(a) Band diagram for a concrete building (20 m × 20 m × 80 m) atop a concrete homogeneous plate (40 m × 40 m × 40 m); Floquet-Bloch conditions are set on vertical sides of the plate and stress-free conditions hold elsewhere; Flat bands correspond to eigenmodes of the building around 1 Hz, 9 Hz, 17 Hz, etc. that couple to the flexural band (lowest band at Γ). (b) Representative eigenmode of (a) at 17 Hz. (c) Eigenmode with suppressed building’s vibration around 17 Hz when the plate is structured with auxetic metamaterial (4³ elementary cells with bars making an angle as in Figure 2c).