Vibration analysis of fractional viscoelastic CNTs conveying fluid resting on fractional viscoelastic foundation considering nonlocal effects

Presented herein is an investigation on the vibrational response of fractional viscoelastic carbon nanotubes (CNTs) conveying fluid and resting on a fractional viscoelastic foundation. The CNTs are modeled according to the Euler-Bernoulli beam theory, and the foundation is considered to be Winkler-type. Also, to incorporate the nanoscale effect into the model, Eringen’s nonlocal elasticity is applied. Derivation of governing equation is done by a variational principle together with the Kelvin-Voigt viscoelastic model. Two solution approaches are developed for obtaining the time response of embedded fluid-conveying CNTs. The first approach is on the basis of Galerkin’s method, while the GDQM and FDM are used in the second approach. Comprehensive numerical results are given to study the effects of elastic foundation, fractional order, damping, fluid, nonlocal parameter, geometrical properties and viscoelasticity coefficient on the time responses of CNTs subject to different boundary conditions.