Optimization of Vibration Band Gaps in Damped Lattice Metamaterials

Recent research on structural dynamics has steered towards elastic metamaterials, as band gap phenomena can be explored to mitigate vibration. A challenge in their design is the determination of configurations resulting in wider band gaps in lower frequency ranges. Since some level of damping is unavoidable in any real engineering structure, it is necessary to extend the current methodology of optimal design to provide a deeper understanding of how damping may affect the desired performance. Therefore, the main objective of this article is to propose and evaluate a numerical procedure for the optimization of band gaps in damped metamaterials. Specifically, a modified objective function that incorporates an evanescence index integral is used and two optimization schemes are implemented, each reflecting whether the structure is undamped or damped. It is shown that the optimal damped metamaterial has wider range of attenuation than the undamped optimal one, but with decreased attenuation levels. The optimization procedure is validated numerically for a finite structure, demonstrating reduced transmissibility of wave motions.