Robust optimal design using passive and active methods of vibration control

This thesis is concerned with the design of a lightweight cantilever structure to optimise the vibrational energy transmitted from the base to the end. The methods by which this is achieved are: i) the use of geometric redesign of the structure (passive optimisation), ii) the application of Active Vibration Control (AVC) techniques (active optimisation), iii) combinations of both passive and active methods. However, even though the nominal performance of a structure may be optimal, the sensitivity of the structure to small geometric perturbations (e.g., those representing manufacturing tolerances) also needs to be considered. For some optimal structures their performance deteriorates rapidly in the face of such perturbations, and a better solution may be a structure with a slightly worse performance but that is robust to such perturbations.Optimised structures were designed using the methods outlined above. For passively optimised structures, good reductions in vibration transmission were achieved using both classical optimisation methods and genetic algorithms (GA). The structures attained using the classical methods were not all robust, to the extent that the nominal performance would not be realised in practice. Using GA, in general, it was found that the wider the frequency band over which the average performance was assessed, the more robust the structures produced. For active control, optimal actuator positions were sought to achieve the best reductions attainable using feedforward control. The control effect associated with an AVC system also needs to be considered when selecting an optimal solution, and as with the performance, the robustness in the face of geometric perturbations needs to be assessed. The choice of the parameter representing the vibration was also investigated and it was found that the choice of parameter can affect the success in reducing the physical vibration. Optimised structures were also produced using both passive and active methods, and the robustness of their performance and control effort evaluated. It was seen that the application of AVC with a geometrically optimised structure is more effective and more efficient than with the unoptimised structure.