Abstract
The subject of this thesis is to establish the basic vibration characteristics of shrouded blades on infinitely rigid and flexible disks using the finite element method. In the first part of the thesis vibrations of blade packets on rigid disks with infinite radius are considered. It is found that there are many more natural frequencies than those indicated by previous studies. The existence of these extra frequencies is established in an original way by drawing the frequency inference diagrams. A comprehensive method of predicting the multi-bladed packet behaviour from a two-bladed packet is introduced. To investigate the behaviour of blade packets on smaller disks the shroud is modified by using curved beam finite elements. A critical survey of finite curved beam elements is presented and a very efficient curved beam element based on the simple strain function concept is developed. The effect of shroud curvature on the frequency of vibration is studied in detail. Finally, the effect of the disk flexibility on the vibration characteristics of the shrouded blades is considered. Some of the available disk finite elements are critically discussed and compared. The finite element method of wave propagation technique with the cyclic symmetry of the system is used to reduce the size of an otherwise very large eigenvalue problem. The resulting eigenvectors from the wave propagation analysis is interpreted for the first time and the calculation of phase difference between the bending and torsional modes is illustrated. The analysis is also extended to include the shroud. A series of tests are conducted on a twenty-bladed disk assembly. Experimentally observed mode shapes are compared with the theoretical mode shapes. The same procedure is repeated with the inclusion of the shroud. Experimental results showed good agreement with the theoretical results.