HYBRID DYNAMIC CONDENSATION FOR EIGENPROBLEMS

An iterative method is presented for the efficient calculation of eige npairs in dynamic problems. Based on the dynamic condensation, the met hod has been improved through the use of a modified subspace iteration and dynamic reduction. While the usual dynamic condensation method ge ts the eigenpairs one by one and requires repeated decomposition of th e dynamic stiffness matrix, several eigenpairs are to be obtained simu ltaneously in the present study. The approximate eigenvectors obtained in the dynamic condensation are used as a starting point in the next step of simplified inverse iteration. The proposed method carries out the inverse calculation for the primary and secondary degrees of freed om separately. Hence, the decomposition of the original stiffness matr ix is not required. The minimization of the Rayleigh quotient gives an eigenproblem in a reduced subspace and provides the orthogonality of the approximate eigenvectors. It should be emphasized that the orthogo nality is only a necessary condition for the solution. For further imp rovement, an expanded subspace can be considered using a transformatio n matrix and the approximate eigenmodes. Numerical examples in a typic al problem show fast convergence. Even when the eigenvalues are closel y distributed, excellent results can be obtained.