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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. 

A locally resonant meta-surface for preferential excitation of a guided mode in a hollow pipe can improve ultrasonic guided wave inspection of pipelines. The proposed meta-surface comprises a periodic arrangement of bonded prismatic rod-like resonators in the circumferential and axial directions of the pipe. We demonstrate the presence of bandgaps for the low-frequency axisymmetric longitudinal modes L(0,1) and L(0,2) and the torsional mode T(0,1). The generated bandgaps can be used to filter the higher harmonics associated with the system nonlinearity to improve nonlinear ultrasonic measurements on pipes. These bandgaps exist even for the non-axisymmetric flexural modes but with their hybridized dispersion curves exhibiting mode-coupling for higher circumferential orders. Moreover, a “partial” bandgap is obtained where preferential transmission of the L(0,2) mode over L(0,1) is possible. We discuss the potential advantages of this partial bandgap to improve pipeline inspections using the L(0,2) mode. Time-domain finite element analyses are used to validate the presence of these bandgaps under radial, circumferential, and axial excitation that mimics the excitation using a ring of piezoelectric transducers. Finally, we discuss the influence of resonator spacing, filling fraction, and the number of resonator rings on the bandgaps for an informed meta-surface design. 

Control of guided waves has applications across length scales ranging from surface acoustic wave devices to seismic barriers. Resonant elastodynamic metasurfaces present attractive means of guided wave control by generating frequency stop-bandgaps using local resonators. This work addresses the systematic design of these resonators using a density-based topology optimization formulated as an eigenfrequency matching problem that tailors antiresonance eigenfrequencies. The effectiveness of our systematic design methodology is presented in a case study, where topologically optimized resonators are shown to prevent the propagation of the S 0 wave mode in an aluminum plate.