Seismic isolation of buildings using composite foundations based on metamaterials

Metamaterials can be engineered to interact with waves in entirely new ways, finding application on the nanoscale in various fields such as optics and acoustics. In addition, acoustic metamaterials can be used in large-scale experiments for filtering and manipulating seismic waves (seismic metamaterials). Here, we propose seismic isolation based on a device that combines some properties of seismic metamaterials (e.g., periodic mass-in-mass systems) with that of a standard foundation positioned right below the building for isolation purposes. The concepts on which this solution is based are the local resonance and a dual-stiffness structure that preserves large (small) rigidity for compression (shear) effects. In other words, this paper introduces a different approach to seismic isolation by using certain principles of seismic metamaterials. The experimental demonstrator tested on the laboratory scale exhibits a spectral bandgap that begins at 4.5 Hz. Within the bandgap, it filters more than 50% of the sei..

Modeling and design of non-linear seismic metamaterials - Invited talk by R. Zivieri

A model used to understand seismic metamaterials from a theoretical point of view is based on the concept of the periodic sub-wavelength resonant mass-in-mass system, see Fig. 1. Figure 1 : Sketch of the system studied. We have already proposed a continuous implementation of those type of seismic metamaterials based on the use of isochronous mechanical oscillators. However, the bandgap of this device has its centre at the resonance frequency of the atomic mass-in-mass element. A key challenge is to achieve a broad extension of the bandgap and a bandgap starting at a frequency as low as possible. Here, we focus on the possible engineering of the non-linearity of the external spring of a mass-in-mass system. In order to do that, first we define an anharmonic force exerted on the mass me resulting from a potential energy developed up to the fourth-order. Second, starting from the Lagrangian equation we obtain the dispersion relation in the presence of the anharmonic contributions. The acoustical branch of the dispersion relation is strongly downshifted with respect to that obtained in the linear case

Design of non-linear seismic metamaterials - Invited talk by R. Zivieri

A model used to understand seismic metamaterials from a theoretical point of view is based on the concept of the periodic sub-wavelength resonant mass-in-mass system, see Fig. 1. We have already proposed a continuous implementation of those type of seismic metamaterials based on the use of isochronous mechanical oscillators. However, the bandgap of the this device is centered at the resonance frequency of the atomic mass-in-mass element. A key challenge is to achieve a broad extension of the bandgap and a bandgap starting at a frequency as low as possible To reach this result, it has been proposed to exploit the non-reciprocity feature of the chiral materials, introducing in the system hybrid modes. Here, we focus on the possible engineering of the non-linearity of the external spring of a mass-in-mass system, we evaluate three cases including an hysteretic ke value. Starting by the Lagrangian equation of the energy, we obtain the dynamical equations taking into account the relationship of ke relate to the displacement of the me. The dynamical equations are then solved numerically. Our results point out that the start frequency of the bandgap can be decreased by 25% by considering ke=A atan(Bue) with proper values of A and B