Book considering FEM analysis for complex eigenvalues (incl. damping)

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Discussion Overview

The discussion revolves around recommendations for books that address complex eigenvalue problems within the context of finite element method (FEM) analysis, particularly those that include damping effects. The scope includes theoretical aspects as well as applications in fields such as composite materials and aerospace engineering, with specific mention of phenomena like wing fluttering.

Discussion Character

  • Exploratory, Technical explanation

Main Points Raised

  • One participant seeks recommendations for books that cover complex eigenvalue problems in FEM analysis, specifically those involving damping.
  • Another participant suggests W.T. Thomson’s "Theory of Vibration with Applications" and the "Shock and Vibration Handbook" as potential resources, noting that FEA software documentation may also provide relevant theoretical insights.
  • A further contribution mentions that complex eigenvalue analyses are applicable to issues like brake squeal and dynamic stability, such as rotor whirl.
  • It is noted that Zienkiewicz, Taylor, and Zhu briefly discuss complex eigenvalues in their work, specifically in chapters addressing the equation Mu" + Cu' + ku = 0.

Areas of Agreement / Disagreement

Participants provide various book recommendations and resources, but there is no consensus on a single definitive source or approach to the topic.

Contextual Notes

The discussion does not resolve the specific applicability of the recommended texts to the participant's needs, nor does it clarify the depth of coverage regarding complex eigenvalues and damping in the suggested materials.

Arjan82
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Can anyone recommend a book in which complex eigenvalue problems are treated? I mean the FEM analysis and the theory behind it. These are eigenvalue problems which include damping. I think that it is used for composite materials and/or airplane engineering (maybe wing fluttering?).
 
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You should find some information on this topic in W.T. Thomson’s book "Theory of Vibration with Applications" as well as in "Shock and Vibration Handbook" published by McGraw-Hill. Apart from such general books about vibrations, I would check the documentation of particular FEA software, theory behid the complex eigenvalue extraction procedure is usually discussed there.

Complex eigenvalue analyses are used for problems such as brake squeal and widely understood dynamic stability (rotor whirl).
 
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Zienkiewicz, Taylor and Zhu briefly mention complex eigenvalues in Ch. 16.6 - 16.8 where they treat the equation Mu" +Cu' + ku = 0
 

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