Abstract
This thesis is concerned with the study of the vibration characteristics of packets of blades having flexible roots and with the determination of forces in the blades and shroud. The main body of the work is divided into three parts: First the development of an improved finite element is shown and applied to a fully fixed cantilever blade. Comparisons show the present method to be considerably more accurate, needing a lower-order matrix, than analyses presented by other investigators. Distributions of bending moment, shear force end-load and mode-shapes are included. In the second part, the finite-element method developed in the first part is extended to apply to packets of blades with fixed roots. Close agreement is shown with experimental results and with results computed by other investigators. The latter comparisons are particularly meaningful when frequencies are presented in parametric form a. Also given, are the development and applications of the frequency-inference diagram and distributions of bending moment shear force, end-load and mode-shapes for various blade packets. Part three shows further development of the finite-element method to include blade flexibility at the root. Good agreement is shown with experiment and with results presented by other investigators, though the latter comparison is limited to single blades. The frequency-inference diagram, to predict the frequencies of blade packets is developed successfully for blades with non-rigid roots. Mode-shapes, end-loads, shear forces and bending moments are determined. A comprehensive study of the effect of infinitely variable root-fixation on the dynamic characteristics of blade packets is presented. It is seen that over certain ranges X is very sensitive to changes in stiffness.