Effects of site–city interaction and polarization of the incident S-wave on the transfer function and fundamental frequency of structures

The variation of 2D fundamental frequency of stand-alone structure on rock $$ ({F}_{{02{\text{D}}}}^{\text{S}} ) $$ ( F 02 D S ) and in a basin $$ ({F}_{{02{\text{D}}}}^{\text{BS}} ) $$ ( F 02 D BS ) with the polarization of the incident S-wave is presented. This paper also presents the role of city density and polarization of the exciting S-wave in the site–city interaction effects on the response of structures in a city as well as free-field motion. The seismic responses of the various considered basin and site–city models are computed using SH-wave and P-SV-wave finite-difference programs. A considerable decrease in the value of $$ {F}_{{02{\text{D}}}}^{\text{S}} $$ F 02 D S of stand-alone structure on rock is obtained with the increase in shape ratio for the SV-wave but not for the SH-wave, as compared to the 1D fundamental frequency of structure ( $$ {F}_{{01{\text{D}}}}^{\text{S}} $$ F 01 D S ). However, a considerable decrease in the value of $$ {F}_{{02{\text{D}}}}^{\text{BS}} $$ F 02 D BS of a stand-alone structure in basin under double resonance condition is obtained for the SH-wave and not for the SV-wave. The spectral amplification factor at the top of a structure at $$ {F}_{{02{\text{D}}}}^{\text{BS}} $$ F 02 D BS of structure is larger for the SV-wave as compared to the SH-wave. A splitting of the bandwidth of the fundamental mode of vibration of structure and very large reduction in spectral amplification factor at $$ {F}_{{02{\text{D}}}}^{\text{BS}} $$ F 02 D BS of structure is obtained due to the site–city interaction effects under double resonance condition for both the S-wave polarizations. Further, an increase in these inferred effects with an increase in city density and number of structures in a city with a constant city density is obtained. This finding raises the question concerning the validity of ground-motion prediction using soil–structure interaction for the design of structures in an urban environment. Further, the decrease in spectral amplification factor at $$ {F}_{{02{\text{D}}}}^{\text{BS}} $$ F 02 D BS of structure due to the site–city interaction effects is larger in the case of SV-wave as compared to SH-wave. Furthermore, a considerable site–city interaction effects on free-field motion is obtained.