Natural Frequencies of a Structure with Bounded Uncertainty
Publication: Journal of Engineering Mechanics
Volume 132, Issue 12
Abstract
Frequency analysis of a structural system with bounded uncertainty is presented. An interval (set-theoretic) formulation is used to quantify the uncertainty present in the structure’s parameters such as material properties. Independent variations for each element are considered. Using the developed interval finite-element method, it is proven that, in the presence of any physically allowable uncertainty in the structural stiffness, the solutions to two deterministic problems are sufficient to obtain the exact bounds on the system’s fundamental frequencies. Therefore, calculating the bounds on frequencies does not require a combinatorial solution procedure. Several example problems that illustrate the developed algorithm with comparison to existing interval eigenvalue solution are presented. The solutions show no overestimation in the bounds of calculated frequencies which has been a difficulty with other interval procedures.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 132 • Issue 12 • December 2006
Pages: 1363 - 1371
Copyright
© 2006 ASCE.
History
Received: Apr 7, 2004
Accepted: Jul 7, 2006
Published online: Dec 1, 2006
Published in print: Dec 2006
Notes
Note. Associate Editor: Raimondo Betti
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