分析了运动条件下该波导中行波的色散关系。通过分离正行波数和负行波数,解决了行波法计算旋转圆环的固有频率问题。同时给出了波数分离的判断依据,并结合简谐波动的相位封闭原理和传递矩阵建立了旋转圆环的特征方程。数值模拟研究了旋转体的固有动态特征,并与有限元方法比较,说明所建模型中假设的有效性和计算结果的可靠性。

Based on the traveling wave theory in solid medium,the fundamental frequency of a rotating circular ring is calculated.According to a governing equation of motion with effects of extensional neutral axis,dispersion relations of the traveling wave in the waveguide for the motion conditions are analyzed.After the separation of the positive traveling wave number and the negative traveling wave number,the fundamental frequency problem for the rotating circular rings can be calculated by means of the traveling wave approach.Meanwhile,an evaluation criterion for the wave number separation is given,and the secular equations of a rotating circular ring are established by the combination of the phase-closed principle and the transfer matrices.The effectiveness of the presented approach is illustrated by an example of numerical computation for the dynamic characters of a rotating circular ring,and the results obtained by the approach are in good agreement with those of FEA.