Planar Nonlinear Coupled Response of Pipes with High Internal Velocity and Transverse Excitation

This study examines the coupled radial and lateral nonlinear forced vibrations of fluid-conveying pipes employing Euler–Bernoulli beam theory. The steady-state response throughout the entire flow velocity range is determined using the Galerkin method and verified numerically via the finite difference method. The influence of system parameters on the characteristics of the coupled nonlinear forced vibration is analyzed. The study reveals that in the supercritical regime, the pipe undergoes non-fully symmetric oscillation about a non-zero configuration. Moreover, the effect of these parameters is found to be distinctly different across various flow velocity regimes. It is observed that an increase in the coupled stiffness parameter advances the subcritical resonant frequency while retarding the supercritical one, with the resonant amplitude growing in both regimes. An increase in the length-to-diameter ratio enhances the resonance frequency but diminishes the resonance amplitude in the subcritical regime, whereas under supercritical conditions, it suppresses both. Furthermore, A comparative study of the planar coupled and transverse nonlinear vibration models shows the responses of the two models differ markedly near the critical flow velocity. This divergence is mitigated by an increased length-to-diameter ratio in the subcritical regime, whereas the same increase amplifies it in the supercritical regime.