Tunable Topological Interface States in Combining Lattices With/Without Symmetric Element

Abstract

Topological interface states have attracted numerous attentions over the past decades in classical wave systems. This paper theoretically and numerically demonstrates the realization of tunable topological interface states elastic wave via the parametric systems in combining lattices with/without symmetric element. The two sub-lattices are designed by swapping the order of unit masses or stiffnesses. Topological interface states transmission features indicate that the energy convergence of elastic wave in the interface. Generally, the topological interface states and the Zak phase were investigated in the lattices with symmetric element. To quantize the topological characteristics of the bands, the modified Zak phase is defined to calculate the topological invariant by the eigenstates for the lattices with/without symmetric element in this paper. The numerical results shown that the tunable frequencies of topological interface states can be realized in combining lattices with/without symmetric elements via modulating the parametric excitation frequency. The tunable topological interface states can be introduced to the vibration energy harvesting to design the efficient and steady energy harvesting system.

Keywords: metamaterial, topological interface states, parametric excitation, modified Zak phase