A pseudo-force iterative method with separate scale factors for dynamic analysis of structures with non-proportional damping

摘要

Dynamic equilibrium equations of structural systems with non-proportional damping are coupled through the damping terms. Such coupling invalidates application of the classical modal superposition method. In this paper, a mode-superposition pseudo-force method is proposed. The coupled equilibrium equations are solved by an iterative process in which the coupling terms are treated as pseudo-forces: A scale factor for each mode of the system is obtained by optimizing the iteration convergence. Through these uniquely solved scale factors, the modified modal equations not only converge much faster but also yield results with higher accuracy. A proof of the convergence of the iterative process is also presented.