A new size-dependent dynamical model for the nonlinear free vibration and primary resonance of fluid-conveying cantilever Graphene Platelet Reinforced (GPL-R) micropipes with fractional viscoelastic damping on nonlinear foundations has been proposed. This study aims to present numerical results that demonstrate the effects of GPL weight fraction and pattern, the length scale parameter, fractional derivative order, and nonlinear viscoelastic foundation coefficients on the steady-state response of the system. The mathematical model incorporates a fractional-order dynamic model for a viscoelastic GPL-reinforced polymeric pipe conveying fluid. The influence of size is integrated into the governing equations of motion through the application of modified coupled stress theory. The multiple scales method in conjunction with the Galerkin’s method is utilized to solve the governing equations. The results indicated that the response amplitude of pipes predicted by the fractional damping models is significantly larger than that reported in earlier studies utilizing the Kelvin-Voigt viscoelastic model. An increase in the weight fraction of the GPLs leads to a reduction in hardening nonlinearity. Various reinforcement patterns did not have a notable impact on the peak of the frequency-response curve. The application of the MCST resulted in a decrease in the maximum response to forced vibration and an increase in the resonance frequency. Finally, the findings of this research can be applied in the field of fluidic force microscopy, medical instruments, drug delivery.
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