高维动力系统在转子稳定性分析中的应用

研究了高维周期性变系数动力系统在转子稳定性分析中的应用，针对转子在有限元离散后产生的周期性高维动力系统，提出了一种新的稳定性分析方法.利用Floquet Lyapunov理论，通过求解Floquet乘子矩阵对数的方法，将周期性高维动力系统转换成等效的常系数动力系统.通过求解该等效系统的Lyapunov方程，判定原系统的稳定性.该方法避开了求解Floquet乘子矩阵全部特征值或最大特征值的难点，可用于分析实际工程中多转盘高速转子的稳定性.

Application of high-dimensional dynamic system in rotor stability analysis

A new approach was proposed to investigate the stability of a periodical time-variable high-dimensional dynamic system based on rotor's FEM model.Based on Floquet-Lyapunov theory,the periodical time-variable high-dimensional dynamic system was transformed into an equivalent linear system with constant coefficients by solving the logarithm of Floquet multipliers matrix.Then the stability of the original dynamic system was determined by solving the Lyapunov's equation of the equivalent system.The approach avoids the solution of all eigenvalues of the Floquet multipliers matrix or the maximal eigenvalue of the matrix, which is important for stability analysis of high-speed multi-dial rotors in engineering.