Comparison of computational generalized and standard eigenvalue solutions of rotating systems

Ali Tatar, Loic Salles, Alexander H. Haslam, Christoph W. Schwingshackl

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)

Abstract

Modal analysis is regularly used to compute natural frequencies and mode shapes of structures via eigenvalue solutions in vibration engineering. In this paper, the eigenvalue problem of a 6 degrees of freedom rotating system with gyroscopic effects, including axial, torsional and lateral motion, is investigated using Timoshenko beam theory. The main focus thereby is the investigation of the computational time and the numerical errors in generalized and standard eigenvalue solutions of rotating systems. The finite element method is employed to compute the global stiffness, mass and gyroscopic matrices of the rotating system. The equations of motion is expressed in the state space form to convert the quadratic eigenvalue problem into the generalized and standard forms. The number of elements in the finite element model was varied to investigate the convergence of the natural frequencies and the computational performance of the two eigenvalue solutions. The numerical analyses show that the standard eigenvalue solution is significantly faster than the generalized one with increasing number of elements and the generalized eigenvalue solution can yield wrong solutions when using higher numbers of elements due to the ill-conditioning phenomenon. In this regard, the standard eigenvalue solution gives more reliable results and uses less computational time than the generalized one.

Original languageEnglish
Title of host publicationTopics in Modal Analysis and Testing, Volume 9 - Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics 2018
EditorsMichael Mains, Brandon J. Dilworth
PublisherSpringer Science and Business Media, LLC
Pages187-194
Number of pages8
ISBN (Print)9783319746999
DOIs
Publication statusPublished - 2019
Externally publishedYes
Event36th IMAC, A Conference and Exposition on Structural Dynamics, 2018 - [state] FL, United States
Duration: 12 Feb 201815 Feb 2018

Publication series

NameConference Proceedings of the Society for Experimental Mechanics Series
ISSN (Print)2191-5644
ISSN (Electronic)2191-5652

Conference

Conference36th IMAC, A Conference and Exposition on Structural Dynamics, 2018
Country/TerritoryUnited States
City[state] FL
Period12/02/1815/02/18

Keywords

  • Generalized eigenvalue
  • Gyroscopic systems
  • Modal analysis
  • Rotor dynamics
  • Standard eigenvalue

Fingerprint

Dive into the research topics of 'Comparison of computational generalized and standard eigenvalue solutions of rotating systems'. Together they form a unique fingerprint.

Cite this