A simplified system is studied analytically, numerically and experimentally. Predictions are based on a linear stability analysis of two subsystems coupled by friction at a sliding point contact. The model describes any two such linear subsystems, though is predominantly discussed in terms of vehicle brakes. As an example of its generality, it is shown to be equivalent to machine tool vibration. Representative uncertainties of the system dynamics are shown to be significant enough to affect whether or not the model predicts instability. The reliability of predictions are assessed systematically. The validity of limited bandwidth approximations to wide band-width models is tested: the convergence behaviour is non-trivial. While inclusion of sufficient bandwidth generally results in convergence, individual modes can sometimes be important. A first-order perturbation analysis is carried out in order to provide a practical estimate of error bounds for predictions. An extensive experiment was carried out using a pin-on-disc test rig to quantify uncertainty, assess repeatability and investigate whether high sensitivity could be experimentally observed. Repeated transfer function measurements of the uncoupled subsystems were made of two fundamentally different pin assemblies, symmetrical and asymmetrical, in the presence of different perturbation masses. Sliding contact tests were carried out with the aim of generating a large number of squeal initiations. Their growth rates and frequencies were estimated. This allowed a direct comparison of predictions with experimental results, enabling informed development of the modelling details. There was compelling evidence that both contact stiffness and a velocity-dependent coefficient of friction were essential features of the model to predict observed instabilities.

The thesis describes modelling studies of amorphous, or non-crystalline, materials. It is split into two parts: modelling the vibrational behaviour of amorphous materials, and modelling their atomic structure. A recurring theme is representing amorphous materials as disordered crystals, and exploring to what extent this is a realistic representation. Adding force-constant and positional disorder to a diamond crystal lattice allows some, but not all, of the features of the vibrational spectrum of a realistic amorphous silicon model to be reproduced. Various properties of realistic amorphous silicon models are then examined: localization, scaling of the width of the spectral density with wavevector, and the boson peak. The medium-range structure of certain amorphous materials is shown to be well reproduced by the simple method of adding positional disorder into the structures of their crystalline counterparts. In particular, the wavevector of the first sharp diffraction peak in amorphous silicon and vitreous silica can be predicted. Further, the medium-range atomic structure of very high-density amorphous (VHDA) ice can be predicted by combining certain disordered crystalline ice phases. The best-fit phase fractions of these crystalline phases are very close to those observed in the experimental recrystallization of VHDA ice. Finally, connections between the structures of the high-pressure amorphous phases of silicon and ice are explored.

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This thesis addresses the problem of controlling the vibration of rotating machines using active bearing seatings. Contributions have been in seven areas: test rig development, rotating machinery modelling, developing appropriate control laws, updating method for piezoelectric actuators, determining specifications for the actuators from FE models, modal correlation methods (with and without frequency weighting) and modal expansion. A rotating machine test rig has been designed and constructed. In this rig, an active bearing seating has been designed to accommodate two actuators, located orthogonally and exerting control forces at each of two bearings. The rig is a versatile unit- the first one of its kind in the UK having a rotor whose bearings are supported on active seatings. Determining the requirements for force, stroke and bandwidth of the actuators for bearing seatings begins with an accurate numerical model of the system. A displacement-based FE model incorporating the active bearing seating has been developed and applied for predicting the dynamic behaviour of a rotating machine. Both steady-state responses and transient responses (run-up / run-down) are considered. The model has been validated experimentally by performing an experimental modal analysis of the test rig. A third area is in the development of suitable control laws. The same numerical model developed for assessing the actuator specifications has been employed to develop the control strategy. A control algorithm has been developed for vibration suppression. In this, the core ideas of classical optimal control are adopted (namely trading-off control effort against tracking performance). The "Simplex" (Nelder- Mead) method has been applied. The optimisation study is carried out for collocated actuation and sensing and for the general case, non-collocated control. Synchronous vibration is minimized in a root mean squares sense. Numerical simulations have shown that the proposed optimal closed-loop control strategy is very effective in reducing the amplitude of the forced vibration under different operating conditions. This controller is easy to implement in practical applications. A complete experimental and computational characterisation has been carried out on the piezoelectric actuators. An experimental arrangement has been established to measure two frequency- response functions. From these the complete dynamic properties of the piezoelectric stack actuators can be determined. Based on the measurements and the basic equations of the actuator, a computational model written in MA TLAB has been developed by which the parameters can be extracted. The experiment is simple to do with standard vibration-laboratory equipment and is very effective in characterising the actuator. The tests have been performed on four nominally-identical actuators and different parameters are obtained in each case. Obtaining accurate values for these parameters is an essential step towards having a reliable model for the complete closed-loop system. A set of novel modal correlation measures for generally-damped systems has been developed. In each case, a dimensionless (n x n) modal-matching array is produced whose entries indicate which pairs of modes from the first system best correlate with any particular pair of modes from the second system. This modal-matching array exhibits 2nd -order behaviour with respect to any scalar measure of that discrepancy. The work was motivated originally by the application of developing Campbell diagrams for rotating machines as continuous curves - rather than simply plotting large set of discrete points. There are several possible motivations for the proposed procedures. The most important is probably the model updating application where a vital first step is to ensure that modes have been correctly paired. The methods have been illustrated in two examples and comparisons with the established Modal Assurance Criterion methods show the new method in a good light. Two frequency dependent operations for generally-damped systems are presented in this thesis. The first operation involves developing a new frequency dependent modal expansion while the second operation generalises a previously-proposed modal correlation approach for these systems such that particular frequencies are targeted. The two suggested methods are illustrated using numerical examples.

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