Multimodal higher-order topological metamaterial for multifunctional elastic wave-based computing

Elastic metamaterials have emerged as a promising platform for the realization of wave-based computing in mechanical devices that mimic electronic computing operations. Higher-order topological metamaterials are a specific class of elastic metamaterials that takes inspiration from condensed matter physics to confine elastic waves through waveguides across a hierarchy of unique dimensions. However, higher-order topological metamaterials have yet to be explored in the context of elastic wave-based computing. To address this research opportunity, this research proposes a 2D higher-order topological metamaterial that harnesses multiband 0D topological corner states to create multifunctional elastic wave-based computing elements. The proposed metamaterial is a 2D thin plate with embedded resonators that are geometrically configured to enable multimodal resonances. Eigenfrequency studies uncover 0D corner states that emerge in four different frequency ranges and have unique displacement field characteristics. Frequency response simulations illustrate how the diverse attributes of the multiband 0D corner states can be employed to create Boolean logic gates. A design scheme is created such that each of the fundamental Boolean logic gates can be realized in the metamaterial, which has versatile modes of operation that depend on the excitation frequency and phase. The outcomes from this study reveal the potential of higher-order topological phases for wave-based mechanical computing.