Analytical and numerical investigation into the longitudinal vibration of uniform nanotubes

• Published in: Frontiers of Mechanical Engineering Vol. 9; no. 2; pp. 142 - 149
• Main Authors: MASOUMI, Masoud, MASOUMI, Mehdi
• Format: Journal Article
• Language: English
• Published: Heidelberg Higher Education Press 01.06.2014
• Subjects: Carbon nanotubes; continuum theory; Derivation; differential quadrature method; Engineering; longitudinal vibration; Mathematical analysis; Mathematical models; Mechanical Engineering; nanorod; Nanorods; Nanostructure; Nanotubes; Research Article; Vibration; 力学性能; 均匀; 数值解; 碳纳米管; 纳米技术; 纳米结构; 纵向振动; 连续体理论; differential quadrature method; continuum theory; nanorod; longitudinal vibration
• ISSN: 2095-0233; 2095-0241
• DOI: 10.1007/s11465-014-0292-z

In recent years, prediction of the behaviors of micro and nanostructures is going to be a matter of increasing concern considering their developments and uses in various engineering fields. Since carbon nanotubes show the specific properties such as strength and special electrical behaviors, they have become the main subject in nanotechnology researches. On the grounds that the classical continuum theory cannot accurately predict the mechanical behavior of nanostructures, nonlocal elasticity theory is used to model the nanoscaled systems. In this paper, a nonlocal model for nanorods is developed, and it is used to model the carbon nanotubes with the aim of the investigating into their longitudinal vibration. Following the derivation of governing equation of nanorods and estimation of nondimensional frequencies, the effect of nonlocal parameter and the length of the nanotube on the obtained frequencies are studied. Furthermore, differential quadrature method, as a numerical solution technique, is used to study the effect of these parameters on estimated frequencies for both classical and nonlocal theories.