Experimental investigation of surface wave propagation in locally resonant metamaterials

Locally Resonant Metamaterials (LRMs) are composite structures with uncommon mechanical properties, such as zero or negative mass density [1] and negative bulk modulus [2]. Recently, LRMs have gained increasing attention in applications related to the control of surface waves across different frequency ranges. In this context, most of the available studies discuss the design and analysis of locally resonant metasurfaces, namely thin resonant layers attached to the surface of elastic waveguides [3]. Given their reduced thickness w.r.t. to the wavelengths of surface waves, these metasurfaces are conveniently modelled as simple dynamic boundary conditions. In this study, we release this modelling assumption to investigate surface wave propagation in thick metasurfaces coupled to elastic half-spaces. The resonant layer consists of an array of sub-wavelength resonators attached to the host material via elastic connectors and periodically arranged in the hosting medium [4]. First, an analytical model is proposed to predict the dispersive features of such resonant composite medium. Next, numerical simulations are performed to confirm the dispersion properties predicted by the developed model and to evaluate the attenuation performance of such LRMs. Finally, a small-scale prototype is fabricated and tested experimentally, exploiting the Laser Doppler vibrometry technique to reconstruct the dispersion curves. The combination of analytical/numerical analyses and experimental evidence reveals that a narrow bandgap is generated in the frequency range of the LRM resonance. Parametric studies show that increasing the thickness of the resonant layer results in an extended frequency range of the bandgap, leading to a more effective attenuation of incoming surface waves. In summary, the developed framework provides a practical and efficient approach for the design and fabrication of LRMs with desirable filtering capability, which could find promising engineering applications in surface acoustic wave (SAW) filters, seismic wave barriers, and ground-borne vibration mitigation systems.