Low-frequency tunable topological interface states in soft phononic crystal cylinders

TL;DR

This paper introduces a method to create and control low-frequency topological interface states in soft phononic crystal cylinders, enabling tunable waveguiding for potential applications in energy harvesting and biomedical sensing.

Contribution

It proposes a novel soft phononic crystal design that allows for mechanical tuning of topological interface states at low frequencies, using nonlinear elasticity theory.

Findings

Demonstrates continuous frequency tuning via external force.

Validates analytical predictions with finite element simulations.

Identifies conditions for topological state existence and tunability.

Abstract

Topological phononic crystals have attracted intensive attention due to their peculiar topologically protected interface or edge states. Their operating frequency, however, is generally fixed once designed and fabricated. Here, we propose to overcome this limitation by utilizing soft topological phononic crystals. In particular, we design a simple one-dimensional periodic system of soft cylindrical waveguides to realize mechanically tunable topological interface states for longitudinal waves. To this end, we employ the nonlinear elasticity theory and its linearized incremental version to fully account for both geometric and material nonlinearities of the system. We derive the dispersion relation for small-amplitude longitudinal motions superimposed on the finitely deformed state. In addition, our analytical results provide information about the corresponding Bloch wave modes, displacement field distributions, and signal transmission coefficients for finite cylindrical waveguides with identical or various unit-cell topologies. Our numerical results illustrate the low-frequency topological interface state occurring at the interface between two topologically distinct soft phononic cylinders. Moreover, we show that the corresponding frequency in the overlapped band gap can be continuously adjusted by an external force. This analytical result is also validated by the finite element simulations. Finally, we provide the topological phase diagrams to demonstrate the tunable position and existence condition of the topological interface states when tuning the external loading. The low-frequency tunable topological interface states with remarkable field enhancement may find a wide range of potential applications such as tunable energy harvesters, low-pass filters and high-sensitivity detectors for biomedical applications.