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Gradients for Large Structural Models with Repeated Frequencies
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English
Abstract
The physical origin and ambiguity of repeated frequency modes, is discussed, followed by a mathematical derivation of the governing equations for the derivatives of repeated eigenvalues. This is followed by a derivation for the associated eigenvector gradient equations and two small examples to illustrate the solution procedure. Physical interpretations are also included to help explain the analytical results. An efficient computation procedure which preserves the bandwidth for very large matrices is also proposed for systems with repeated or closely spaced eigenvalues.
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Citation
Ojalvo, I., "Gradients for Large Structural Models with Repeated Frequencies," SAE Technical Paper 861789, 1986, https://doi.org/10.4271/861789.Also In
References
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- Ojalvo, I.U. “Efficient Computation of Mode-Shape Derivatives for Large Dynamic Systems” 27th SDM Conference, AIAA/ASME/ASCE/AHS San Antonio, TX May 1986 242 247
- Crandall, S.H. “Engineering Analysis” McGraw-Hill N.Y. 1956
- Fox, R.L. Kapoor, M.P. “Rates of Change of Cigenvalues and Eigenvectors,” AIAA Journal 6 12 Dec. 1968 2426 2429