A preconditioned iterative method for modal frequency-response analysis of structures with non-proportional damping

A new stationary-type iterative method, the hybrid Jacobi iterative method, is developed for solving modal frequency-response problems with non-proportional damping, which is indefinite linear system. The hybrid Jacobi iterative method is derived by introducing a new preconditioning matrix that results in combining the Jacobi iterative method with the block Jacobi iterative method for solving an indefinite linear system. Numerical demonstrations show accurate results and high performance compared to the direct method.