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A pseudo‐force iterative method with separate scale factors for dynamic analysis of structures with non‐proportional damping
Author(s) -
Lin FengBao,
Wang YungKuo,
Cho Young S.
Publication year - 2003
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.234
Subject(s) - superposition principle , modal , convergence (economics) , coupling (piping) , iterative method , scale (ratio) , iterative and incremental development , mathematics , mode (computer interface) , modal analysis , scale factor (cosmology) , control theory (sociology) , mathematical analysis , mathematical optimization , computer science , physics , structural engineering , engineering , finite element method , materials science , software engineering , artificial intelligence , economic growth , operating system , control (management) , quantum mechanics , mechanical engineering , polymer chemistry , economics , metric expansion of space , dark energy , cosmology
Abstract 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. Copyright © 2002 John Wiley & Sons, Ltd.