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A method for the transfer function matrix of combined primary–secondary systems using classical modal decomposition
Author(s) -
HerediaZavoni E.,
PérezPérez A.,
BarrancoCicilia F.
Publication year - 2006
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.525
Subject(s) - sequence (biology) , transfer function , convergence (economics) , damping matrix , modal , computation , matrix (chemical analysis) , function (biology) , damping ratio , modal analysis , mathematics , natural frequency , iterative method , mathematical analysis , algorithm , structural engineering , engineering , physics , vibration , acoustics , materials science , stiffness matrix , genetics , finite element method , evolutionary biology , polymer chemistry , electrical engineering , economics , composite material , biology , economic growth
An iterative method is presented to compute the transfer function matrix of combined primary–secondary systems for seismic response analysis. It accounts for non‐proportional damping and dynamic interaction of the combined system. A closed form sequence is developed for the iterative computation of the transfer function matrix. Such sequence is assembled using independently the real classical mode frequencies, shapes and damping ratios of the primary system, and the natural frequency and critical damping ratio of the SDOF secondary system. The necessary and sufficient condition for convergence of the sequence is given in the paper. The method is illustrated through a couple of examples, including one of an appendix connected to a multi‐storey shear building. Convergence of the method is thoroughly analysed and peak responses are obtained using a spectral density function approach. Copyright © 2005 John Wiley & Sons, Ltd.