The Application of the IRS and Balanced Realisation Methods to Obtain Reduced Models of Structures with Local Nonlinearities

MI Friswell (University of Wales Swansea), JET Penny & SD Garvey (Aston University)

Journal of Sound and Vibration, Vol. 196, No. 4, October 1996, pp. 453-468


This paper considers the application of model reduction methods, which are popular for linear systems, to systems with local non-linearities, modelled using finite element analysis. In particular these methods are demonstrated by obtaining the receptance of a continuous system with cubic stiffening discrete springs, using the harmonic balance method. The model reduction methods available and the choice of master coordinates are considered. In the IRS method there is a conflict in the choice of master coordinates between the demands in the modelling of the non-linearity and the accuracy of the linear reduction. Other reduction methods considered are the reduction to modal coordinates and a balanced realisation approach. Reduction to modal coordinates is easy to apply and gives acceptable results, although a more accurate reduced model may be obtained with IRS and the best choice of master coordinates. Reduction based on observability and controllability considerations, via balanced realisations, gives the most accurate reduced model. The reduction methods were compared in a time domain analysis by calculating the Poincare map of a pinned beam with clearance. The balanced realisation approach gave more accurate results than the reduction to modal coordinates for these simulations.

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Link to paper using doi:10.1006/jsvi.1996.0495

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