Natural Frequencies of a Structure with Bounded Uncertainty

This paper presents frequency analysis of a structural system with bounded uncertainty. 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 2 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 and compare it to existing interval eigenvalue solutions 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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  • Authors:
    • Modares, Mehdi
    • Mullen, Robert L
    • Muhanna, Rafi L
  • Publication Date: 2006-12


  • English

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  • Accession Number: 01042260
  • Record Type: Publication
  • Files: TRIS
  • Created Date: Feb 14 2007 6:01PM