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

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SUMMARY

This discussion focuses on the need for resources regarding complex eigenvalue problems in Finite Element Method (FEM) analysis, particularly those involving damping. Recommended texts include W.T. Thomson’s "Theory of Vibration with Applications" and the "Shock and Vibration Handbook" by McGraw-Hill. Additionally, the documentation of specific Finite Element Analysis (FEA) software often contains valuable insights into the complex eigenvalue extraction procedure. The topic is relevant for applications in composite materials and dynamic stability issues such as brake squeal and rotor whirl.

PREREQUISITES
  • Understanding of Finite Element Method (FEM) analysis
  • Familiarity with complex eigenvalue problems
  • Knowledge of damping effects in engineering
  • Basic principles of dynamic stability in mechanical systems
NEXT STEPS
  • Research the complex eigenvalue extraction procedure in specific FEA software documentation
  • Study W.T. Thomson’s "Theory of Vibration with Applications" for foundational concepts
  • Examine the "Shock and Vibration Handbook" for practical applications
  • Explore Zienkiewicz, Taylor, and Zhu's treatment of complex eigenvalues in their textbook
USEFUL FOR

Engineers, researchers, and students involved in mechanical engineering, particularly those focusing on vibration analysis, dynamic stability, and FEM applications in composite materials and aerospace engineering.

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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