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The gravity-induced depth-dependent elastic properties of a granular half-space result in multiple dispersive surface modes and demand the consideration of material heterogeneity in metabarrier designs to suppress surface waves. Numerous locally resonant metabarrier configurations have been proposed in the literature to suppress Rayleigh surface waves in homogeneous media, with little focus on extending the designs to a heterogeneous half-space. In this work, a metabarrier comprising partially embedded rod-like resonators to suppress the fundamental dispersive surface wave modes in heterogeneous granular media known as first order PSV (PSV1; where P is the longitudinal mode and SV is the shear-vertical mode) and second order PSV (PSV2) is proposed. The unit-cell dispersion analysis, together with an extensive frequency-domain finite element analysis, reveals preferential hybridization of the PSV1 and PSV2 modes with the longitudinal and flexural resonances of the resonators, respectively. The presence of the cutoff frequency for the longitudinal-resonance hybridized mode facilitates straightforward suppression of the PSV1 mode, while PSV2 mode suppression is possible by tailoring the hybridized flexural resonance modes. These PSV1 and PSV2 bandgaps are realized experimentally in a granular testbed comprising glass beads by embedding 3D-printed resonator rods. Also explored are novel graded metabarriers capable of suppressing both PSV1 and PSV2 modes over a broad frequency range for potential applications in vibration control and seismic isolation. 

Locally resonant elastodynamic metasurfaces for suppressing surface waves have gained popularity in recent years, especially because of their potential in low-frequency applications such as seismic barriers. Their design strategy typically involves tailoring geometrical features of local resonators to attain a desired frequency bandgap through extensive dispersion analyses. In this paper, a systematic design methodology is presented to conceive these local resonators using topology optimization, where frequency bandgaps develop by matching multiple antiresonances with predefined target frequencies. The design approach modifies an individual resonator's response to unidirectional harmonic excitations in the in-plane and out-of-plane directions, mimicking the elliptical motion of surface waves. Once an arrangement of optimized resonators composes a locally resonant metasurface, frequency bandgaps appear around the designed antiresonance frequencies. Numerical investigations analyze three case studies, showing that longitudinal-like and flexural-like antiresonances lead to nonoverlapping bandgaps unless both antiresonance modes are combined to generate a single and wider bandgap. Experimental data demonstrate good agreement with the numerical results, validating the proposed design methodology as an effective tool to realize locally resonant metasurfaces by matching multiple antiresonances such that bandgaps generated as a result of in-plane and out-of-plane surface wave motion combine into wider bandgaps.