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Errors in natural frequency calculations using eigenvalue economization

✍ Scribed by D. L. Thomas

Publisher: John Wiley and Sons
Year: 1982
Tongue: English
Weight: 346 KB
Volume: 18
Category: Article
ISSN: 0029-5981
DOI: 10.1002/nme.1620181007

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✦ Synopsis

Abstract

The eigenvalue economization process is an efficient way of reducing the size of eigenvalue problems to manageable proportions, at the expense of introducing approximations. The use of automatic criteria for selecting the slave variables to be eliminated has considerably eased the use of this technique recently. However, it is necessary to ensure that unacceptable errors are not introduced by the condensation process. Until recently, there has been little available to guide the user in estimating errors except past experience. In this paper, the errors introduced in the condensation process are considered theoretically, using an algebraic approach. This enables an absolute error bound to be stated, together with an approximate bound which can be very easily evaluated. Examples are given of the use of the approximate bound.

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