Limitations of an inextensible model for the vibration of high-speed rotating elastic rings with attached space-fixed discrete stiffnesses

This study examines the inextensible vibration of rotating elastic rings coupled to space-fixed discrete stiffnesses. For axisymmetric, rotating, elastic rings without discrete stiffnesses, closed-form solutions for the natural frequencies are derived. Galerkin's method is used to determine the natural frequencies for systems with attached discrete stiffnesses. Limitations of the inextensible ring model compared to the extensible one are demonstrated. The inextensible elastic ring model works poorly at high rotation speeds. For systems with discrete stiffnesses the inextensible ring model does not accurately predict vibration modes that have large strain energy in the discrete stiffnesses.