Nonlinear vibration and regulation of a double-span functionally graded pipe conveying pulsating flow

This paper investigates the parametric resonance characteristics of a double-span functionally graded pipe conveying pulsating flow, with a focus on nonlinear dynamic behavior and effective vibration regulation strategies. The governing vibration equations of the two span segments of the double-span pipe are connected through the coupling continuity conditions at the clip support. The multiple-scale method is employed to derive the parametric resonance instability boundary and frequency response curve, which are verified numerically. Bifurcation and chaos analyses reveal that the pipe exhibits limit cycles, period-doubling, quasi-periodic, and chaotic motions near the critical flow velocity. Vibration regulation mechanisms using graphene and clip support are explored in detail. Results show that increasing the graphene mass fraction or clip support stiffness helps suppress complex motions. Graphene offers effective vibration regulation across a wide frequency range, though it may reduce stability. In contrast, the clip support enhances stability and enables optimal suppression by adjusting its position. Midpoint installation is optimal for low-amplitude, medium-frequency conditions, while a one-fifth point installation is more effective under high-frequency, large-amplitude excitations. This work provides a comparative analysis of material enhancement and structural constraint in regulating parametric resonance, providing theoretical guidance for the safe design of pipe systems.