Weakly nonlinear wave propagation in nanorods embedded in an elastic medium using nonlocal elasticity theory

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.