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Krylov vectors and the concept of parameter matching are combined together to develop a model reduction algorithm for a damped structural dynamics system. The obtained reduced-order model matches a certain number of low-frequency moments of the full-order system. The major application of the present method is to the control of flexible structures. It is shown that, in the control of flexible structures, three types of control energy spillover generally exist: control, observation, and dynamic. The formulation based on Krylov vectors can eliminate both the control and observation spillovers while leaving only the dynamic spillover to be considered. Two examples are used to illustrate the efficacy of the Krylov method.

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When the response of a structural system to dynamic excitation must be analyzed, a substructure coupling method (or component-mode synthesis method) is frequently employed to reduce the order of the finite element model of the structure. This paper reviews procedures used to formulate component modes for substructures and to assemble substructure models to form reduced-order models of the original system. A brief literature survey covering several applications of substructure coupling is also presented.