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A dynamic stiffness formulation for the analysis of secondary systems
Author(s) -
Bernal Dionisio
Publication year - 1999
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/(sici)1096-9845(199911)28:11<1295::aid-eqe867>3.0.co;2-2
Subject(s) - substructure , flexibility method , flexibility (engineering) , stiffness , structural engineering , truncation (statistics) , modal analysis , structural system , degrees of freedom (physics and chemistry) , modal , residual , mathematics , engineering , finite element method , algorithm , physics , statistics , chemistry , quantum mechanics , polymer chemistry
Formulation of a frequency‐domain substructure approach for the analysis of secondary systems is presented. The total system contemplated includes the primary structure, the secondary system, and the foundation medium, which is also treated as a substructure. A dynamic stiffness matrix in physical co‐ordinates characterizes each one of the substructures. Elimination of the internal degrees of freedom of the primary structure prior to assembly of the equations for the coupled system is carried out with the aid of a truncated set of unconstrained normal modes. Accounting for the residual static flexibility of the truncated modes obviates potential problems of rank deficiency resulting from modal truncation. The formulation contemplates an arbitrary multi‐component scattered motion at the soil–structure interface and imposes no limitations on the configuration of the primary or the secondary system. Connectivity between the systems is treated as an arbitrary linear relation between selected co‐ordinates in each substructure. This feature is shown to be useful for modelling the commonly encountered situation where secondary systems are attached to torsionally eccentric structures. Copyright © 1999 John Wiley & Sons, Ltd.