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The mid-frequency region, where neither a low frequency deterministic method nor a high frequency statistical method may be amenable requires special treatment. For structures such as automotive vehicles, ships and aircraft, this region corresponds to an important part of perceived sound spectrum, and it is necessary to develop practical methods to predict the response in this region. This thesis develops and compares approaches that can deal with built-up structures in the mid-frequency range. Most previous work on this region has been limited in application to a simple structure, for example, a one-dimensional system or a single beam coupled to a plate so that its applicability to more complex structures has yet to be determined. Thus, an objective of this thesis is to develop approaches that can deal with more complicated structures in the mid-frequency region. Two principal configurations considered are a fully framed rectangular plate and a rectangular plate with two beams on opposite parallel edges. While the beams are relatively stiff, the plate is more flexible. Such systems are typical components in industrial applications and it is important to identify their dynamic behaviour at the mid and high frequencies. The analytical models considered are based on a wave method, proposed by Grice and Pinnington. The beam is assumed infinitely stiff to torsion and thus the plate edge at a junction is sliding. This method starts from free wavenumbers of subsystems and uses approximate impedance for the plate in determining the coupled beam wavenumbers. It is reasonable as long as the beam is much stiffer than the plate. This approximate wave method is enhanced by introducing Muller's method to solve for the wavenumbers. The model is extended from a single-beam-plate system, to a plate with two parallel beams which is modelled using a symmetric-antisymmetric wave model, and a plate surrounded by four beams which is modelled using a plate-decoupled wave model. The modelling techniques for the two systems are different, although a similar wave approach is used. Because the wave methods provide an approximate response, a Fourier technique and a modal method based on simplified boundary conditions are also considered for comparison. These provide exact responses for the two-beam-plate and four-beam-plate systems respectively for the particular boundary conditions. The wave method can be applied more generally and is computationally more efficient but involves approximations that are not always justified. For example, mobilities show some discrepancy when the coupled beam wavenumbers found from the travelling wave have a high rate of decay. An experimental study is performed to verify the analytical models. Comparisons based on power and subsystem energy ratios show that the wave models replicate well the experimental results at mid and high frequencies. Also, the modal and Fourier models show good agreement at these frequencies, which justifies their use of simplified boundary conditions. A wavenumber correlation technique has been used to verify experimentally that the wavenumbers in the plate follow those of the beam in the direction parallel to the beam.

This thesis is in the area of active vibration control of Civil Engineering structures subject to earthquake loading. Existing structural control methods and technologies including passive, active, semi-active and hybrid control are first introduced. An extensive analysis of a frame-pendulum model is developed and analysed to investigate under what conditions effective energy dissipation is achieved in Tuned Mass Damper systems and the limitation of these devices under stiffness degradation when the structure enters the inelastic region. Linear Quadratic Gaussian and H-infinity active control schemes are designed, simulated and assessed for buildings, modelled as lumped parameter systems, including base and actuator dynamics. Various aspects of the designs are extensively evaluated using multiple criteria and loading conditions and validated in large-scale benchmark problems under practical limitations and implementation constraints. A novel design method is proposed for minimising peak responses of regulated signals via a deadbeat parametrisation of all stabilising controllers in discrete-time. The method incorporates constraints on the magnitude and rate of the control signal and is solved via efficient Linear Programming methods. It is argued that this type of optimisation is more relevant for structural control, as failure occurs when maximum member displacements are exceeded. The problem of stiffness matrix estimation from experimental data is formulated as an optimisation problem and solved under various conditions (positive definiteness, tridiagonal structure) via an alternating convex projection scheme. Both static and dynamic loading is considered. The method is finally incorporated in an adaptive control scheme involving the redesign in real-time of an LQR (Linear Quadratic Regulator) active vibration controller. It is shown that the method is successful in recovering the stability and performance properties of the nominal design under conditions of significant uncertainty in the stiffness parameters.