Free vibration of axially loaded zigzag and armchair nanobeams using doublet mechanics

Based on doublet mechanics theory and various beam theories, this paper presents free vibration of axially loaded zigzag and armchair nanobeams. A two-noded higher order beam element is used to solve the problems of nanobeams with various boundary conditions. The verification studies in terms of fundamental frequencies and buckling loads are performed by comparing the results by the present model with Molecular Dynamic Simulations, Doublet Mechanics, and Eringen's nonlocal theory. The effects of material length scale parameter, slenderness ratio, nanotube model and boundary conditions on the fundamental frequencies of axially loaded nanobeams are investigated in details. Softening material behavior is detected for zigzag and armchair nanobeams. Having stiffer boundary conditions lead to the effect of material length scale parameter to be observed more prominently.

Automated summary

This paper investigates the free vibration of axially loaded zigzag and armchair nanobeams using the doublet mechanics theory and various beam theories. A two-noded higher order beam element is used to solve the nanobeams' problems with different boundary conditions. The results are verified by comparing with Molecular Dynamic Simulations, Doublet Mechanics, and Eringen's nonlocal theory. The effects of material length scale parameter, slenderness ratio, nanotube model, and boundary conditions on the fundamental frequencies of axially loaded nanobeams are investigated in detail.