Frequency bandgap enhancement in locally resonant metasurfaces for <i>S</i>0 Lamb wave mode using topology-optimized resonators

Abstract

Elastodynamic metasurfaces composed of surface-mounted resonators show great promise for guided wave control in diverse applications, e.g., seismic and vibration isolation, nondestructive evaluation, or surface acoustic wave devices. In this work, we revisit the well-studied problem of “rod-shaped” resonators coupled to a plate to reveal the relationship between the resonator's resonances and antiresonances obtained under unidirectional harmonic excitation, and the resultant frequency bandgap for S0 Lamb mode propagation once a metasurface is arranged. This relationship is shown to hold true even for non-prismatic resonators, such as those presented in our recent studies, in which we established a systematic resonator design methodology using topology optimization by matching a single resonator's antiresonance with a predefined target frequency. Our present study suggests that considering the waveguide (plate) during the resonator design is not essential and encourages a feasible resonator design approach to achieve wide bandgaps just by customizing a single resonator's resonances and antiresonances. We present a topology optimization design methodology for resonators that drive resonances away from antiresonances, i.e., a resonance gap enhancement, yielding a broadband S0 mode bandgap while ensuring the desired bandgap formation by matching antiresonances with a target frequency. The transmission loss of metasurfaces composed with topology-optimized resonators is numerically verified, confirming the generation of wider bandgaps compared to resonators designed without resonance gap enhancement and broadening the applicability of locally resonant metasurfaces.