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.

在本研究中，非局部弹性理论被用于检查非线性波在纳米棒中的传播，纳米棒被嵌入弹性介质中。在公式中使用了基于Eringen的非局部弹性理论的本构方程。根据材料坐标编写运动方程，并根据非局部弹性理论获得纳米棒的非线性方程。在研究中，棒材料被视为单壁碳纳米管。利用还原摄动法求解场方程，得到了Korteweg-de Vries（KdV）方程作为演化方程，该方程由弹性介质中的纳米棒控制。