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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. 

An array of surface-mounted prismatic resonators in the path of Rayleigh wave propagation generates two distinct types of surface-wave bandgaps: longitudinal and flexural-resonance bandgaps, resulting from the hybridization of the Rayleigh wave with the longitudinal and flexural resonances of the resonators, respectively. Longitudinal-resonance bandgaps are broad with asymmetric transmission drops, whereas flexural-resonance bandgaps are narrow with nearly symmetric transmission drops. In this paper, we illuminate these observations by investigating the resonances and anti-resonances of the resonator. With an understanding of how the Rayleigh wave interacts with different boundary conditions, we investigate the clamping conditions imposed by prismatic resonators due to the resonator’s resonances and anti-resonances and interpret the resulting transmission spectra. We demonstrate that, in the case of a single resonator, only the resonator’s longitudinal and flexural resonances are responsible for suppressing Rayleigh waves. In contrast, for a resonator array, both the resonances and the anti-resonances of the resonators contribute to the formation of the longitudinal-resonance bandgaps, unlike the flexural-resonance bandgaps where only the flexural resonances play a role. We also provide an explanation for the observed asymmetry in the transmission drop within the longitudinal-resonance bandgaps by assessing the clamping conditions imposed by the resonators. Finally, we evaluate the transmission characteristics of resonator arrays at the anti-resonance frequencies by varying a few key geometric parameters of the unit cell. These findings provide the conceptual understanding required to design optimized resonators based on matching anti-resonance frequencies with the incident Rayleigh wave frequency in order to achieve enhanced Rayleigh wave suppression. 

Rayleigh waves are very useful for ultrasonic nondestructive evaluation of structural and mechanical components. Nonlinear Rayleigh waves have unique sensitivity to the early stages of material degradation because material nonlinearity causes distortion of the waveforms. The self-interaction of a sinusoidal waveform causes second harmonic generation, while the mutual interaction of waves creates disturbances at the sum and difference frequencies that can potentially be detected with minimal interaction with the nonlinearities in the sensing system. While the effect of surface roughness on attenuation and dispersion is well documented, its effects on the nonlinear aspects of Rayleigh wave propagation have not been investigated. Therefore, Rayleigh waves are sent along aluminum surfaces having small, but different, surface roughness values. The relative nonlinearity parameter increased significantly with surface roughness (average asperity heights 0.027–3.992 μm and Rayleigh wavelengths 0.29–1.9 mm). The relative nonlinearity parameter should be decreased by the presence of attenuation, but here it actually increased with roughness (which increases the attenuation). Thus, an attenuation-based correction was unsuccessful. Since the distortion from material nonlinearity and surface roughness occur over the same surface, it is necessary to make material nonlinearity measurements over surfaces having the same roughness or in the future develop a quantitative understanding of the roughness effect on wave distortion.