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A family of modal methods for computing eigenvector derivatives with repeated roots

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Abstract

A family of modal methods for computing eigenvector derivatives with repeated roots are directly derived from the constraint generalized inverse technique which is originally formulated by Wang and Hu. Extensions are made to Akgün's method to allow treatment of eigensensitivity with repeated roots for general nondefective systems, and Bernard and Bronowicki's modal expansion approach is expanded to a family of modal methods.

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References

  1. Wang WL, Hu HC. Small parameter technique with repeated eigenvalues.J Fudan Univ, 1993, 32(2): 168–176 (in Chinese)

    MATH  MathSciNet  Google Scholar 

  2. Wang BP. Improved approximate methods for computing eigenvector derivatives in structural dynamics.AIAA J, 1991, 29(6): 1018–1020

    Google Scholar 

  3. Akgün MA. New family of modal methods for calculating eigenvector derivatives.AIAA J, 1994, 32(2): 379–386

    Article  MATH  Google Scholar 

  4. Bernard ML, Bronowicki AJ. Modal expansion method for eigensensitivity with repeated roots.AIAA J, 1994, 32(7): 1500–1506

    MATH  Google Scholar 

  5. Zhang YQ, Wang WL. Eigenvector derivatives of generalized nondefective eigenproblems with repeated eigenvalues.ASME J Engineering for Gas Turbines and Power. 1995, 117(1): 207–212

    Google Scholar 

  6. Murthy DV, Haftka RT. Derivatives of eigenvalues and eigenvectors of a general complex matrix.Int J Numer Methods Eng, 1988, 26: 293–311

    Article  MATH  MathSciNet  Google Scholar 

  7. Wang RC, Wang WL. On the application of generalized inverse for computing eigensensitivity.Acta Mechanica Solida Sinica, 1994, 7(4): 292–305

    Article  Google Scholar 

  8. Wang WL. Sensitivity analysis of discrete vibratory systems.Acta Mechanica Sinica, 1995, 27(2): 180–188 (in Chinese)

    Google Scholar 

  9. Wang RC, Wang WL. Further demonstration for eigensensitivity analysis of nondefective vibrating systems.J Vibration and Shock, 1994, 13(4): 1–6 (in Chinese)

    Google Scholar 

  10. Hu HC. Theory of Natural Vibration for MDOF Structures. Beijing: Science Press, 1987. 1–7 (in Chinese)

    Google Scholar 

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The project supported by the National Natural Science Foundation of China

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Wenliang, W. A family of modal methods for computing eigenvector derivatives with repeated roots. Acta Mech Sinica 12, 158–168 (1996). https://doi.org/10.1007/BF02486794

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  • DOI: https://doi.org/10.1007/BF02486794

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