Tunable Topological Phase Transition in Soft Rayleigh Beam System with Imperfect Interfaces

Abstract

Acoustic metamaterials, especially topological insulators, have garnered substantial research attention due to their unique wave properties. Recent studies have pointed out that the role of imperfect interfaces is pivotal for accurately simulating and understanding wave propagation behaviors in acoustic metamaterials. In this study, a comprehensive model of a soft Rayleigh beam system with these imperfect interfaces is proposed. The model reveals that the topological phase transition process can be observed by modifying the distance between imperfect interfaces in the system. When a uniaxial stretch is applied, the topological phase transition points for longitudinal waves decrease within a limited frequency range, while they increase within a larger frequency scope for transverse waves. To the contrary, enhancing the rigidity of the imperfect interfaces enables shifting of the topological phase transition point within a broader frequency range for longitudinal waves and a confined range for transverse waves, and the decisive dimensionless factor in such system is found theoretically. The transition of topologically protected interface modes in the transmission performance of a twenty-cell system is verified, which include altering frequencies, switching from interface mode to edge mode. Overall, this study offers a novel methodology and framework for managing topological phase transition in composite and soft phononic crystal systems.

Keywords: Topological phase transition, topological insulator, Soft Rayleigh beam, Imperfect interface, Interface mode.