Optimal modal reduction of vibrating substructures

A 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