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A conforming unified finite element formulation for the vibration of thick beams and frames
Author(s) -
Hirdaris Spyridon E.,
Lees Arthur W.
Publication year - 2004
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.1211
Subject(s) - timoshenko beam theory , finite element method , beam (structure) , structural engineering , rotary inertia , distortion (music) , vibration , mathematics , computer science , physics , classical mechanics , engineering , inertia , amplifier , computer network , bandwidth (computing) , quantum mechanics
Beams and frames are common features in many engineering structures and in this paper an approach is given to model their dynamic behaviour adequately. Whilst the eigen‐frequencies of continuous systems comprising of slender beams can be identified, in most cases of practical interest, by means of Euler or Timoshenko beam theory, for structures comprising of thick beam models this is not necessarily true since such idealizations constrain the cross‐sections to remain planar. This paper suggests an alternative approach by means of a unified fully conforming plane stress rectangular finite element which is believed to allow for more realistic representation of the shear effects and hence the strain field around the joints of such structures. The usefulness and functionality of this improved numerical approach is explored via comparison against a non‐conforming two‐dimensional plate as well as one‐dimensional Euler–Bernoulli and Timoshenko finite element formulations corresponding to a variety of beam aspect ratios representing the structures of a rotor and a portal frame. The idealization is shown to be particularly advantageous for simulating the effects of shear distortion where beams join at right angles and the transverse forces in one member interact with the extensional forces of the adjoining structure. Copyright © 2004 John Wiley & Sons, Ltd.