Session: 07-23-01: 100th Anniversary of the Timoshenko-Ehrenfest Beam Model

Paper Number: 95836

95836 - Did S.P. Timoshenko and P. Ehrenfest Overestimate the Importance of the Fourth-Order Time Derivative in Their Theory of Beams? 

In this study we investigate two topics: (a) question of priority, namely, was S.P. Timoshenko the sole author of this beam theory? (b) the importance of the fourth order time derivative that appears in the equations derived  by Stephen Prokofievich  Timoshenko and Paul  Ehrenfest during years 1912-1913 and reported by Timoshenko in the 1916 book on theory of elasticity in the Russian language and then in two papers dated 1920 and 1921, in English.

The contribution consists in the arrived conclusion that the 4^th order derivative which complicates the treatment, is not needed in most cases. Methodology is analytical.

Now we celebrate several dates: Publication of the Timoshenko  (1916) book, Timoshenko’s articles (1920, 192, 1922), and associated technical subjects.Preliminary conclusion: Timoshenko was not alone, he was assisted by paul Ehrenefest. Additionally, the 4^th order derivative can be neglected.

References

Almeida Júnior D.S., Elishakoff  I., Ramos A.J.A. and Rosário Miranda L.G., The Hypothesis of Equal Wave Speeds for Stabilization of Timoshenko Beam is Not Necessary Anymore: The Time Delay Cases, IMA Journal of Applied Mathematics, Vol.  84(4), pp.763-796, 2019.

Bhat K. S., Sarkar K., Ganguli R. and Elishakoff I., 2018. Slope-Inertia Model of Non-Uniform and Inhomogeneous Bresse-Timoshenko Beams. AIAA Journal, 56(10), 4158-4168, 2018.

Bresse J.A.C., Cours de mécanique appliquée – Résistance des matériaux et stabilité des constructions, Paris, Gauthier-Villars, 1859 (in French).

Challamel  N. and Elishakoff I., “A brief history of first-order shear-deformable beam and plate models”, Mechanics Research Communications, article 103389, 2019.

Timoshenko S.P., A Course of Elasticity Theory. Part 2: Rods and Plates, St. Petersburg: A.E. Collins Publishers, 1916 (in Russian), (2^nd Edition, Kiev: “Naukova Dumka” Publishers, pp. 337-338, 341, 1972).

Timoshenko SP, On the differential equation for the flexural vibrations of prismatic rods, Glasnik Hrvatskoga Prirodaslovnoga Drusˇtva (Herald of the Croatian Nature Association) 1920; 32: 55–57.

 

Timoshenko S.P., On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bar, Philosophical Magazine Series 6, Vol. 41/245, 744-746, 1921a.

Timoshenko S. P., On the Transverse of Bars of Uniform Cross Sections, Philosophical Magazine, Series 6, Vol. 43, 125-131, 1922b (See also, Timoshenko S. P., The Collected Papers, 288-290, McGraw-Hill, New York, 1953).

Timoshenko S.P., Vibration Problems in Engineering, London: Constable and Company, p. 231, 1928.

 Timoshenko S.P., Vibration Problems in Engineering, Second Edition, New York: Van Nostrand Reinhold Company, 1937.

Timoshenko S.P., Collected Papers, New York: McGraw-Hill, 1953c.

Timoshenko S.P., Remembrances, Paris, 1963 (in Russian).

 

Timoshenko S.P., As I Remember: The Autobiography of Stephen P. Timoshenko, Princeton: Van Nostrand, 1968.

Timoshenko S.P., A Course in Theory of Elasticity, 2^nd edition, Kiev: Naukova Dumka, 1972 (in Russian).

Timoshenko S.P., Vospominaniya (Remembrances), Kiev: Naukova Dumka,1993 (in Russian).

Presenting Author: Isaac Elishakoff Florida Atlantic University

Presenting Author Biography: Serves as a Distinguished Research professor at the Florida Atlantic University.

Authors:

Isaac Elishakoff Florida Atlantic University