Propagation of weakly nonlinear waves in nanorods using nonlocal elasticity theory

Abstract

The present research examines the propagation of weakly solitary waves in nanorods by employing nonlocal elasticity theory. 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 technique with increasing popularity for the purpose of conducting the mechanical analysis of microelectromechanical and nanoelectromechanical systems. The nonlinear equation of motion of nanorods is derived by utilizing nonlocal elasticity theory. The reductive perturbation technique is employed for the purpose of examining the propagation of weakly nonlinear waves in the longwave approximation, and the Korteweg-de Vries equation is acquired as the governing equation. The steady-state solitary-wave solution is known to be admitted by the KdV equation. To observe the nonlocal effects on the KdV equation numerically, the existence of solitary wave solution has been investigated using the physical and geometric properties of carbon nanotubes.