A modified nonlocal beam model for vibration and stability of nanotubes conveying fluid

In this paper, a new, modified nonlocal beam model is developed for analyzing the vibration and stability of nanotubes conveying fluid, in which one single nonlocal nanoscale parameter is included. Using Hamilton’s principle, a new higher-order differential equation of motion and the corresponding higher-order, non-classical boundary conditions are obtained for nanotubes conveying fluid. Based on this modified nonlocal model, effect of nonlocal nanoscale parameter on natural frequencies and critical flow velocities is presented and discussed through numerical calculations. It is found that this factor has great influence on the vibration and stability of nanotubes conveying fluid. In particular, the nonlocal effect tends to induce higher natural frequencies and higher critical flow velocities as compared to the results obtained from the classical and partial nonlocal beam models.