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SUMMARYA structure which consists of a main part and a number of attached substructures is considered. A 'model reduction' scheme is developed and applied to each of the discrete substructures. Linear undamped transient vibrational motion of the structure is assumed, with general external forcing and initial conditions. The goal is to replace each discrete substructure by another substructure with a much smaller number of degrees of freedom, while minimizing the e ect this reduction has on the dynamic behaviour of the main structure. The approach taken here involves Ritz reduction and the Dirichlet-to-Neumann map as analysis tools. The resulting scheme is based on a special form of modal reduction, and is shown to be optimal in a certain sense, for long simulation times. The performance of the scheme is demonstrated via numerical examples, and is compared to that of standard modal reduction.

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SUMMARYA linearly behaving vibrational substructure (or more generally a linear dynamic subsystem) attached to a main structure (or a main dynamic system) is considered. After discretization, the substructure is represented by a finite, typically large, number of degrees of freedom, N s and hence also by N s eigenmodes. In order to reduce the computational effort, it is common to apply 'modal reduction' to the subsystem such that only N r modes out of the total number of N s modes are retained, where N r >N s . The following question then arises: 'Which N r modes should be retained?' In structural dynamics, it is traditional to retain those modes associated with the lowest frequencies. In this paper, the question is answered by solving an appropriate optimization problem. The most important modes of the subsystem are shown to be those whose coupling matrices, which are defined in a particular way, have the highest norm. This leads to a simple and effective algorithm for optimal modal reduction. The new criterion for 'modal importance' is explained both mathematically and physically, and is demonstrated by numerical examples.