A new algorithm, fast frequency response analysis (FFRA), for the modal frequency response analysis (FRA) with gyroscopic effects is presented for a large and complex structural system. Because the modal gyroscopic matrix is low rank matrix compared to other modal matrices, the FFRA algorithm uses the Sherman-Morrison-Woodbury formula for computing the inverse of coefficient matrix efficiently. The new method, FFRA algorithm, dramatically improve the performance of the modal frequency response analysis with gyroscopic matrix compared to conventional methods in industry with the same accuracy.
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