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This paper aims to investigate the stability and nonlinear dynamics of an initially curved viscoelastic clamped–clamped pipe conveying pulsatile fluid, with special attention to the non-smooth dynamics of this gyroscopic system under the influence of initial curvature and gravity. In this study, the impacting contact is modeled as a trilinear repulsive force. Based on the Euler–Bernoulli beam theory, the nonlinear governing equations, which take into account geometric, curvature, and damping nonlinearities, are developed using Hamilton's principle. The continuous model is discretized using the Galerkin method and then solved using the arc-length technique and a time integration method. A linear analysis of the natural frequency and complex mode shape shows the unexpected frequency intersection and modal asymmetry. The qualitative changes in the nonlinear dynamics of the impacting pipe in both sub- and super-critical regions are examined and presented in the form of bifurcation diagrams, frequency–amplitude curves, force–amplitude curves, time histories, and phase portraits. Numerical results show that some complex dynamical behaviors can occur in different impact constraint cases, including a grazing bifurcation, sticking, period doubling, and chaos at the impact location, may occur. The initial curvature and gravity result in different behaviors, such as the asymmetry change of the equilibrium configuration and the occurrence of the flutter instability. The current analysis is significant to understand the non-smooth dynamic mechanisms and also provide design and technology guidance for the pipe system with motion-limiting constraints. • A theoretical model is developed for an impacting viscoelastic pipe conveying fluid. • The effects of initial curvature and gravity on vibration characteristics are shown. • Symmetry and asymmetry of the non-smooth vibration characteristics are presented. • Grazing bifurcation, sticking, period doubling, and chaos at impacts are found. • Sensitivity of the nonlinear dynamics to impact constraint parameters are discussed. [ABSTRACT FROM AUTHOR]