A new stochastic analysis is developed to estimate the response of multiple supported mdof secondary systems to dynamic loading. In the proposed stochastic analysis, the effect of the dynamic interaction between the secondary and primary systems is included. An outline for the theoretical formulation of the proposed stochastic analysis is presented. The assumptions adopted in the formulation are discussed. The dynamic interaction is shown to comprise two effects: the effect of the interaction forces arising at the attachment points, and the effect of the changes in the primary system properties resulting from the attachment of the secondary system. In addition, numerical examples are provided to demonstrate the validity of the proposed analysis.

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