Classical techniques for mitigating vibration in rotating structures are divided into three main categories viz. careful design and manufacture, correct installation and effective control strategies. The balancing sleeves analysed in this thesis were developed as a ‘semi active’ method of vibration control to improve the state of balance of dynamically unstable coupling shafts. However, the addition of the balancing sleeves affects the natural dynamics of the shaft, and requires a detailed understanding of their characteristics and the impact on the overall shaft dynamics in order to be useful in practice. As a first approximation, the sleeves are initially modelled as part of a full coupling shaft using the Extended Hamilton’s Principle. The simulation studies show that the flexibility of the sleeves have little impact upon the dynamics of the system and can therefore be neglected. However, when compared to results from the use of computational finite element methods with different sleeve lengths, discrepancies are identified. Experimental validation using a purpose built high speed test facility is used to show that the difference is due to the lack of appropriate modelling of sleeve flexibility characteristics. A full system model using finite element methods is therefore devised. More widely, a study of the impact of sleeve lengths shows that the classical definition of a ‘shaft mode’ does not encompass sufficient fidelity to discriminate between modes that are initially considered as being shaft dominated and those that are considered as sleeve dominated mode shapes, and the sharp transition that occurs between the two. It is notable that the transition between the two dominant modal contributors occurs at sleeve lengths that impart a natural frequency that is close to that corresponding to the shaft. It is concluded that the mechanism of passive control via use of the sleeves is a combination of softening due to the added mass of the sleeves and coherence of the individual modes of the shaft and sleeves. In this way, it is shown that the sleeves act in a manner similar to a tuned mass-damper. By appropriate design therefore, use of balancing sleeves offer the opportunity to increase the critical speed margin in practical applications and reduce unwanted lateral vibrations
