One of us recently developed a theory of contact mechanics for randomly rough surfaces ͓B.N.J. Persson, J. Chem. Phys. 115, 3840 ͑2001͔͒. In this paper we compare the results of the analytical model with ͑exact͒ numerical results. We also present some analytical results related to the theory.

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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 seismic energy via an internal dissipation process. Our results open a path toward the seismic resilience of buildings and a critical infrastructure to shear seismic waves, achieving higher efficiency compared to traditional seismic insulators and passive energy-dissipation systems.

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