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Improved Finite Elements for Vibration Analysis of Tapered Beams

Published online by Cambridge University Press:  07 June 2016

J Thomas  and
E Dokumaci
J Thomas
Affiliation:
University of Surrey
E Dokumaci
Affiliation:
University of Surrey
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Summary

This paper gives two improved tapered elements for vibration analysis derived using quintic polynomial displacement functions. The elements employ different nodal continuity conditions. Results are compared with those given by the basic cubic approximations and analytical solutions for various end conditions. The advantages of the new elements over the basic element are discussed.

Type
Research Article
Information
Aeronautical Quarterly , Volume 24 , Issue 1 , February 1973 , pp. 39 - 46
Copyright
Copyright © Royal Aeronautical Society. 1973

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References

1 Zienkiewicz, O C The Finite Element Method in Structural and Continuum Mechanics. McGraw-Hill, 1967.Google Scholar
2 Carnegie, W Thomas, J Dokumaci, E An improved method of matrix displacement analysis in vibration problems. Aeronautical Quarterly, Vol XX, p 321, 1969.CrossRefGoogle Scholar
3 Leckie, F A Lindberg, G M The effect of lumped parameters on beam frequencies. Aeronautical Quarterly, Vol XIV, p 224, 1963.CrossRefGoogle Scholar
4 Archer, J S Consistent mass matrix for distributed mass systems. Proceedings, American Society of Civil Engineers, Vol 89, p 161, 1963.Google Scholar
5 Zurmühl, R Ein Matrizen verfahren zur Behandlung von Biegesschwingungen nach der Derformationsmethode. Ingenieur-Archiv, Vol 32, p 201, 1963.CrossRefGoogle Scholar
6 Hurty, W C Dynamic analysis of structural systems using component modes. AIAA Journal, Vol 3, p 678, 1965.CrossRefGoogle Scholar
7 Argyris, J H Some results on the free-free oscillations of aircraft type structures. Revue Française de Mécanique, Vol 14, p 59, 1965.Google Scholar
8 Pestel, E Dynamic-stiffness matrix formulation by means of Hermitian polynomials. Air Force Conference on Matrix Methods in Structural Mechanics at Wright-Patterson Air Force Base, Ohio, 26–28th October 1965. Proceedings, November 1966.Google Scholar
9 Lindberg, G M Vibration of non-uniform beams, Aeronautical Quarterly, Vol XIV, p 387, 1963.CrossRefGoogle Scholar
10 Timoshenko, S Vibration Problems in Engineering. 3rd Edition, Van Nostrand, 1955.Google Scholar
11 Courant, R Methods of Mathematical Physics. 1st Edition, Interscience Publishers, 1953.Google Scholar
12 Argyris, J H Energy theorems and structural analysis. Aircraft Engineering, Vol 42, 1955.Google Scholar
13 Sanger, D J Tranverse vibration of a class of non-uniform beams. Journal of Mechanical Engineering Science, Vol 10, p 111, 1968.CrossRefGoogle Scholar
14 Martin, A I Some integrals relating to the vibration of a cantilever beam and approximation for the effect of taper on overtone frequencies. Aeronautical Quarterly, Vol VII, p 109, 1956.CrossRefGoogle Scholar