Harmonic vibration analysis with coherent-nodal-cluster two-stage model reduction

Linear finite element harmonic vibration analysis is an important tool when investigating structural performance. In order to construct the requested frequency response functions by sweeping through the frequencies, the full finite element model is typically reduced by a Galerkin projection, using either the solution of a free vibration problem, or with load-dependent Ritz vectors. Here we construct an approximation of the model reduction matrix using an intermediate reduced-model stage based on the Coherent Nodal Clusters technique. Thus we arrive at a two-stage model-reduction procedure. Although there is an additional approximation the reduced models are obtained at a much lower cost than the one-stage models. In order to ameliorate the loss of accuracy involved in the additional approximation, we introduce enhancement of the reduced bases by inexpensive residual-minimizing iterations.