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Review Article

Celebrating the Centenary of Timoshenko's Study of Effects of Shear Deformation and Rotary Inertia

[+] Author and Article Information
Isaac Elishakoff

Fellow ASME
Department of Ocean and
Mechanical Engineering,
Florida Atlantic University,
Boca Raton, FL 33431-0991
e-mail: elishako@fau.edu

Julius Kaplunov

School of Computing and Mathematics,
Keele University,
Keele,
Staffordshire ST5 5BG, UK
e-mail: j.kaplunov@keele.ac.uk

Evgeniya Nolde

Department of Mathematics,
Brunel University,
Uxbridge,
Middlesex UB8 3PH, UK
e-mail: Evgeniya.Nolde@brunel.ac.uk

This paper is dedicated to blessed memories of our teachers, Professors V.V. Bolotin (1926–2008) and A.L. Goldenveizer (1910–2003), who instilled in us unyielding love of structural mechanics.Manuscript received May 29, 2015; final manuscript received October 29, 2015; published online December 11, 2015. Assoc. Editor: Prashant K Purohit.

Appl. Mech. Rev 67(6), 060802 (Dec 11, 2015) (11 pages) Paper No: AMR-15-1067; doi: 10.1115/1.4031965 History: Received May 29, 2015; Revised October 29, 2015

This study revisits Timoshenko beam theory (TBT). It discusses at depth a more consistent and simpler governing differential equation. The so-called second spectrum is also addressed. Then, we provide the asymptotic justification of the aforementioned differential equation along with detailed discussion of the boundary and initial conditions. The paper also presents remarks of historical character, in the context of other pertinent studies.

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Figures

Grahic Jump Location
Fig. 1

A cantilever beam of length 2L vibrating with wavelength l, lL

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