This paper reports the evidence of the tunable sub-wavelength topological interface state in local resonance piezoelectric metamaterials. An elastic beam serves as the host medium with periodically arranged local resonators and attached piezoelectric layers. Thus, the shunt circuits connected with the piezoelectric layers can easily change the electromechanical stiffness in any unit cell. By inspired the band-folding mechanism, doubling the primitive unit cell generates two Dirac points, whose one lower point falls below the locally resonant bandgap and is in the sub-wavelength region. Then, employing the shunt circuit's tunability opens band-folding points to develop two bandgaps associated with the Bragg scattering effect. Band inversion and topological transition exist during the negative capacitance parameter variation. Numerical simulations demonstrate interface wave propagation for excitation at the interface frequency in the heterostructure, composted of two media with different topological invariants. With the assistance of the piezoelectric shunting circuit, our proposed design can induce wave localization over multiple frequency bands, which has potential for applications such as signal filters, energy harvesting and vibration isolation. Finally, we investigate the relationship between the interface frequency and capacitance and consider the local resonance effect on topological interface modes.
- Local resonance
- Piezoelectric metamaterial
- Tunable topological interface state