Reduced Order Models of Structures with Viscoelastic Components

MI Friswell (University of Wales Swansea) & DJ Inman, (Virginia Tech, USA)

AIAA Journal, Vol. 37, No. 10, October 1999, pp. 1318-1325

Abstract

A useful method of modelling viscoelastic effects in structures for transient response analysis is to treat the frequency dependence of the usual damping model through the introduction of extra dissipation co-ordinates or internal variables. These new co-ordinates require a curve fit to the material loss factor data over a range of frequencies. These methods have the disadvantage of introducing a large number of extra degrees of freedom that make response calculations and controller design very computationally intensive. This paper examines methods to reduce the model size and hence ease this burden. Eigensystem truncation and balanced realisations are used to successfully reduce the full model. It is demonstrated that methods where the reduction transformation is based on the undamped model produce poor results. An iterative method to calculate the full eigensystem is introduced, using the frequency dependent material modulus. An alternative scheme, whereby the model based on the physical degrees of freedom is reduced before the extra dissipation co-ordinates for the GHM are introduced. Also considered is the possibility of reducing the model at the element level, before assembly, although this approach has difficulty retaining the damping characteristics of the full model.

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