Vibration of fluid-filled multi-walled carbon nanotubes seen via nonlocal elasticity theory

Vibration characteristics of fluid-filled multi-walled carbon nanotubes are studied by using nonlocal elastic Flügge shell model. Vibration governing equations of an N-layer carbon nanotube are formulated by considering the scale effect. In the numerical simulations, the effects of different theories, small-scale, variation of wavenumber, the innermost radius and length of double-walled and triple-walled carbon nanotubes are considered. Vibrational frequencies decrease with an increase of scale coefficient, the innermost radius, length of nanotube and effects of wall number are negligible. The results show that the cut-off frequencies can be influenced by the wall number of nanotubes.