  This document deals with a method for eigenvalue extraction for the analysis
of structures with viscoelastic materials. A generalized Maxwell model is used
to model linear viscoelasticity. Such kind of model necessitates a state-space
formulation to perform eigenvalue analysis with standard solvers. This
formulation is very close to ADF formulation. The use of several materials on
the same structure and during the same analysis may lead to a large number of
internal states. This article purpose is to identify simultaneously all the
viscoelastic materials and to constrain them to have the same time-constants.
As it is usually possible, the size of the state-space problem is therefore
widely reduced. Moreover, an accurate method for reducing mass and stiffness
operators is proposed; The enhancement of the modal basis allows to obtain good
results with large reduction. As the length of the paper is limited, only
theoretical development are presented in the present paper while numerical
results will be presented in the conference.
