Investigation of the Size Effect in Euler-Bernoulli Nanobeam Using the Modified Couple Stress Theory

Year 2017, Volume: 13 Issue: 4, 893 - 899, 29.12.2017

Necla Togun , Süleyman Murat Bağdatlı

https://doi.org/10.18466/cbayarfbe.370362

Cited By: 3

Abstract

This paper presents the implementation of non-classical continuum theory
for simply supported nanobeam. Hamilton’s principle and modified couple stress
methods are employed for obtaining differential equation of motion of nanobeam
in cooperation with suitable boundary conditions. An approximate solution of
the presented system is developed considering the method of multiple scales
which is one of the perturbation techniques. The
effect of material length scale parameter ζ and the Poisson’s ratio υ on the natural
frequencies are determined and represented in table form and graphically. Besides,
dimensionless natural of frequency of nanobeam are investigated by taking into
account various system parameters. The results of the system show that the size
influence is very crucial for extremely thin beams with a height of nanoscale
dimension. Besides, the outcome of the system shows that the beam modeled
considering non-classical continuum theory is stiffer than those of classical
one.

Keywords

Modified couple stress theory, nanobeam, perturbation method, vibration

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