Complete and simplified models for estimating vibration instability of cyclically symmetric ring structures: comparison and validation

[+] Author and Article Information
Shiyu Wang

School of Mechanical Engineering, Tianjin University, Tianjin 300072, P. R. China; Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin 300072, P. R. China

Penghui Zhang

School of Mechanical Engineering, Tianjin University, Tianjin 300072, P. R. China

Wenjia Sun

China Automotive Technology & Research Center, Tianjin 300399, P. R. China

1Corresponding author.

ASME doi:10.1115/1.4038446 History: Received August 01, 2017; Revised November 05, 2017


In-plane vibration of cyclically symmetric ring structures is examined with emphasis on the comparison of instabilities estimated by complete and simplified models. The aim of this paper is to understand under what conditions and to what degree the simplified models can approach the complete model. Previous studies develop time-variant models and employ perturbation method by assuming weak support. In this work, the rotating-load problem is cast into a non-rotating-load problem. A complete model with time-invariant coefficients is developed in rotating-support-fixed frame, where the bending and extensional deformations are incorporated. It is then reduced into two simplified ones based on different deformation restrictions. Due to the time-invariant effect observed in the rotating-support-fixed frame, the eigenvalues are formulated directly by using classical vibration theory and compared based on a sample structure. The comparisons verify that the two types of models are comparable only for weak support, though the simplified models cannot accurately predict all unstable regions in particular for strong support. Even in the comparable regions, the corresponding eigenvalues are still different. For verification purpose, the time-invariant models are transformed into time-variant ones in the inertial frame, based on which numerical calculations using Floquét theory are made to estimate instability. Consistence between the time-invariant and -variant models verifies the comparison between the complete and simplified models.

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