Elastic vibration of rotationally ring-shaped periodic structure subjected to three-axis angular velocity components

Abstract

The elastic vibration of rotationally ring-shaped periodic structure (RRPS) subjected to angular velocities applied about three orthogonal directions are examined. An analytical model having in-plane radial and tangential displacements is developed by using Hamilton's principle. The modeling leads to a partial differential equation with revolution effect, based on which the eigenvalue splitting, mode contamination and vibration instability are examined by focusing on their evolutions with the support count, support strength and revolution speed. The eigensolutions are formulated by perturbation-superposition method. The results imply that the splitting, contamination and instability follow similar rules with those of stationary RRPS, which are heavily affected by the revolution speed. The dependence of parameters on eigensolutions and especially the relationships between eigenvalue splitting and principal instability, and those between mode contamination and combination instability are demonstrated based on a sample RRPS. The principal instability can occur at splitting eigenvalues, and the combination instability can arise in the presence of mode contamination. Main results are compared with the existing ones in the open literature.