Comparison of linear beam theories

Mathematical and Computer Modelling

Volumn 49, Issue 1-2, 2009, Pages 20-30

  Labuschagne, A ^a   van Rensburg, N F J ^a   van der Merwe, A J ^b  

^a UNIVERSITY OF PRETORIA   (South Africa)

^b CAPE PENINSULA UNIVERSITY OF TECHNOLOGY   (South Africa)

Author keywords

Beam; Euler Bernoulli; Timoshenko; Vibration

Indexed keywords

TWO DIMENSIONAL;

BEAM; BERNOULLI; EULER-BERNOULLI; LINEAR BEAM THEORIES; LINEAR THEORIES; PRACTICAL IMPORTANCES; TIMOSHENKO; TIMOSHENKO THEORIES; VIBRATION;

VIBRATION MEASUREMENT;

EID: 55549124178     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2008.06.006     Document Type: Article

References (21)

1. Fung Y.C. Foundations of Solid Mechanics (1965), Prentice-Hall Inc., Englewood Cliffs, New Jersey
2. Davies R.M. A critical study of the Hopkinson pressure bar. Philosophical Transactions of the Royal Society, Series A 240 (1948) 375-457
3. Love A.E.H. A Treatise on the Mathematical Theory of Elasticity. 4th edition (1927), Cambridge University Press Reprinted New York Dover (1963)
4. Bancroft D. The velocity of longitudinal waves in cylindrical bars. Physical Review 59 (1941) 588-593
5. Hudson G.E. Dispersion of elastic waves in a solid circular cylinder. Physical Review 63 (1943) 46-51
6. Abrahamson H.N. Flexural waves in elastic beams of circular cross section. Journal of the Acoustical Society of America 29 (1957) 42-46
7. Duva J.M., and Simmonds J.G. The usefulness of elementary theory for the linear vibrations of layered, orthotropic elastic beams and corrections due to two-dimensional end effects. Trans of ASME, Journal of Applied Mechanics 58 (1991) 175-183
8. Timoshenko H. Vibration Problems in Engineering. second edition (1937), D van Nostrand Company, Inc., New-York
9. Inman D.J. Engineering Vibration (1994), Prentice-Hall Inc., Englewood Cliffs, New Jersey
10. Newland D.E. Mechanical Vibration Analysis and Computation (1989), Longman, Essex
11. Cowper G.R. The shear coefficient in Timoshenko's beam theory. Trans of ASME, Journal of Applied Mechanics 33 (1966) 335-340
12. Boresi A.P., Sidebottom O.M., Seely F.B., and Smith J.O. Advanced Mechanics of Materials. Third edition (1978), John Wiley & sons, New York
13. Myklestad N.O. Statics of Deformable Bodies (1966), The Macmillan Company, New York
14. van Rensburg N.F.J., and van der Merwe A.J. Natural frequencies and modes of a Timoshenko beam. Wave Motion 44 (2006) 58-69
15. Shubov M.A. Asymptotic and spectral analysis of the spatially nonhomogeneous Timoshenko beam model. Mathematische Nachrichten 241 (2002) 125-162
16. Strang G., and Fix G.J. An Analysis of the Finite Element Method (1973), Prentice-Hall, New Jersey
17. Zietsman L., van Rensburg N.F.J., and van der Merwe A.J. A Timoshenko beam with tip body and boundary damping. Wave Motion 39 3 (2004) 199-211
18. Atkin R.J., and Fox N. An Introduction to the Theory of Elasticity (1980), Longman, London and New York
19. Carey G.F., and Oden J.T. Finite Elements: A Second Course, Volume II (1983), Prentice-Hall, Inc., Englewood Cliffs, New Jersey
20. Russell D.L. In: Chen G., and Zhou J. (Eds). Vibration and Damping in Distributed Systems, Volume II (1993), CRC Presss, Boca Raton, Ann Arbor, London, Tokyo (Chapter 5)
21. Banks H.T., and Inman D.J. On damping mechanisms in beams. ASME, Transactions, Journal of Applied Mechanics 58 (1991) 716-723