Natural frequencies of structures with interval parameters

Author Type

Outside Researcher

Co-Author Type 1

Outside Researcher

Co-Author Type 2

Faculty

Co-Author Type 3

Outside Researcher

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

Journal of Sound and Vibration

Publication Status

Version of Record

Abstract

This paper deals with the evaluation of the lower and upper bounds of the natural frequencies of structures with uncertain-but-bounded parameters. The solution of the generalized interval eigenvalue problem is pursued by taking into account the actual variability and dependencies of uncertain structural parameters affecting the mass and stiffness matrices. To this aim, interval uncertainties are handled by applying the improved interval analysis via extra unitary interval (EUI), recently introduced by the first two authors. By associating an EUI to each uncertain-but-bounded parameter, the cases of mass and stiffness matrices affected by fully disjoint, completely or partially coincident uncertainties are considered. Then, based on sensitivity analysis, it is shown that the bounds of the interval eigenvalues can be evaluated as solution of two appropriate deterministic eigenvalue problems without requiring any combinatorial procedure. If the eigenvalues are monotonic functions of the uncertain parameters, then the exact bounds are obtained. The accuracy of the proposed method is demonstrated by numerical results concerning truss and beam structures with material and/or geometrical uncertainties.

First Page

79

Last Page

95

DOI

10.1016/j.jsv.2015.02.037

Publication Date

7-7-2015

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