Fast frequency response analysis of partially damped structures with non-proportional viscous damping

This paper presents a new method for the modal frequency response analysis of partially damped structural system with non-proportional viscous damping. The basic idea is to handle the modal viscous damping matrix by noting that the rank of the viscous damping matrix is typically very low for problems of interest. Then, the Sherman–Morrison–Woodbury formula provides a convenient expression for the inverse of equation which includes the low-rank matrix. The new method, fast frequency response analysis (FFRA) algorithm, dramatically improves the performance of the modal frequency response analysis compared to conventional methods in industry with the same accuracy.