Robust Optimization of Attenuation Bands of Three-Dimensional Periodic Frame Structures

Vibration may lead to several problems and, therefore, must be considered in structural design. Periodic structures may present wave propagation phenomena capable of attenuating waves as they propagate, thus minimizing vibration transmission. When considering the numerical evaluation of wave propagation, the imaginary part of the wavenumbers leads to a measure of attenuation per unit cell. Periodic structures such as phononic crystals can be designed using the spatial repetition of a unit cell. Thus, defining the geometric and material properties of such unit cell is of paramount importance to the design of periodic structures. However, the manufacturing processes cannot perfectly reproduce the designed structure, thus generating unwanted variability. Robust optimal design should be applied such that variations in the optimal design parameters do not cause large variation of the optimum value in a considered objective function. A combination of Gaussian processes, kernel smoother, and Delaunay triangulation can be used for robust optimization of more than one design parameter. In this work, considering a combination of lower and wider first attenuation band as the objective function, conventional and robust optimization methodologies are applied to define the optimal shape of a three-dimensional frame structure. Bayesian statistics is used in the statistical inference. The results shown that the robust optimized design is indeed more robust than the conventional optimization design against variations of the geometrical parameters. However, it is not possible to assure robustness related to variability that was not considered in the robust optimization procedure.