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Some error bounds and numerical experiments in modal methods for dynamics of systems
Author(s) -
Gladwell I.,
Hanson P. M.
Publication year - 1984
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.4290120103
Subject(s) - modal , equivalence (formal languages) , variety (cybernetics) , vibration , modal testing , mathematics , modal analysis , mathematical analysis , physics , pure mathematics , statistics , acoustics , chemistry , polymer chemistry
We present some error expressions for approximate modal solutions of viscously damped linear structural vibration equations; these approximations are calculated by a variety of modal techniques. Motivated by our numerical experience, we show the equivalence of some different modal solutions in the presence of classical damping and, in passing, we obtain a previously unremarked manifestation of this type of damping. We make some brief comments about obtaining error estimates and, finally, we show some numerical results for a standard test problem which illustrate properties of the modal solutions.