Mechanical metamaterials with penetrating struts for tunable low-frequency bandgaps

Mechanical metamaterials show promise for controlling elastic waves and managing vibrations, yet the intrinsic coupling between geometric parameters of the locally resonant system poses a challenge in designing metamaterials with a desired bandgap frequency. Leveraging the design freedom of additive manufacturing, here we present a design strategy that overcomes this constraint by allowing the inner struts to penetrate into the resonant mass, thereby decoupling the effective mass and stiffness. This method expands the accessible design space and allows independent and precise tuning of bandgap boundaries, thereby opening up unprecedented access to ultra-low frequency regimes. The bandgap behaviour is predicted using lumped mass analytic equations, validated through finite element Bloch analysis, and further confirmed by experimental transmittance measurements. As a demonstration of functionality, we construct a wave filter composed of two types of unit cells with tailored bandgaps, capable of separating multi-frequency inputs. This approach provides a practical pathway for low-frequency vibration isolation and versatile elastic wave manipulation.