A formulation has been proposed for the transfer function of a secondary system response while the primary system is supported on a compliant soil and the excitation comprises of translational ground motion at its base. For this purpose, the earlier formulation of the authors for the fixed-base case, which exactly considers the interaction between the two sub-systems and is based on the use of their individual modal properties, has been extended. Also, the concept of modifying the input excitation for the interaction accelerations (associated with the soil-structure interaction) has been used. An example P-S system and three example earthquake excitations have been considered to illustrate the proposed formulation and to estimate the expected response peak amplitudes in the secondary system. This study shows that 'detuning' of the tuned systems may occur in case of significant soil-structure interaction. Further, for the reasons of both safety and economy, ignoring the interaction effects in designing the secondary systems may not always be justified.

SUMMARYA new formulation of the transfer function has been proposed for the seismic analysis of linear, multiply supported secondary systems. The transfer function for a given response quantity has been formulated by directly using the ÿxed-base modes of the primary and secondary systems. This approach is exact and does not involve the determination of the combined system properties. Further, it is applicable to the secondary systems with various mass ratios and conÿgurations. A few example primary-secondary systems have been considered to illustrate the proposed formulation in case of di erent mass ratios. It has also been shown how the proposed formulation can be used to obtain reasonably accurate stochastic estimates of the secondary system responses. ?

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