A Novel Algorithm for Coupled Vibration Characteristics of Cyclically Symmetric Structures

When rotating machinery operates at high speeds, the interaction between the rotor and blades becomes highly pronounced, necessitating treatment of the rotor-blade system as an integrated entity when examining its vibration characteristics. However, the coupled system's large number of degrees of freedom poses significant challenges. One of the most prominent issues with traditional finite element methods is the extremely high order of the coefficient matrix, which leads to substantial computational demand. Recognizing the cyclic symmetry intrinsic to rotating machinery, this study introduces a novel algorithm intended for efficient analysis of the coupled vibration characteristics of cyclically symmetric structures. Grounded in modal superposition and cyclic symmetry theory, the algorithm partitions the rotor and blades into multiple substructures. First, the internal degrees of freedom in these substructures are condensed, and then cyclic interface displacement compatibility is applied to couple the rotor and blades into a unified system. This process significantly decreases both the total degrees of freedom in the coupled system and the order of the coefficient matrix. To validate the approach, the proposed algorithm was implemented in Matlab for a specific test case. The results indicate that the computed vibration frequencies deviate by no more than five percent from those obtained through conventional software. Additionally, the coupled mode shapes align closely with those reported in the literature, and the required computation time is only 45 percent of the original duration. These findings highlight the practicality and feasibility of the proposed algorithm for analyzing cyclically symmetric structures.