  The article analyses two potential metamaterial designs, the metafoundation
and the metabarrier, capable to attenuate seismic waves on buildings or
structural components in a frequency band between 3.5 to 8 Hz. The
metafoundation serves the dual purpose of reducing the seismic response and
supporting the superstructure. Conversely the metabarrier surrounds and shields
the structure from incoming waves. The two solutions are based on a cell layout
of local resonators whose dynamic properties are tuned using finite element
simulations combined with Bloch-Floquet boundary conditions. To enlarge the
attenuation band, a graded design where the resonant frequency of each cell
varies spatially is employed. If appropriately enlarged or reduced, the
metamaterial designs could be used to attenuate lower frequency seismic waves
or groundborne vibrations respectively. A sensitivity analysis over various
design parameters including size, number of resonators, soil type and source
directivity, carried out by computing full 3D numerical simulations in time
domain for horizontal shear waves is proposed. Overall, the metamaterial
solutions discussed here can reduce the spectral amplification of the
superstructure between approx. 15 to 70% depending on several parameters
including the metastructure size and the properties of the soil. Pitfalls and
advantages of each configuration are discussed in detail. The role of damping,
crucial to avoid multiple resonant coupling, and the analogies between graded
metamaterials and tuned mass dampers is also investigated.
