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

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Recommendations for books addressing complex eigenvalue problems in finite element method (FEM) analysis include W.T. Thomson's "Theory of Vibration with Applications" and the "Shock and Vibration Handbook" by McGraw-Hill. These texts cover the theory behind eigenvalue problems, including damping, which is relevant in fields like composite materials and aerospace engineering, particularly in relation to phenomena such as wing flutter and brake squeal. Additionally, the documentation of specific FEA software often provides insights into the complex eigenvalue extraction process. Zienkiewicz, Taylor, and Zhu also touch on complex eigenvalues in their work, specifically in sections discussing dynamic stability and the governing equation Mu" + Cu' + ku = 0.
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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