This paper aims at examining the effects of soil-structure interaction (SSI) on the response of a structure which is equipped with multiple tuned mass dampers (MTMD) and founded on multiple soil layers overlying bedrock. Closed-form solutions have been obtained for the entire system, which consists of a shear beam type superstructure, multiple tuned mass dampers, and multiple soil layers overlying bedrock, while subjected to ground motion. The proposed formulations simplify the problem in terms of well-known frequency ratios, mechanical impedance and mass ratio, which can take into account the effects of SSI, mass ratio of the MTMD at each excitation frequency and damping ratio in the entire system. These formulations are capable of explicitly interpreting the major dynamic behavior of a structure equipped with multiple tuned mass dampers and interacting with the multiple soil layers overlying bed rock. The SSI effects on the dynamic response of a tuned-mass-damped structure as a result of multiple soil layers overlying bedrock were extensively investigated through a series of parametric studies.

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