Damped dynamic response determination in the frequency domain for partially damped large scale structures

A methodology is developed to solve the modal frequency response problem for the structural system with partially distributed structural and viscous damping materials and/or components. For the problems of interest, it is noted that the finite element viscous and structural damping matrices are typically very sparse, so the rank of the matrices are identified with the singular value decomposition (SVD) method. Then the modal frequency response problem is reformulated with the low rank matrices obtained from the SVD method. The strategy of the new approach is to compute the modal solution using the Sherman–Morrison–Woodbury formula for the inverse of equation which is subjected to low rank modifications, instead of factoring the coefficient matrix at each excitation frequency. Numerical results are presented to validate and assess the proposed approach, and the advantages of this method are examined.