Vibration of high-speed rotating rings coupled to space-fixed stiffnesses

This study investigates the vibration of high-speed rotating rings coupled to space-fixed discrete stiffnesses. The ring radial and tangential deformations are defined using space-fixed (Eulerian) coordinates, where material particles pass through fixed locations in space. Engineering strain is used in the strain energy expression. The derived nonlinear equations from Hamilton's principle are linearized about the steady non-trivial configuration that results from constant ring rotation. Comparisons are made to other models in the literature that use different assumptions. The governing equations are cast in terms of matrix differential operators that reveal the system's standard gyroscopic system structure. The natural frequencies and vibration modes are calculated over a wide-range of rotation speeds for axisymmetric free rings and a non-axisymmetric ring with a space-fixed discrete stiffness element.