Efficient redesign of damped large structural systems via domain decomposition with exact dynamic condensation

A new redesign technique via domain decomposition with exact dynamic condensation is proposed to enhance computational efficiency of redesign of damped large structural systems. A structural system is regarded as an assemblage of substructures. Nodes in each substructure are classified into boundary nodes and interior nodes. The design variables are determined so that the undamped fundamental natural frequency of the total system and deformation component ratios in the resonant damped steady-state vibration would attain the target values. It is shown that new design sensitivity expressions of the lowest eigenvalue (square of the fundamental circular frequency) can be derived in terms of a condensed coordinate system including boundary nodes only. Incremental inverse problem formulation is then applied to the model in terms of the condensed coordinate system. Different from the conventional static domain decomposition method within the context of redesign, difficulties resulting from inertial force terms in eigenvalue problems and forced steady-state vibration problems are resolved. The validity and order of approximation of the proposed method are demonstrated through an example model.

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