Reduced-Order Models of Structures with Viscoelastic Components

Abstract

A useful method of modeling 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 coordinates or internal variables. These new coordinates require a curve e t to the material loss factor data over a range of frequencies. Such a method has the disadvantage of introducing a large number of extra degrees of freedom that make response calculations and controller design very computationally intensive. Methods are examined to reduce the model size and, hence, ease this burden. Eigensystem truncation and balanced realizations 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. 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 considered is the possibility of reducing the model at the element level, before assembly, although this approach has dife culty retaining the damping characteristics of the full model.