Dynamic condensation method of nonclassically damped vibration systems

Abstract

Dynamic condensation scheme, which has been widely applied to reduce the number of degrees of freedem of finite element modeling, is presented in this paper. Most of them, however, are valid for undamped systems. An efficient iterative approach for the dynamic condensation of nonclassically damped systems is proposed. The classical subspace iteration method for undamped models is extended to nonclassically damped models. Then, a governing equation for the dynamic condensation matrix in state space is derived from the extended subspace iteration. Two iterative schemes are proposed to slove the governing equation. Because the dynamic condensation matrix is independent of the system matrices and the eigenpairs (eigenvalues and eigenvectos) of the reduced model, it is unnecessary to compute them in every iteration. This makes the proposed method much more computationally efficient than those approaches proposed in the past. The convergence of the proposed approach is also proven. Two numerical examples, one discrete mass-damper-spring system and one floating raft isolation system, are included to demonstrate the convergence of the proposed method. The results show that the convergence of the proposed method is much faster than the previous approaches, especially when the dynamic characteristics of the reduced model are very close to the full model.