Design optimization of flexible space structures for passive vibration suppression
This research is concerned with the development of a computational framework for the design of large flexible space structures with non periodic geometries to achieve passive vibration suppression. The present system combines an approximation model management framework (AMMF) developed for evolutionary optimization algorithms (EAs) with reduced basis approximate dynamic reanalysis methods. Formulations based on reduced basis representations are presented for approximating the eigenvalues and eigenvectors, which are then used to compute the frequency response. The second method involves direct approximation of the frequency response via a dynamic stiffness matrix formulation. Both the reduced basis methods use the results of a single exact analysis to approximate the dynamic resp9onse. An AMMF is then developed to make use of the computationally cheap approximate analysis techniques in lieu of exact analysis to arrive at better designs on a limited computational budget. A coevolutionary genetic search strategy is developed here to ensure that design changes during the optimization iterations lead to low-rank perturbations of the structural system matrices. This ensures that the reduced basis methods developed here give good quality approximations for moderate changes in the geometrical design variables. The k-means algorithm is employed for cluster analysis of the population of designs to determine design points at which exact analysis should be carried out. The fitness of the designs in an EA generation is then approximated using reduced basis models constructed around the points where exact analysis is carried out. Results are presented for optimal design of a two-dimensional space structure to achieve passive vibration suppression. It is shown that significant vibration isolation of the order of 50 dB over a 100 Hz bandwidth can be achieved. Further, it is demonstrated that the coevolutionary search strategy can arrive at a better design as compared to conventional approaches, when a constraint is imosed on the computational budget available for optimization. Detailed computational studies are presented to gain insights into the mechanisms employed by the optimal design to achieve this performance. It is also shown that the final design is robust to parmetric uncertainties.