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New approaches for non‐classically damped system eigenanalysis
Author(s) -
Khanlari Karen,
GhaforyAshtiany Mohsen
Publication year - 2005
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.467
Subject(s) - eigenvalues and eigenvectors , mathematics , differential equation , differential (mechanical device) , equations of motion , state vector , motion (physics) , computer science , algorithm , mathematical analysis , engineering , physics , classical mechanics , quantum mechanics , artificial intelligence , aerospace engineering
This paper presents three new approaches for solving eigenvalue problems of non‐classically damped linear dynamics systems with fewer calculations than the conventional state vector approach. In the latter, the second‐order differential equation of motion is converted into a first‐order system by doubling the size of the matrices. The new approaches simplify the approach and reduce the number of calculations. The mathematical formulations for the proposed approaches are presented and the numerical results compared with the existing method by solving a sample problem with different damping properties. Of the three proposed approaches, the expansion approach was found to be the simplest and fastest to compute. Copyright © 2005 John Wiley & Sons, Ltd.