Free transverse vibration of the fluid-conveying single-walled carbon nanotube using nonlocal elastic theory

The effects of flow velocity on the vibration frequency and mode shape of the fluid-conveying single-walled carbon nanotube are analyzed using nonlocal elastic theory. Results show that the frequency and mode shape are significantly influenced by the nonlocal parameter e(0)a/L. Increasing the nonlocal parameter decreases the real component of frequency and the decrease is more obvious for a lower flow velocity and a higher-order mode. In addition, a higher mode shape is observed with increasing the value of e(0)a/L. When a critical flow velocity is reached, the combination of first and second modes takes place. The mode shape for the combination is large relative to mode 3 due to the coupled frequency effect, especially including negative imaginary frequency. Furthermore, the mode shape of the combination increases as the nonlocal effect increases. (c) 2008 American Institute of Physics.