Comparison of complete and simplified models in terms of eigenvalues of cyclically symmetric ring structures

Abstract

This work examines the free and parametric vibrations of constrained cyclically symmetric ring structures and compares the restrictions from different modeling assumptions. A complete model and two simplified models are developed by introducing different restrictions on deflections. The eigenvalues are formulated by direct perturbation and mode superposition. The results verify that they are comparable on the condition that the stiffness ratio of the rotating support to ring bending is relatively small. The eigenvalue splitting, parametric instability and their relationships are determined in closed form. The simplified models can correctly predict the splitting behavior before or after the loci veering. Two types of models obtain the same rules governing the instability, but the simplified models cannot accurately approach the time-evolution of the instability. Hence, it needs to be cautious to use the simplified models to estimate the instability behaviors for a cyclically symmetric ring structure with larger stiffness ratios especially within the loci veering range. Main results are verified by numerical calculations.