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

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. T he 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.