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In recent years, a new type of seismic isolation system which exploits the filtering effect of bandgaps, named Periodic Foundation, has been proposed to isolate the upper structure from ground motion. To date, several works have been conducted to validate the feasibility and efficiency of this new isolation system. However, these works focused on the filtering effect related to the foundation periodicity, while energy dissipation due to materials absorption was ignored. To fill this gap, in this paper we investigate the effect of material damping on the performance of layered periodic foundations. Both the dispersion (related to the periodicity of the periodic foundation) and dissipation (related to the material damping of the periodic foundation) attenuation mechanisms, as well as their interaction, are investigated. First, the complex dispersion relation of a damped layered periodic foundation is formulated to assess the influence of material damping on the dispersive properties of the infinite periodic system. Second, the Riccati-transfer matrix method is used to calculate the dynamic transfer function of the damped layered periodic foundation, from which the energy dispersion and dissipation properties of the system are studied. Third, seismic responses of six-story shear-type buildings equipped with a solid foundation (fixed base), a traditional base isolation (i.e., equivalent of a layered periodic foundation with one unit-cell) and a layered periodic foundation with three unit-cells, are studied and compared. In more detail, the pseudo-excitation method is used to deal with non-classical damped systems under seismic accelerations for different soil conditions. Results show that, thanks to the filtering effect of the layered periodic foundation, the seismic responses of the upper structure are significantly mitigated within the expected frequency attenuation zone. Furthermore, including material damping leads to a further reduction of the upper structure seismic response, within the pass bands. Overall, the seismic performance of the upper structure under ground motions in different site conditions is improved by employing a damped layered periodic foundation with more than one unit cell.

Seismic vibrations attenuation via damped layered periodic foundations