FORCED HARMONIC RESPONSE OF GROUPED BLADE SYSTEMS .1. DISCRETE THEORY

The vibration of grouped blades on a flexible disk cannot be analyzed using procedures developed for individual, uncoupled groups. The blade d-disk system must be considered either in whole, eras a structure com posed of cyclically symmetric sectors. The latter approach, while bein g computationally more economical, is more complicated to implement be cause both the structural system and the applied forces must be transf ormed to a system based on the geometry of a single sector. However, t he 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 displace ments of the complete structure. This approach leads to an easier inte rpretation of the analytical results and an improved physical understa nding 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.