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Variable Elasticity Effects in Rotating Machinery

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Analytical Methods in Rotor Dynamics

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 9))

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Abstract

The effects of variable elasticity in rotating machinery occur with a large variety of mechanical, electrical, etc., systems, in the present case, geometrical and/or mechanical problems. Parameters affecting elastic behavior do not remain constant, but vary as functions of time. Systems with variable elasticity are governed by differential equations with periodic coefficients of the Mathieu-Hill type and exhibit important stability problems. In this chapter, analytical tools for the treatment of this kind of equations are given, including the classical Floquet theory, a matrix method of solution, solution by transition into an equivalent integral equation and the BWK procedure. The present analysis is useful for the solution of actual rotor problems, as, for example, in case of a transversely cracked rotor subjected to reciprocating axial forces. Axial forces can be used to control large-amplitude flexural vibrations. Flexural vibration problems can be encountered under similar formulation.

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Notes

  1. 1.

    Named after three authors: L. Brillouin (J. Phys., 7, 1926, 353); G. Wentzel (Z. Phys., 38, 1926, 518); and E.C. Kemble (The Fundamental Principles of Quantum Mechanics, McGraw-Hill, New York, 1937).

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Authors and Affiliations

  1. Mechanical Engineering Department, Washington University, St. Louis, Missouri, USA

    Andrew D. Dimarogonas

  2. Mechanical Engineering and Aeronautics, University of Patras, Ostfold Fylke, University Campus, Rio, 26500, Patras, Greece

    Stefanos A. Paipetis & Thomas G. Chondros

Authors
  1. Andrew D. Dimarogonas
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  2. Stefanos A. Paipetis
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  3. Thomas G. Chondros
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Correspondence to Thomas G. Chondros .

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Dimarogonas, A.D., Paipetis, S.A., Chondros, T.G. (2013). Variable Elasticity Effects in Rotating Machinery. In: Analytical Methods in Rotor Dynamics. Mechanisms and Machine Science, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5905-3_2

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  • DOI: https://doi.org/10.1007/978-94-007-5905-3_2

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-5904-6

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