Seismic analysis of coupled structural systems with nonproportional damping

In analyzing seismic response of a sub-structure contained in a building or heavy-industry structure, the current industry practice is to first analyze the building subjected to the seismic ground motion, and then analyze the sub-structure using the response of the building floor where the sub-structure is attached to. Such uncoupled analysis approach ignores the interaction effect between the sub-structure and the building. This interaction effect has generally been assumed insignificant for cases in which the mass of the sub-structure is relatively small compared to the building. However, recent researches have revealed that under certain conditions, the interactions can be significant even for very light sub-structures. In order to account for such interaction effect, it is required to analyze the entire building including the sub-structure concurrently. Since the damping characteristics of the building and the sub-structure are different the damping matrix of the coupled structure is non-proportional.; Structural systems with non-proportional damping invalidate the application of the conventional modal superposition method because these systems yield coupled second-order differential equations. To retain the advantage of using the conventional modal superposition method for non-proportionally damped systems, complex modes are required instead of the real modes.; An alternative approach to obtain accurate solutions of non-proportionally damped systems was introduced by Udwadia in 1991. It is an iterative method based on the pseudo-force concept. Since then, a number of approaches have been developed by several different research groups. Basically, all these approaches are intended to modify the diagonal terms of the generalized damping matrix in order to improve the analysis process. However, each approach has its application limitations as well as accuracy deficiencies.; The new pseudo-force based iterative method proposed in this dissertation is different from the existing ones. A scale factor for each mode of the system was obtained by optimizing the iteration convergence. Through this uniquely solved scale factor, the modified modal equations can not only converge faster but also yield much better results. Various typical problems were analyzed using the proposed method and two existing methods and the results were compared to demonstrate the superiority of the proposed method.