Resonant metasurfaces for the mitigation of elastic wave propagation

  • Li, Pengbo (Sapienza University of Rome)
  • Pau, Annamaria (Sapienza University of Rome)
  • Lepidi, Marco (Università di Genova)

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Resonant surface layers provide a powerful route to tailor wave propagation in otherwise homogeneous media with finite or semi-infinite domains, enabling metamaterial-like functionalities [1]. This work investigates the manipulation of elastic shear-horizontal guided waves in a homogeneous isotropic non-dissipative plate, coated with a superficial resonant layer modelled as a continuous two-dimensional distribution of linear spring–mass oscillators. The dynamic problem is addressed combining the partial wave technique with resonator equilibrium and traction boundary conditions, leading to an eigenproblem that yields dispersion relations and associated wave modes [2,3]. The resonant layer profoundly modifies the low-frequency dispersion scenario by generating an additional guided branch characterized by strong superficial localization [1]. The interaction between plate-dominated and resonator-dominated responses produces avoided-crossing phenomena with a progressive exchange of modal polarization. A compact nondimensional formulation highlights the existence of isospectral configurations governed by a reduced set of interaction parameters and provides explicit conditions for bandgap formation through a unique elasto-geometric parameter, which links the resonator time scale to the plate shear thickness frequency. An asymptotic analysis of the dispersion relation further clarifies the limiting regimes of propagation: in the long-wavelength limit the fundamental branch exhibits a reduced slope due to resonator-induced effective stiffness, whereas at short wavelengths the spectrum approaches both bulk-like shear-wave behaviour and a resonator-dominated asymptote near the local resonance frequency. Finally, time domain finite-element simulations of wave scattering in a finite resonator-coated region validate the dispersion-based predictions and confirm strong attenuation and negligible transmission within the bandgap, supporting the spectral design of metaplate-type waveguides. REFERENCES [1] Maznev, A.A., Gusev, V.E., Waveguiding by a locally resonant metasurface, Physical Review B, Vol.92, id.115422, 2015. [2] Wang, M., Pau, A., Lepidi, M., Elastoacoacoustic wave propagation in a biphasic mechanical metamaterial, Journal of the Acoustical Society of America, Vol. 155 (5), pp.3322-3335, 2024. [3] Pau, A., Lepidi, M., Dispersion properties of guided elastic waves in micropolar plates, International Journal of Mechanical Sciences, Vol. 209, id.111038, 2026.