An Energy Measure for Mode Localization

  • Michael I. Friswell
  • Arun Chandrashaker
  • Sondipon Adhikari
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


The vibration characteristics of periodic structures are highly sensitive to its mass distribution, stiffness distribution and geometrical properties. Parametric uncertainties in structures that arise due to material defects, structural damage or variations in material properties can break the symmetry of periodic structures. This often leads to mode localization, where the deformation in a mode is concentrated in a small region of the structure. Localization can be directly detected by visually inspecting animated mode shapes given by finite element software. Although a visual approach is physically intuitive, for complex geometries the identification of mode localization can be subjective and may not be obvious. Hence this paper presents a reliable method to measure the degree of mode localization based on the distribution of energy within the modes of the finite element model. The properties of this measure are demonstrated by examples. Such a measure will be of great value in optimization studies where it can be included directly in objective functions or constraints.


Mode veering Mistuning Localization Uncertainty Periodic structure 


  1. 1.
    Ewins, D.J.: Vibration characteristics of bladed disc assemblies. J. Mech. Eng. Sci. 15(3), 165–186 (1973)CrossRefGoogle Scholar
  2. 2.
    Pierre, C., Murthy, D.V.: Aeroelastic modal characteristics of mistuned blade assemblies - mode localization and loss of eigenstructure. AIAA J. 30(10), 2483–2496 (1992)CrossRefGoogle Scholar
  3. 3.
    Castanier, M.P., Pierre, C.: Modeling and analysis of mistuned bladed disk vibration: status and emerging directions. J. Propul. Power 22(2), 384–396 (2006)CrossRefGoogle Scholar
  4. 4.
    Nikolic, M.: New insights into the blade mistuning problem. Ph.D. thesis, Imperial College (2006)Google Scholar
  5. 5.
    Slater, J.C., Blair, A.J.: Minimizing sensitivity of bladed disks to mistuning. In: Proceedings 16th IMAC Conference, Society of Experimental Mechanics, Santa Barbara, pp. 284–290 (1998)Google Scholar
  6. 6.
    Parker, G.R., Brown, J.J.: Kinetic energy DMAP for mode identification. In: Proceedings of the MSC/NASTRAN Users Conference, Pasadena (1982)Google Scholar
  7. 7.
    Parker, G.R., Rose, T.L., Brown, J.J.: Kinetic energy calculation as an aid to instrumentation location in modal testing. In: Proceedings of the MSC World Users Conference, Los Angeles (1990)Google Scholar
  8. 8.
    Chung, Y.T., Kahre, L.L.: A general procedure for finite element model check and model identification. In: Proceedings of the MSC World Users Conference, Universal City, California (1995)Google Scholar
  9. 9.
    Nehad, B.I., Fiorelli, K.J., Le, A.D., Leuer, J.P., Wright, D.R.: A quantitative approach to target mode selection for component-level modal survey. In: Proceedings of IMAC XVI, Santa Barbara, pp. 1401–1408 (1998)Google Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2016

Authors and Affiliations

  • Michael I. Friswell
    • 1
  • Arun Chandrashaker
    • 1
  • Sondipon Adhikari
    • 1
  1. 1.College of Engineering, Swansea UniversitySwanseaUK

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