Transfer Matrix Method for Calculating Rotor Natural Frequencies

The transfer matrix method for calculating rotor natural frequencies incorporates various computational techniques such as Prohl's method, Ricatti's method, and other advanced numerical approaches. This methodology is extensively applied in rotor dynamics and represents a robust approach for determining rotor natural frequencies. The implementation typically involves constructing state vectors at discrete rotor stations and computing transfer matrices that relate these vectors across different sections. These matrices are derived by solving the rotor's equations of motion, often through numerical integration techniques. The natural frequencies are identified by solving the eigenvalue problem formulated through the boundary conditions and the overall transfer matrix. The method proves particularly valuable for complex rotor systems where analytical solutions are impractical, as it efficiently handles systems with multiple disks, bearings, and variable cross-sections through systematic matrix operations. Key implementation aspects include proper discretization of rotor elements, numerical stability considerations for Ricatti's method, and efficient eigenvalue solvers for large-scale systems.