Attenuation Zones of Two-Dimensional Periodic Foundations Including the Effect of Vertical Loads

Periodic foundations for seismic isolation are getting increasing attention in the field of civil engineering. Initial stresses due to the vertical loads from the upper structures exist in periodic foundations. In the present paper, attenuation zones of two-dimensional periodic foundations including the effect of vertical loads are studied by the weak form quadrature element method. Comparisons with existing results in special cases without the effect of vertical loads are conducted to validate the proposed method, and good agreement is found. A comprehensive parametric study is conducted to investigate the effects of vertical loads on the attenuation zones. Moreover, frequency-domain and time-domain response analyses of a two-dimensional periodic foundation with finite unit cells are conducted to verify the theoretical results. The results show that bound frequencies of the attenuation zones, corresponding to the vibration mode of the core, are affected by vertical loads. It is also found that vertical loads shift the complete attenuation zones to lower frequencies and reduce the attenuation coefficients in the attenuation zones.