Mode-Based Frequency Response Analysis With Frequency-Dependent Material Properties

A new algorithm for mode-based frequency response analysis, which takes into account frequency-dependent material properties, is proposed. First, the projection subspace is determined by computing the eigenmodes of the system. If the AMLS-type eigensolver is used and the frequency-dependent material is confined to a limited area (often less than 1% of the whole model), eigenmodes are computed only in the region with the frequency-dependent material. Next, during the frequency response analysis portions (corresponding to the frequency-dependent material) of the stiffness, viscous damping, and structural damping operators are computed and projected onto the modal subspace. The original contribution of this paper is the algorithm, which augments the projected operators (stiffness, viscous damping, or structural damping) by the contributions from the area with the frequency-dependent material properties without the need to recompute the operator over the whole domain. This algorithm was successfully implemented in a commercial finite element code, Abaqus 6.8. The results for a vehicle body-in-prime model show good agreement with a direct-solution frequency response analysis. In the addition, the cost of the proposed algorithm is a fraction of the directsolution analysis.