Small-scale effect on the vibration of non-uniform carbon nanotubes conveying fluid and embedded in viscoelastic medium

Vibration characteristics of non-uniform single-walled carbon nanotubes (SWCNTs) conveying fluid embedded in viscoelastic medium are investigated using nonlocal Euler–Bernoulli beam theory. The governing differential equations are solved with the finite element method and the frequencies are obtained by solving a quadratic eigenvalue problem. The effects of taper ratio, small-scale parameter and viscoelastic medium on resonant frequencies and critical steady flow velocity are discussed. It is shown that by increasing the taper ratio, the critical flow velocity decreases and the combined mode observed for uniform SWCNTs in the previous works does not occur when the taper ratio is non-zero.