This paper attempts to investigate the effects of soil-structure interaction (SSI) and higher modes on the dynamic responses of base-isolated structures through closed-form solutions for a superstructure, seismic isolator, and soil system under various conditions, comprising the cases of rigid and half-space foundations. The proposed system considers continuum media for both the superstructure and soil foundation, which can take the effects of higher modes into account, along with a discontinuous layer with a governing equation that interprets the mechanical behavior of the base-isolation system. Then, the closed-form solutions in terms of well-known frequency and impedance ratios under various conditions of soil foundations were obtained through rigorous mathematical derivations and validations by collapsing the entire system to a single degree-of-freedom system in structural dynamics and well-known cases of wave propagation in elastic solids. The closed-form solutions derived in this study explicitly revealed the characteristics of the SSI and higher mode effects in influencing the seismic behavior of base-isolated structures. Furthermore, the SSI effects on the dynamic responses of the entire system were extensively evaluated. The conclusive results of this paper will be useful for understanding the SSI and higher mode effects on the dynamic responses of base-isolated structures.

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