An optimal method for periodic structures design

Periodic structures act as mechanical filters for elastic wave propagation, therefore they can be used to attenuate vibrations within precise frequency bands, that are known as band-gaps. Nowadays, the design of such structures is faced using dispersion band-maps: varying the system parameters, one can figure out how position and width of the attenuation regions move. However, this approach is not satisfactory, being the solution based on the designer experience. Furthermore, it is impossible to make considerations about its optimality. In this paper, a new method is proposed, providing an optimal solution in the sense that the designed structure exhibits the maximum attenuation at the desired frequency, under certain physical and geometrical constraints. Starting from waves reflection and transmission coefficients, a purely analytical model for rods and beams design has been developed. The design of band-gap position has been decoupled from its magnitude of attenuation by means of a corrective factor depending on how a wave is bounced at cells interfaces. Plus, the same model has been used to predict the position of the neighboring band-gaps. As a result, dispersion band-maps are needed just for optimality check, but not for design purposes. In order to validate the model, a passive periodic structure has been manufactured, and experimental response is compared to the analytical one.