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A dynamic analysis of the fractional viscoelastic nanobeam conveying fluid, resting on a viscoelastic foundation, with simply-supported boundary conditions and uniformly loaded, is performed. The existence of a significant internal damping of the nanotube led to the choice of a nonlinear and fractional Zener model for the nanotube material. Solving of the integral-differential governing equation is done using Galerkin’s method and an iterative method that uses the Laplace transformation techniques, Bessel functions theory and the binominal series. The effects of the nonlocal parameter and of the fractional order on the transverse displacements of the nanotube conveying fluid are studied. In order to validate the approached iterative method, the results of the dynamic analysis were compared with those of the quasi-static calculation of the structure. The proposed algorithm for solving the governing equation and the accompanying graphical data are useful in the engineering design of the nanotubes conveying fluid.

An iterative algorithm for studying forced vibrations of a nanotube conveying fluid