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Topological phononic crystals have attracted intensive attention due to theirpeculiar topologically protected interface or edge states. Their operatingfrequency, however, is generally fixed once designed and fabricated. Here, wepropose to overcome this limitation by utilizing soft topological phononiccrystals. In particular, we design a simple one-dimensional periodic system ofsoft cylindrical waveguides to realize mechanically tunable topologicalinterface states for longitudinal waves. To this end, we employ the nonlinearelasticity theory and its linearized incremental version to fully account forboth geometric and material nonlinearities of the system. We derive thedispersion relation for small-amplitude longitudinal motions superimposed onthe finitely deformed state. In addition, our analytical results provideinformation about the corresponding Bloch wave modes, displacement fielddistributions, and signal transmission coefficients for finite cylindricalwaveguides with identical or various unit-cell topologies. Our numericalresults illustrate the low-frequency topological interface state occurring atthe interface between two topologically distinct soft phononic cylinders.Moreover, we show that the corresponding frequency in the overlapped band gapcan be continuously adjusted by an external force. This analytical result isalso validated by the finite element simulations. Finally, we provide thetopological phase diagrams to demonstrate the tunable position and existencecondition of the topological interface states when tuning the external loading.The low-frequency tunable topological interface states with remarkable fieldenhancement may find a wide range of potential applications such as tunableenergy harvesters, low-pass filters and high-sensitivity detectors forbiomedical applications.

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