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Vibration of shear‐deformable beams using a spline‐function approach
Author(s) -
Dawe D. J.,
Wang S.
Publication year - 1992
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.1620330410
Subject(s) - deflection (physics) , vibration , rayleigh–ritz method , shear (geology) , displacement field , spline (mechanical) , structural engineering , mathematics , mathematical analysis , physics , engineering , classical mechanics , acoustics , geology , finite element method , petrology
B ‐spline functions are used as trial functions in a Rayleigh‐Ritz analysis of the free vibration of shear‐deformable Timoshenko beams. In a first approach it is demonstrated in numerical applications that when the lateral deflection and the cross‐sectional rotation are represented by functions of equal order the calculated natural frequencies are of good accuracy for stocky beams but can overestimate the true frequencies very considerably for slender beams. This is identified as a shear‐locking difficulty and consideration of its causes points clearly to the adoption of a new displacement field in which the deflection is represented by a B ‐spline function which is one order higher than that used to represent the rotation. Numerical results using this new displacement field demonstrate good accuracy for both stocky and slender beams: the shear‐locking difficulty is completely eliminated. This has clear significance for the analysis of shear‐deformable plates and shells when using B ‐spline functions.