Investigating the robustness of interface topological modes in rods

Topological phononic crystals and metamaterials are structures that can present waveguiding and energy concentration phenomena, which can be of interest in structural dynamics for energy harvesting and passive vibration and noise control. The periodicity of the typical phononic crystals and metamaterials is broken for these structures, which need to present at least two crystal lattices with different topological characteristics. Thus, the topological invariant, such as the Zak phase, which defines the topological characteristic, must be computed. A rod metastructure exhibiting two low-frequency band gaps, each with a topological interface mode, was designed. It has bolt sets whose weights generate variability, which was modeled and inferred. In order to increase variability along the rod metastructure, washers were included or removed. Experiments were performed to validate the simulations. It was observed that the variability of the topological mode in the first band gap is more robust considering its mode shape, natural frequency, and energy concentration at the interface than the second interface mode, at higher frequency. As variability increases, the robustness of the energy concentration at the interface and of the mode shape of both topological modes decreases. The same behavior was observed for the natural frequencies of the topological modes.