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

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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