In this paper, an valid numerical algorithm is presented to solve
variable fractional viscoelastic pipes conveying pulsating fluid in the
time domain and analyze dynamically the vortex-induced vibration of the
pipes. Firstly, Coimbra variable fractional derivative operators are
introduced. Meanwhile, using Hamilton's principle and a nonlinear
variable fractional order model, the governing system of equations is
established. The unknown functions of the system of equations are
approximated with shifted Legendre polynomials. Then, convergence
analysis and numerical example investigate the effectiveness and
accuracy of the proposed algorithm. Finally, the influences of different
parameters on the dynamic response of the viscoelastic pipe are studied.
The influencing factors and their ranges of the transient and long-term
chaotic states of the pipe are analyzed. In addition, the proposed
algorithm shows enormous potentials for solving the dynamics problems of
viscoelastic pipes with the variable fractional order models.