Forced Harmonic Response of Grouped Blade Systems: Part I—Discrete Theory

Abstract

The vibration of grouped blades on a flexible disk cannot be analyzed using procedures developed for individual, uncoupled groups. The bladed-disk system must be considered either in whole, or as a structure composed of cyclically symmetric sectors. The latter approach, while being computationally more economical, is more complicated to implement because both the structural system and the applied forces must be transformed to a system based on the geometry of a single sector. However, the sector transformation permits a natural ordering of the modes that cannot be obtained from a complete system model. This paper describes the development of the sector model, and the associated transformation of the applied harmonic forces typically prevalent in turbomachinery. The displacements are expressed in a series of the natural modes of a transformed sector, and expressions are developed for maximum displacements of the complete structure. This approach leads to an easier interpretation of the analytical results and an improved physical understanding of the response. For example, it is shown that a single harmonic, or engine-order excitation, can cause response in only a restricted subset of modes.