Reduced-order models of structures with viscoelastic components

A useful method of modeling viscoelastic effects in structures far transien t response analysis is to treat the frequency dependence of the usual dampi ng model through the introduction of extra dissipation coordinates or Inter nal variables. These new coordinates require a curve fit to the material lo ss factor data over a range of frequencies. Such a method has the disadvant age of introducing a large number of extra degrees of freedom that make res ponse calculations and controller design very computationally Intensive. Me thods are examined to reduce the model size and, hence, ease this burden. E igensystem truncation and balanced realizations are used to successfully re duce the full model. It is demonstrated that methods where the reduction tr ansformation is based on the undamped model produce poor results. An iterat ive method to calculate the full eigensystem is introduced, using the frequ ency-dependent material modulus. In an alternative scheme, the model based on the physical degrees of freedom is reduced before the extra dissipation coordinates for the Golla-Hughes-McTavish method are introduced. Also consi dered is the possibility of reducing the model at the element level, before assembly, although this approach has difficulty retaining the damping char acteristics of the full model.