Approximate Evaluation of Eigenfrequencies

  • Andrew D. Dimarogonas
  • Stefanos A. Paipetis
  • Thomas G. Chondros
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 9)


Approximate evaluation of rotors flexural eigenfrequencies is investigated in Chap. 1. However, the formulation is similar for torsional vibrations of shafts or even vibrations of elastic systems in general. The Dunkerley's rule for the determination of lowest eigenfrequency of a lumped-mass, multi-degree-of-freedom elastic shaft is applied along with its extension to higher modes. This procedure generally provides lower bounds for the eigenfrequencies, but its accuracy can be increased at will by means of the root-squaring process, as suggested by Graeffe and Lobachevsky, applicable both to undamped and damped systems. Extension to continuous systems is considered too, and an integral equation formulation of the eigenvalue problem, providing upper and lower bounds for the eigenvalues, which by means of an iterative process can be brought as close as desired. Those methods are useful for predicting bending and torsional fatigue life of rotors and shafts, and furthermore, for developing methodologies for damage detection, and the estimation of position and size of flaws and cracks in rotating machinery.


Critical Speed Torsional Vibration Equal Mass Elastic System Complex Root 
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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Andrew D. Dimarogonas
    • 1
  • Stefanos A. Paipetis
    • 2
  • Thomas G. Chondros
    • 2
  1. 1.Mechanical Engineering DepartmentWashington UniversitySt. LouisUSA
  2. 2.Mechanical Engineering and AeronauticsUniversity of PatrasPatrasGreece

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