Three-dimensional nonlinear dynamics of pipes conveying pulsatile fluid subjected to external cross flow

This paper investigates the three-dimensional nonlinear dynamics of pipes conveying pulsatile fluid simultaneously subjected to external cross flow. The governing equations are derived using Hamilton’s principle, discretized via the Galerkin’s method, and numerically solved by the Runge-Kutta integration algorithm. First, frequency and stability analyses are performed to examine the variations of the three lowest natural frequencies with internal flow velocity and to identify parametric instability regions by means of Floquet theory. Subsequently, bifurcation characteristics are systematically analyzed with the internal pulsating frequency and the external flow velocity as key parameters. The results reveal that the hybrid excitations can induce rich and complex parametric resonance phenomena, including pronounced combination, subharmonic, and superharmonic resonances, demonstrating the system’s strong nonlinearity. A particularly noteworthy finding is the synergistic resonance between internal and external flows, which occurs when the internal pulsating frequency approaches certain integer multiples of the external vortex-shedding frequency, resulting in intensified pipe resonance. These findings provide new insights into the nonlinear resonance mechanisms of fluid-conveying pipes under multi-source fluid excitations and offer valuable guidance for engineering design and vibration suppression.