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Computer analysis of a rotating axial‐turbomachine blade in coupled bending‐bending‐torsion vibrations
Author(s) -
Fu C. C.
Publication year - 1974
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620080312
Subject(s) - turbomachinery , vibration , extrapolation , rate of convergence , torsion (gastropod) , turbine blade , digital computer , timoshenko beam theory , mathematical analysis , structural engineering , turbine , computer science , mathematics , engineering , mechanical engineering , acoustics , physics , medicine , computer network , channel (broadcasting) , surgery , computer engineering
Basic equations are derived for a comprehensive computer analysis for an equivalent lumped parameter system which simulates a pre‐twisted, rotating or non‐rotating. Timoshenko beam in coupled bending‐bending‐torsion vibrations. These equations enable one to develop straightforwardly digital computer programs for studying vibration problems related to compressor or turbine blades in turbomachinery as well as in other structural dynamics applications. The validity of the lumped parameter approach is established through a free vibration study. Good agreement between the present computer results and those obtained theoretically or experimentally by other investigators is demonstrated. In particular, it is found that the natural frequencies obtained in the free vibration study for all beams examined converge from below the exact values at a convergence rate of N −4 , where N is the total number of the lumped parameters used in the computer simulation. The rapid rate of convergence shows that the mathematical model used in deriving the basic equations can adequately represent the type of beams under consideration. The known convergence rate also provides an estimate on the accuracy of the computer results, and a means to improve these results by extrapolation.