Inertial amplification band-gap generation by coupling a levered mass with a locally resonant mass

Inertial amplification has been utilized in phononic media as a mechanism for the generation of large band gaps at low subwavelength frequencies. A unique feature in an inertial-amplification band gap is that it may exhibit two coupled peaks in the imaginary wavenumber portion of its band diagram. This unique double-attenuation band gap has been shown to emerge from a periodic arrangement of a levered mass whose motion is directly connected to that of an independent degree of freedom in the system through the motion of the lever base. Here we demonstrate a double-attenuation band gap emerging specifically from a modal coupling of the levered mass with a conventional local-resonance mass separately attached to the base. This presents a fundamentally distinct mechanical mechanism for the shaping of inertially-amplified band gaps and provides a pathway for realising a combination of strength and breadth in the wave attenuation characteristics. We theoretically present this concept, analytically identify critical conditions for the coupling of the attenuation peaks, and provide a series of parametric sweeps to further highlight the phenomenon and guide design. For example, we find a design with a relatively elevated level of minimum attenuation over practically the entire width of a band gap with a relative size of 130% , and another design with a smaller band gap but a 15-fold increase in the minimum attenuation strength compared to a pure IA chain.