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Errors in response calculations for non‐classically damped structures
Author(s) -
Warburton G. B.,
Soni S. R.
Publication year - 1977
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.4290050404
Subject(s) - damping matrix , modal , diagonal , matrix (chemical analysis) , modal testing , excitation , simple (philosophy) , range (aeronautics) , mathematical analysis , modal analysis , mode (computer interface) , diagonal matrix , mathematics , normal mode , product (mathematics) , physics , computer science , structural engineering , engineering , vibration , acoustics , geometry , stiffness matrix , materials science , philosophy , aerospace engineering , composite material , operating system , epistemology , quantum mechanics , finite element method , polymer chemistry
The classical normal mode method of determining response is extremely useful for practical calculations, but depends upon the damping matrix being orthogonal with respect to the modal vectors. Approximations that allow the method to be used when this condition is not satisfied have been suggested; the simplest approach is to neglect off‐diagonal terms in the triple matrix product formed from the damping and modal matrices. In this paper the errors in response caused by this approximation are determined for several simple structures for a wide range of damping parameters and different types of excitation. Based on these results a criterion, relating modal damping and natural frequencies, is formulated; if this is satisfied, the errors in response caused by this diagonalization procedure are within acceptable limits.