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Nonlocal vibration analysis of FG nano beams with different boundary conditions
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  • Journal title : Advances in nano research
  • Volume 4, Issue 2,  2016, pp.85-111
  • Publisher : Techno-Press
  • DOI : 10.12989/anr.2016.4.2.085
 Title & Authors
Nonlocal vibration analysis of FG nano beams with different boundary conditions
Ehyaei, Javad; Ebrahimi, Farzad; Salari, Erfan;
 Abstract
In this paper, the classical and non-classical boundary conditions effect on free vibration characteristics of functionally graded (FG) size-dependent nanobeams are investigated by presenting a semi analytical differential transform method (DTM) for the first time. Three kinds of mathematical models, namely; power law (P-FGM), sigmoid (S-FGM) and Mori-Tanaka (MT-FGM) distribution are considered to describe the material properties in the thickness direction. The nonlocal Eringen theory takes into account the effect of small size, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators. Governing equations are derived through Hamilton`s principle and they are solved applying semi analytical differential transform method. The good agreement between the results of this article and those available in literature validated the presented approach. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as small scale effects, spring constant factors, various material compositions and mode number on the normalized natural frequencies of the FG nanobeams in detail. It is explicitly shown that the vibration of FG nanobeams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.
 Keywords
DT method;functionally graded material;non-classical boundary condition;nanobeams;vibration;
 Language
English
 Cited by
1.
On thermal stability of plates with functionally graded coefficient of thermal expansion,;;;;

Structural Engineering and Mechanics, 2016. vol.60. 2, pp.313-335 crossref(new window)
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On thermal stability of plates with functionally graded coefficient of thermal expansion, Structural Engineering and Mechanics, 2016, 60, 2, 313  crossref(new windwow)
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Forced Vibration Analysis of Functionally Graded Nanobeams, International Journal of Applied Mechanics, 2017, 09, 07, 1750100  crossref(new windwow)
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