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This investigation deals with the vibration problem of a rotating shrouded bladed disc and with the dynamic stresses of blades and packets of turbine blades. The wave propagation technique in periodic structures is introduced into the finite element method to reduce the overall number of degrees of freedom. The application of wave propagation technique to discs, disc-blades and shrouded bladed disc results in a small size eigenvalue problem which is easily solved to obtain the frequencies and mode shapes of these assemblies under the effects of rotation, disc thickness variations, disc flexibility and other design parameters. The numerical integration is used to evaluate the integrals of the stiffness and mass matrices of the variable thickness discs. The influence of rotational speeds and other design parameters such as; pretwist angles and stagger angles on the free vibration characteristics of blades, curved beams and packets of blades is studied using finite element method. The results of the natural frequencies are compared with the experimental results and with the results of other investigators. The dynamic stresses of blades and packets of blades are derived from the eigenvectors obtained in the vibration study of these components. The effects of rotational speeds, pretwist angles, stagger angles and shrouding on the dynamic stresses are studied.

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In the current gas turbine market, the traditional design-test-redesign loop is not a viable solution to deploy new products within short timeframes. Hence, to keep the amount of testing to an absolute minimum, theoretical simulation tools like Finite Element Modelling (FEM) have become a driving force in the design of blades to predict the dynamic behaviour of compressor and turbine assemblies in high-speed and unsteady flows. The predictions from these simulation tools need to be supported and validated by measurements. For the past five years, Rolls-Royce Blade Tip Timing (BTT) technology has been replacing rotating Strain Gauge systems to measure the vibration of compressor blades, reducing development times and costs of new aero engine programmes. The overall aim of the present thesis is to progress the BTT technology to be applied to aero engine turbine modules. To this end, the two main objectives of this project are: i. To improve the current validated Rolls-Royce BTT extraction techniques, through the development of novel algorithms for single/multiple asynchronous and responses. ii. To validate the improved extraction using simulated and real engine test data in order to bring the Turbine BTT technology to a Rolls-Royce Technology Readiness Level (TRL) of 4 (i.e. component and/or partial system validation in laboratory environment). The methodology adopted for the development of the novel algorithms is entirely based on matrix algebra and makes extensive use of singular value decomposition as a means for assessing the degree optimisation achieved through various novel manipulations of the input (probe) raw data. The principle contributions of this thesis are threefold: i. The development of new BTT matrix-based models for single/multiple non-integral and integral engine order responses that removed certain pre-processing assumptions required by the current method. ii. The development of BTT technology to operate under the constraint of having equally spaced probes, which is unavoidable in turbines and renders current BTT methods unusable for turbine applications. iii. The development of methods for extracting measurement uncertainty and signal to noise ratios that are based solely on the raw data, without reliance on simulated reference data. Following the verification and validation of the new processing algorithms against simulated data and against validated software with numerous examples of actual engine test data, a Rolls-Royce's Research & Technology (R&T) Critical Capability Acquisition and Capability Readiness (CCAR) review has accredited the novel techniques with a TRL of 4.

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