On the number of cells for flexural vibration suppression in periodic beams

Vibration suppression is an important topic for many engineering applications. There are different techniques, typically involving passive and active controllers. However, it can alternatively be obtained by designing structures based on the concept of periodicity, which involves identical elements or parts connected repeatedly. Periodic structures are designed to exhibit stop bands for a pre-defined range of frequency. The stop bands introduce an effect similar to the filter. In this context, this article presents a modeling for designing periodic beams. The approach considers a beam with a periodic part, and two homogeneous (not periodic) connected in both left and right-hand sides of the periodic part. The results demonstrate that five periodic cells generate an effect equivalent to an infinite periodic beam, in terms of flexural vibration suppression.