Third-order non-local beam theories for the analysis of symmetrical nanobeams
Author(s)
Author(s)
Niu, J. C.
Lim, C. W.
Date Issued
2009
Publisher
Sage Publications
Journal
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
Volume
223
Issue
10
Start page
2451
End page
2463
Abstract
This article presents formulation of third-order non-local beam theories based on Eringen's non-local continuum theory and the Reddy and Leung higher-order beam models for bending, buckling, and vibration of nanobeams. By applying the variational principle, an asymptotic governing differential equation of infinite-order strain gradients is derived and subsequently the governing equation of motion of the nanobeams is obtained. For practical applications, the Navier solutions of the asymptotic non-local model are presented and discussed. Bending, buckling, and vibration of nanobeams with simply supported boundary conditions are investigated. Numerical examples are presented to illustrate the corresponding effects of non-local scale parameter, rotary inertia and transverse shear deformation on deflections, buckling loads, and natural frequencies of nanobeams.
SFU Affiliated Publication
No
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