Iterative system solvers for the frequency analysis of linear mechanical systems

The paper deals with the numerical treatment of the direct frequency domain (DFD) analysis of linear mechanical systems. Attention is mainly focused on the solution of the complex system of equations needed for each analyzed frequency. Strategies for transforming the system into the `shifted' form (T-σI)z = d are proposed and discussed, where σ is related to the frequency. For two formulations of the shifted system the performance of some Krylov sub-space iterative solvers is tested and compared to that of a multi-frontal direct method. Advantage is taken of the shifted form in solving simultaneously a large number of systems resulting from different values of the shift (frequency). Numerical experiments on some prototype structural dynamics problems are reported; the results shown demonstrate how the devised strategies for the iterative solution can outperform, in many cases, the direct solver.