Weakly nonlinear wave propagation in nanorods embedded in an elastic medium using nonlocal elasticity theory
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(2020) 42:564
TECHNICAL PAPER
Weakly nonlinear wave propagation in nanorods embedded in an elastic medium using nonlocal elasticity theory Guler Gaygusuzoglu1 · Sezer Akdal2 Received: 24 January 2020 / Accepted: 25 September 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract In the present research, the nonlocal elasticity theory is utilized with the aim of examining nonlinear wave propagation in nanorods, which are embedded in an elastic medium. Constitutive equations on the basis of Eringen’s nonlocal elasticity theory are used in the formulations. Equations of motion are written in terms of material coordinates, and nonlinear equations of nanorods are obtained according to nonlocal elasticity theory. In the study, the rod material is treated as a single-walled carbon nanotube. With the solution of the field equation by the reductive perturbation method, the Korteweg–de Vries (KdV) equation is acquired as the evolution equation, which is governed by the nanorod in an elastic medium. The solitary wave solution of the KdV equation characterizing the motion of carbon nanorods in the elastic medium is given depending on the nonlocal parameter and the parameter of the stiffness of the elastic medium, and it is demonstrated how the nonlocal parameter and the stiffness parameter affect the wave profile. Keywords Nonlocal elasticity theory · Nonlinear wave propagation · Reductive perturbation method · Carbon nanotubes
1 Introduction Nowadays, nanotechnology is an attractive area for scientists and engineers. Among nanoscale structures, nanobeams, nanorods, and nanotubes are the most attention and interest drawing ones because of their exceptional thermal, mechanical, and electrical characteristics. Carbon nanotubes are the materials on which many experimental studies have been carried out for using them as an electrode in supercapacitors, cable material in space elevators, structural material in nanoscale instruments, support in nanocomposites, and for using them in biomedical, bioelectrical, high-speed microelectronic chips, and solar cells. The exceptional thermal, mechanical, and electrical features of carbon nanotubes Technical Editor: José Roberto de França Arruda. * Guler Gaygusuzoglu [email protected] 1
Department of Civil Engineering, Corlu Faculty of Engineering, Tekirdag Namık Kemal University, Tekirdag, Turkey
Department of Civil Engineering, Graduate School of Natural and Applied Sciences, Tekirdag Namık Kemal University, Tekirdag, Turkey
2
(CNTs) have been studied with extensive research since they were discovered by Iijima [1]. Therefore, it has become very important to determine the mechanical behavior of carbon nanotubes. The physical and mechanical features of CNTs are categorized into two groups. The first one of these is atomic molecular dynamic modeling. The second group is based on a number of size-dependent continuum theories, e.g., nonlocal elasticity theory [2], micropolar theory [3], modified couple stress theory [4], and strain gradient theo
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