Vibration analysis of a multi-span rotating ring with ray tracing method

• The ray tracing method is more efficient and faster approach in the dynamic modeling of rotating structures.
• The ray tracing method is able to significantly reduce the computational complexity of the characteristic equation and the impulse response.
• It can be extended to calculate the complex rotating structures.

A ray tracing method is applied to analyze both the free and forced responses in a rotating multi-span section ring. In this paper, element coordinates are established and coupled by dispersion and transmission matrices. Structure vibration displacements are expressed in a wave form with a combination of propagation, fast-attenuating and near-field waves. Meanwhile, an exciting force is considered as a point discontinues with different elements on both sides. The wave reflection and transmission matrices are introduced through coupling different elements by applying wave transmission coefficients and transfer matrices. For numeric computation, the reflection and transmission matrices are assembled, independent waveguide elements are integrated and the responses of rotating rings with non-uniform section area are derived. The structure modeling and a numeric computation with corresponding solutions illustrate the validity of the presented approach. The investigation result also shows that the presented approach can be extended to compute accurately on the dynamic characteristics of a rotating complex structure (high speed bearing cage).