Nonlinear Wave Modulation in Nanorods Based on Nonlocal Elasticity Theory by Using Multiple-Scale Formalism

Year 2018, Volume: 10 Issue: 3, 140 - 158, 04.11.2018

Güler Gaygusuzoğlu

https://doi.org/10.24107/ijeas.422906

Abstract

Many systems in physics,
engineering, and natural sciences are
nonlinear and modeled with nonlinear equations. Wave propagation, as a branch
of nonlinear science, is one of the most widely studied subjects in recent
years. Nonlocal elasticity theory represents a common growing technique used
for conducting the mechanical analysis of microelectromechanical
and nanoelectromechanical systems. In this study, nonlinear wave modulation in
nanorods was examined by means of nonlocal elasticity theory.  The nonlocal constitutive equations of Eringen
were utilized in the formulation, and the nonlinear equation of motion of nanorods was obtained. By applying the multiple scale formalism, the propagation of
weakly nonlinear and strongly dispersive waves was investigated, and the Nonlinear Schrödinger (NLS) equation was
obtained as the evolution equation. A part of spacial solutions of the NLS
equation, i.e. nonlinear plane wave,
solitary wave and phase jump solutions, were presented. In order to investigate
the nonlocal impacts on the NLS equation numerically, whether envelope solitary
wave solutions exist was investigated by utilizing the physical and geometric
features of carbon nanotubes (CNTs).

Keywords

Nanorods, nonlinear wave modulation, nonlocal elasticity theory

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