Conformally Graded Metamaterials for Elastic Wave Guidance

TL;DR

This paper introduces conformally graded metamaterials that enable elastic wave guidance and attenuation without relying on bandgap engineering, using conformal mappings to control wave dispersion in non-periodic structures.

Contribution

It presents a novel design approach for elastic wave control using conformal mappings to create graded metamaterials that guide and attenuate waves without bandgaps.

Findings

Demonstrated low-pass elastic wave filtering in experiments.

Showed control of wave dispersion via conformal grading.

Developed a systematic design framework for 3D curved metamaterials.

Abstract

Although metamaterials have been widely used for controlling elastic waves through bandgap engineering, the directed guidance of stress waves in non-periodic structures has remained a challenge. This work demonstrates that spatially graded metamaterials based on conformal mappings present a rich design space for controlling and attenuating wave motion - without the need for bandgaps. Conformal mappings transform an elementary unit cell by scaling and rotation into graded lattices with approximately geometrically similar unit cells. This self-similarity allows for control over the local wave dispersion throughout the metamaterial. As a key mechanism, it is shown that elastic waves cannot propagate through graded unit cells with significant size differences, except at low frequencies. This is exploited to create low-pass elastic wave guides, extending beyond classical bandgap engineering, since bandgaps are not required to achieve wave guiding and attenuation. Experiments confirm the low-pass elastic wave filtering capability of a planar truss metamaterial with conformal grading. Finally, a systematic design of curved metamaterial surfaces is presented, providing a flexible framework for programming low-pass attenuation and wave guiding in three dimensions.