Vibration Characteristics of a Ring Under General Boundary Conditions using Euler-Bernoulli and Timoshenko Theories

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  • Ring vibration analysis is more challenging than straight beams analysis. In straight beams, the structural deformations depend on rotational and translational displacements; however, in rings, in addition to these, they also depend on the coupled tangential displacement caused by the curvature of structures. In this study, the free in-plane vibration problem for thin- and thick-walled rings are solved, and the explicit relationships between the radial, tangential, and rotational displacements are revealed. This paper introduces an analytical method for finding exact solutions for the natural frequencies and associated mode shapes of a ring under general boundary conditions. Both Euler-Bernoulli and Timoshenko theories are used in this work, and the corresponding results are compared.

    Part of the Proceedings of the Canadian Society for Mechanical Engineering International Congress 2022.

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    Article (Published)
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    Attribution-NonCommercial 4.0 International