Low-frequency multiple topological interface modes in metamaterial beams with quasi-zero-stiffness resonators

To achieve multiple low-frequency topological interface modes (TIMs) while maintaining lightweight and load-bearing capacities in metamaterial beams, we propose novel topological beams equipped with double quasi-zero-stiffness (QZS) resonators. Following the introduction of the negative stiffness (NS) mechanism, we derived the dispersion relations of the topological beams with double QZS resonators using the transfer matrix method (TMM), and performed comparative and parametric analyses of stiffness ratio on folded Dirac cones (DCs) and locally resonant band gaps (LRBGs). Thanks to the NS mechanism and the double degrees of freedom (DOFs) in the QZS resonators, we can realize double low-frequency DCs (< 500 Hz) in metamaterial beams. It is notable that adjusting the stiffness of oblique springs can tune the resonators' effective stiffness, implying that we can custom the frequency of DCs and LRBGs by adjusting the QZS resonator. By altering the distance between two QZS resonators, we obtain two topologically distinct unit cells. Transmission simulations confirm the presence of multiple low-frequency TIMs at the interface between these two domains. We also find that the effect of mass and geometric defects at various positions on TIMs is minimal. The proposed metamaterial beams could inspire innovative low-frequency vibration energy harvesters and lightweight topological devices.