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It is well known in metamaterials that local resonance and hybridizationphenomena dramatically influence the shape of dispersion curves; themetasurface created by a cluster of resonators, subwavelength rods, atop anelastic surface being an exemplar with these features. On this metasurface,band-gaps, slow or fast waves, negative refraction and dynamic anisotropy canall be observed by exploring frequencies and wavenumbers from the Floquet-Blochproblem and by using the Brillouin zone. These extreme characteristics, whenappropriately engineered, can be used to design and control the propagation ofelastic waves along the metasurface. For the exemplar we consider, twoparameters are easily tuned: rod height and cluster periodicity. The height isdirectly related to the band-gap frequency, and hence to the slow and fastwaves, while the periodicity is related to the appearance of dynamicanisotropy. Playing with these two parameters generates a gallery ofmetasurface designs to control the propagation of both flexural waves in platesand surface Rayleigh waves for half-spaces. Scalability with respect to thefrequency and wavelength of the governing physical laws allows the applicationof these concepts in very different fields and over a wide range oflengthscales.

Elastic wave control beyond band-gaps: shaping the flow of waves in plates and half-spaces