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The Effect of Lumped Parameters on Beam Frequencies

Published online by Cambridge University Press:  07 June 2016

F. A. Leckie  and
G.M. Lindberg
F. A. Leckie
Affiliation:
Engineering Department, University of Cambridge
G.M. Lindberg
Affiliation:
Engineering Department, University of Cambridge
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Summary

An investigation has been made into the errors involved in using certain lumped parameter methods for the solution of beam frequencies. It is found that existing methods are not consistent for all boundary conditions. A new dynamic stiffness matrix has been formulated, which gives consistently good results for even a few elements. The error in the solution is always inversely proportional to the fourth power of the number of elements used.

Type
Research Article
Information
Aeronautical Quarterly , Volume 14 , Issue 3 , August 1963 , pp. 224 - 240
Copyright
Copyright © Royal Aeronautical Society. 1963

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References

1. Minhinnick, I. T. The Theoretical Determination of Normal Modes and Frequencies of Vibration. R. & M. 3039, 1957.Google Scholar
2. Morris, J. and Minhinnick, I. T. The Calculation of the Natural Frequencies and Modes of Vibration of Aeroplane Wings. R. & M. 1928, 1940.Google Scholar
3. Myklestad, N. O. A New Method of Calculating Natural Modes of Uncoupled Bending Vibration of Airplane Wings and Other Types of Beams. Journal of the Aeronautical Sciences, Vol. 11, April 1944.CrossRefGoogle Scholar
4. Tarooff, W. P. The Associated Matrices of Bending and Coupled Bending-Torsion Vibrations. Journal of the Aeronautical Sciences, Vol. 14, October 1947.Google Scholar
5. Duncan, W. J. A Critical Examination of the Representation of Massive and Elastic Bodies by Systems of Rigid Masses Elastically Connected. The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 5, 1952.CrossRefGoogle Scholar
6. Livesley, R. K. The Equivalence of Continuous and Discrete Mass Distributions in Certain Vibration Problems. The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 8, 1955.CrossRefGoogle Scholar
7. Milne-Thomson, L. M. The Calculus of Finite Differences. Macmillan, 1951.Google Scholar
8. Clough, R. W. The Finite Element Method in Plane Stress Analysis. Proceedings of the Second Conference on Electronic Computation, American Society of Civil Engineers, September 1960.Google Scholar
9. Jones, R. P. N. The Effect of Small Changes in Mass and Stiffness on the Natural Frequencies and Modes of Vibrating Systems. International Journal of Mechanical Sciences, Vol. 1, 1960.CrossRefGoogle Scholar