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Research Papers

A Consistent Set of Nonlocal Bresse–Timoshenko Equations for Nanobeams With Surface Effects

[+] Author and Article Information
Isaac Elishakoff

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

Clement Soret

Doctoral Candidate
Mines Paris Tech,
Centre des Matériaux,
CNRS UMR 7633, BP 87,
F-91003 Evry Cedex, France

Manuscript received December 14, 2011; final manuscript received January 21, 2013; accepted manuscript posted February 12, 2013; published online August 19, 2013. Assoc. Editor: Wei-Chau Xie.

J. Appl. Mech 80(6), 061001 (Aug 19, 2013) (6 pages) Paper No: JAM-11-1474; doi: 10.1115/1.4023630 History: Received December 14, 2011; Revised January 21, 2013; Accepted February 12, 2013

In this study, we propose governing differential equations for beams, taking into account shear deformation, rotary inertia, locality, and surface stress effects. It is shown that the equation is both simpler and more consistent than the appropriate Bresse–Timoshenko equations extended to include locality and surface stress effects. The proposed equation contains 11 terms with respect to displacement versus 19 terms appearing in the equations that extend the Bresse–Timoshenko equations to include nonlocality and surface effects.

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Figures

Grahic Jump Location
Fig. 1

Variation of the ratio ωO2/ωBE2 natural frequency with number of half-waves in x direction (e0a = 0.6h0—nonlocality taken into account, e0a = 0—nonlocality is neglected)

Grahic Jump Location
Fig. 2

Variation of the ratio ωC2/ωBE2 natural frequency with number of half-waves in x direction (e0a = 0.6h0—nonlocality taken into account, e0a = 0—nonlocality is neglected)

Grahic Jump Location
Fig. 3

Variation of the ratio ωC2/ωO2 natural frequency with number of half-waves in x direction (e0a = 0.6h0—nonlocality taken into account, e0a = 0—nonlocality is neglected)

Grahic Jump Location
Fig. 4

Variation of the ratio ωO2/ωBE2 natural frequency with number of half-waves in x direction (e0a = 0.6h0—nonlocality taken into account, e0a = 0—nonlocality is neglected)

Grahic Jump Location
Fig. 5

Variation of the ratio ωC2/ωBE2 natural frequency with number of half-waves in x direction (e0a = 0.6h0—nonlocality taken into account, e0a = 0—nonlocality is neglected)

Grahic Jump Location
Fig. 6

Variation of the ratio ωC2/ωO2 natural frequency with number of half-waves in x direction (e0a = 0.6h0—nonlocality taken into account, e0a = 0—nonlocality is neglected)

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