“Borrow-force-attack-force” by multi-scale elastic metamaterial with nonlinear damping

The powerful energy carried by low-frequency vibration is often challenging to be effectively attenuated using traditional damping materials. If low-frequency vibration can be controlled through the energy carried by the excitation itself, the cost of achieving ultra-wide low-frequency vibration control would be significantly reduced. To this end, this paper constructs a multi-scale elastic metamaterial with nonlinear damping (MEMND) to achieve the efficient suppression of ultra-wide low-frequency vibration through its unique transmission characteristics and the effect of “borrow-force-attack-force” (leveraging the excitation to dampen vibration), which is amplified with increasing external excitation. Theoretical, simulation, and experimental results demonstrate that MEMND can achieve over 10 dB damping enhancement at the expense of losing a small amount of the bandgap effect. It exhibits high sensitivity to external excitation in the low-frequency region, offering a promising opportunity for “borrow-force-attack-force”. This work integrates a natural nonlinear damping element into elastic metamaterials and leverages the nonlinear action mechanism of external excitation, presenting a different approach for nonlinear metamaterial design with potential engineering applications.