Robustness of optimal design solutions to reduce vibration transmission in a lightweight 2D structure, part II: application of active vibration control techniques

This is the second paper which considers the reduction of the vibration transmission along a lightweight cantilever structure consisting of 40 rigidly joined beams over a frequency band. In the first paper [1] the reduction was achieved by allowing the geometry of the structure to be altered, such that the structure provided an inherently better vibration isolation. In this paper, the variation reduction over a band of frequencies is achieved using feedforward active vibration control (AVC) techniques applied to the original structure geometry. The success of AVC depends strongly on the position of the actuators. The actuator positions on the structure which achieve the best reductions in vibration transmission are found for one, two and thee actuators. A robustness analysis is then performed to show the sensitivity of each of the best solutions to small geometric perturbations. These solutions are the most practical, being less sensitive to small geometric changes that might occur, for example, as manufacturing tolerances. This is achieved by applying a sufficient number of random perturbations to determine the statistical distribution of the performance. A probability limit is then applied in order to predict a likely average minimum performance criterion, In addition to considering the robustness of the performance, the control effort required to achieve active control must be considered. If this increases significantly when the structure is perturbed the demand may not be met be a practical system, and the predicted performance cannot be obtained