Eur. Phys. J. Plus (2017) 132: 115
https://doi.org/10.1140/epjp/i2017-11395-x

Regular Article

Comparison of modeling a conical nanotube resting on the Winkler elastic foundation based on the modified couple stress theory and molecular dynamics simulation

Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Postal code: 3414916818, Qazvin, Iran

^* e-mail: ghadiri@eng.ikiu.ac.ir

Received: 4 January 2017
Accepted: 2 February 2017
Published online: 6 March 2017

Abstract

In this article, the free vibration analysis of a thin conical nanotube resting on an elastic foundation is investigated for the first time by means of the modified couple stress theory (MCST) and molecular dynamics (MD) simulation. The proposed model in the MCST framework, its equations of motion and boundary conditions are derived by Hamilton's principle based on the thin shell model of Love. The differential quadrature method (DQM) is applied to discretize the equations of motion. Molecular dynamics (MD) simulation is performed via the AIREBO potential function, which is recommended in vibrational studies. The accuracy of the presented model is verified for previous studies with both methods. The novelty of the current study is reporting a specified length scale parameter of MCST which has a good conformity with MD results. This value is exclusively related to the proposed model of the present study. The effect of the elastic foundation stiffness is investigated with molecular dynamics for the first time as well. The results can have many applications, such as in modeling of scanning probe microscopy and biomedical microsystems.