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

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