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Abstract In this paper, the coupled axial and transverse non-linear vibrations of a simply supported pipe, subjected to motion-limiting constraints, conveying pulsating fluid are investigated. The equations of motion are discretized into a set of coupled ordinary differential equations via Galerkin's method, which are then solved using Houbolt's method combined with Newton-Raphson iterative technique. The bifurcation diagrams are constructed to present the global dynamics of the system. Phase-plane portraits, Poincaré maps and power spectrum diagrams are plotted to show the characteristics of some typical motions, such as quasi-periodic and chaotic motions. Finally, the influence of axial motion on the system dynamics is investigated. [ABSTRACT FROM AUTHOR]