Study on the small-scale effect on wave propagation characteristics of fluid-filled carbon nanotubes based on nonlocal fluid theory

In this article, Timoshenko’s beam model is established to investigate the wave propagation behaviors for a fluid-conveying carbon nanotube when employing the nonlocal stress–strain gradient coupled theory and nonlocal fluid theory. The governing equations of motion for the carbon nanotube are derived. The small-scale influences induced by the nanotube are simulated by nonlocal and strain gradient effects, and the scale effect induced by fluid flow is first investigated applying nonlocal fluid theory. Numerical results obtained by solving the governing equations indicate that the nonlocal effect induced by the nanotube leads to wave damping and a decrease in stiffness, while the strain gradient effect contributes to wave promotion and an enhancement in stiffness. The scale effect caused by the inner fluid only leads to a decay for a high-mode wave since there is no influence from fluid flow on the low-mode wave. The numerical solution is validated by comparing with Monte Carlo simulation and interval analysis method.