Dynamic condensation method for viscously damped vibration systems in engineering

Abstract

An iterative dynamic condensation method for the model reduction of viscously damped vibration systems is presented in this paper. The dynamic condensation matrix, which relates the displacements on kept and deleted degrees of freedom, is defined in state space. A governing equation for the dynamic condensation matrix is derived from the dynamic equations of the full model in state space. Since the dynamic condensation matrix is independent of the eigenpairs of the reduced model, it is unnecessary to calculate them in every iteration. This makes the iterative scheme very efficient especially when the number of kept degrees of freedom is large. It is proven that the dynamic condensation matrix is a natural characteristic of the system and is not affected by the external forces. Two engineering systems, a tall building with tuned mass damper and a floating raft isolation system, are also included in this paper. The effect of the selection of kept degrees of freedom on the accuracy of the reduced model is examined by using the first example. The results show that the proposed iterative method is efficient for the model reduction of viscously damped systems.