Nonlinear Wave Interaction of Nanorods Embedded in a Viscoelastic Medium

Nonlinear interactions between two acoustic waves in nanorods traveling at various wave numbers, group velocities, and frequencies are examined in this study.

The nonlinear equation of the nanorod in a viscoelastic medium is obtained using the theory of nonlocal elasticity. Furthermore, the multiple-scale expansion method is applied to study strongly dispersive, weakly nonlinear waves in a nonlocal viscoelastic medium. Using this expansion technique, we can derive the coupled nonlinear Schrödinger equations as the governing equations, which we solve as differential equations of some parameters by expanding the field quantities into an asymptotic series of the smallness parameter.

We give the nonlinear plane wave solutions to these equations in several special cases. The plane wave solutions show how the wave amplitude affects the frequencies of nonlinear plane waves. Additionally, we show numerically how the real and imaginary parts of the group velocities and natural frequency of the system for a carbon nanotube in a viscoelastic medium are affected by the nonlocal, damping, and stiffness parameters.