The method of substructure synthesis, originally conceived for undamped and viscously damped systems, has been extended to systems with viscoelastic damping in the hereditary integral form. Based on a new variational principle, the substructure synthesis method is formulated in the time domain. The displacement in each substructure is represented by a set of real admissible trial vectors. The traditional state space formulation is avoided by the proposed method so that the approach is independent of the form of viscoelastic models. Effectiveness of the method is illustrated through numerical examples.

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