Robustness of optimal design solutions to reduce vibration transmission in a lightweight 2-D structure, Part I: Geometric design

A two-dimensional lightweight cantilever structure is studied, comprising 40 rigidly joined beams, of which the geometry is optimized to reduce vibration transmission over a given bandwidth. In this paper, the optimization is achieved by using genetic algorithms. Ten optimized design candidates were achieved for each of three cases resulting from minimizing an objective function (the vibration transmission between two points on the structure) which is calculated (i) using a single frequency, (ii) the frequency average over a narrow bandwidth, and (iii) the frequency average over a broad frequency range. All the candidates show performance improvements and normally the best performance is taken to be best candidate. This paper then considers the sensitivity of each optimal candidate to small changes in the geometry of the structure. If the performance of a structure is too sensitive to perturbations its practical application is limited or may not be realizable in practice. The robustness of the optimized candidates is studied in order to find those candidates which are least sensitive to changing design parameters. This is achieved by perturbing the positions of the joints by an ensemble of sets of random numbers. The statistical effect on the objective function is investigated, and some candidates are seen to be more robust to such perturbations than others and generally the greater the bandwidth over which the structure is optimized the more robust the design. A selection criterion is then applied which enables the best candidates to be identified on grounds of both nominal optimized performance and robustness. Finally, the advantage of using genetic algorithms over traditional "hill-climbing" optimization methods is shown, on the grounds of both nominal performance and robustness.