1 14/03/97 Superelement representation of a model with frequency dependent properties. Etienne Balmès ONERA Direction des structures B.P. 72, 92322 Chatillon Cedex, FRANCE ABSTRACT The paper analyses problems linked to the prediction of the frequency response of a truss composed of tubes filled with a sand assumed to have frequency dependent properties. The full order model being too large for its solution to be affordable, it is proposed to use superelements parametrized in terms of tube length and frequency dependent complex modulus of the sand. Problems addressed in the paper include numerical representation of the parametrized model, superelement interface reduction, reduction of a parametrized model, verification of the reduced model validity, and prediction of the damped frequency response for a tube and a truss. 1. INTRODUCTION 1.1. Motivation Isolation devices made of polymers, tubes filled with propergol, distributed vibration damping treatments and a number of other structures have vibration characteristics that have a significant dependence on the properties of viscoelastic materials. It has been shown (see [1,2] for example) that the properties of such materials can be represented over a broad frequency range by a linear elastic model with a frequency dependent complex modulus. When using a complex modulus, the relation between applied forces u and physical displacements y is linear (there is a transfer function from u to y) and it can be computed by inverting, at each frequency of interest, the dynamic stiffness matrix. If a simple parametric model of the dependence of the modulus on frequency is available, it is possible to consider additional degrees of freedom in the model and build a model that is linear in frequency [3]. This approach, however, is limited to relatively simple parametric models of the modulus, implies the need to create specific finite elements, and leads to the use of larger models. The frequency dependent modulus leads to simpler formulations but is not directly compatible with traditional modal methods based on frequency independent matrices. This is a problem for large models (with tens of thousands of DOFs) and/or large frequency bands (with many frequency points), for which the cost of an assembly and direct solution at each frequency point is often too high. To resolve this difficulty, it is proposed to project the models used on constant bases of Ritz ______________________________________ Copyright © 1996 by Etienne Balmès. To appear in the proceedings of ISMA 21. Leuven, September, 1996.