The presented work examines the dynamic behavior of an asymmetric rotor with asymmetric flexible disk, contrary to previous works on the subject, where researchers examined the effect of either rigid disk asymmetry or disk flexibility at a time. Account for the asymmetry of flexible disk in rotors constitutes the new contribution in this work. The suggested mathematical model combines Lagrangian approach with Rayleigh–Ritz method to derive the governing equations of motion of the rotor. Account for asymmetry of the flexible disk results in complicated and lengthy expressions for the potential and kinetic energies of the rotor, required in the adopted Lagrangian approach. Using symbolic computation simplified the derivation of the governing equations of motion with constant coefficients in terms of rotating coordinate system. Solution of the resulting eigenvalue problem provided numerical results for rotors with symmetric and asymmetric flexible disks, required to assess the effect of disk flexibility and asymmetry on the resulting frequencies and stability boundaries of the examined rotor system.

提出的工作检查了具有不对称柔性盘的不对称转子的动力学行为，这与之前在该主题上进行的研究相反，研究人员一次检查了刚性盘不对称或盘柔性的影响。转子中柔性磁盘的不对称性构成了这项工作的新贡献。建议的数学模型将拉格朗日方法与瑞利-里兹方法结合起来，得出转子运动的控制方程。考虑到软盘的不对称性，导致采用的拉格朗日方法需要复杂且冗长的转子势能和动能表达式。使用符号计算简化了在旋转坐标系方面具有恒定系数的运动控制方程的推导。