Iterative techniques for eigenvalue solutions of damped structures coupled with fluids

When computing the dynamic response of a structure, eigenvalue computations play a central role. For structures with internal compressible fluids, a pressure formulation leads to non symmetric real matrices so that one typically uses complex eigenvalue solvers. Moreover, if one considers structures containing damped materials, the matrices become complex. The present paper discusses a class of partial eigenvalue solvers that are applicable to these problems. The main characteristics of the proposed techniques are the use of iterations on real subspaces, basis enrichment using residues computed at a particular step, and the separate factorization of the real part of the structure and fluid stiffness matrices. These ingredients are key to the significant speedup obtained over a standard complex eigenvalue solver. The paper discusses energy norms which are used to evaluate convergence by estimating the size of residues, and how these residues are used to enrich the basis for the next iteration. The effectiveness of using standard modal approximations of the exact solutions to start the iterations is finally discussed. Evaluations in terms of speed and accuracy are shown for a 57,000 DOFs model of a PSA Peugeot Citroën oil pan, with a constrained viscoelastic layer, and for a model of the main cryogenic stage of Ariane 5 consisting of 88,000 DOFs. Computations are performed using the Structural Dynamics Toolbox for MATLAB taking the MSC/NASTRAN com-plex eigenvalue solver as reference for comparisons