Metadamping in inertially amplified metamaterials: Trade-off between spatial attenuation and temporal attenuation

Metadamping is the phenomenon of either enhanced or diminished intrinsic dissipation in a material stemming from the material's internal structural dynamics. It has previously been shown that a locally resonant elastic metamaterial may be designed to exhibit higher or lower dissipation compared to a statically equivalent phononic crystal with the same amount of prescribed damping. Here we reveal that even further dissipation, or alternatively further reduction of loss, may be reached in an inertially amplified metamaterial that is also statically equivalent and has the same amount of prescribed damping. This is demonstrated by a passive configuration whereby an attenuation peak is generated by the motion of a mass supported by an inclined lever arm. We further show that by coupling this inertially amplified attenuation peak with that of a local resonance attenuation peak, a trade-off between the intensity of spatial attenuation versus temporal attenuation is realized for a range of the inclination angle. Design for performance along this trade-off is therefore possible by adjustment of the lever angle. A regime of monotonic increase in both attenuation types is also possible for a different range of the inclination angle. These findings open the way for highly expanding the Ashby space for stiffness-damping capacity or stiffness-spatial attenuation capacity through design of the internal structure of materials.

Automated summary

Metadamping, the enhanced or diminished intrinsic dissipation in a material, can be achieved by designing the internal structure of the material. By coupling inertially amplified metamaterial with locally resonant metamaterial, a trade-off between spatial attenuation and temporal attenuation can be achieved within a certain range.